X4Automorphism
Subgroups of the automorphism group of X4
The page displays a subgroup lattice of PSp4(F3), and generators of every subgroup of the automorphism group of the Burkhardt quardtic defined in P4 by
y[1]^4-y[1]*(y[2]^3+y[3]^3+y[4]^3+y[5]^3)+3*y[2]*y[3]*y[4]*y[5],
In particular, if the class of the subgroup
- has cohomology obstructions to linearizability, or
- contains the nonlinearizable C2-involution fixing a K3 surface,
- has invariant classs group of rank 1,
then it is not linearizable. There are 103 such nonlinearizable classes. The indices of these groups corresponding to the subgroup lattice below are
[ 2, 6, 8, 9, 10, 11, 14, 15, 16, 17, 19, 21, 22, 23, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73,
74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110,
111, 112, 113, 114, 115, 116 ].
There are 12 classes left. Their indices are
[ 3, 4, 5, 7, 12, 13, 18, 20, 24, 25, 39, 41],
8 classes among the 13 are linearizable, their indices are
[ 3, 4, 5, 7, 12, 13, 20, 24].
The source code of matrices of generators of all groups can be found here.
Partially ordered set of subgroup classes of PSp4(F3)
-----------------------------------------
[116] Order 25920 Length 1 Maximal Subgroups: 111 112 113 114 115
---
[115] Order 960 Length 27 Maximal Subgroups: 77 102 103 109
[114] Order 576 Length 45 Maximal Subgroups: 73 108 109 110
---
[113] Order 720 Length 36 Maximal Subgroups: 86 87 88 95 96 107
[112] Order 648 Length 40 Maximal Subgroups: 68 97 105 106
[111] Order 648 Length 40 Maximal Subgroups: 89 97 104
[110] Order 288 Length 45 Maximal Subgroups: 89 99 100 101
[109] Order 192 Length 135 Maximal Subgroups: 84 98 99
[108] Order 192 Length 45 Maximal Subgroups: 87 98 100
---
[107] Order 360 Length 36 Maximal Subgroups: 64 67 72 77 78
[106] Order 324 Length 40 Maximal Subgroups: 36 79 91
[105] Order 216 Length 120 Maximal Subgroups: 69 88 91 93 94
[104] Order 216 Length 40 Maximal Subgroups: 63 92
[103] Order 160 Length 162 Maximal Subgroups: 25 82 90
[102] Order 96 Length 270 Maximal Subgroups: 69 82 83 84 86
[101] Order 96 Length 90 Maximal Subgroups: 63 80 85
[100] Order 96 Length 45 Maximal Subgroups: 62 66 80
[ 99] Order 96 Length 45 Maximal Subgroups: 61 65 80
[ 98] Order 64 Length 135 Maximal Subgroups: 80 81 82
---
[ 97] Order 162 Length 160 Maximal Subgroups: 74 76 79
[ 96] Order 120 Length 216 Maximal Subgroups: 41 49 67 77
[ 95] Order 120 Length 216 Maximal Subgroups: 37 49 68 78
[ 94] Order 108 Length 120 Maximal Subgroups: 39 72 75
[ 93] Order 108 Length 120 Maximal Subgroups: 70 73 75 76
[ 92] Order 108 Length 120 Maximal Subgroups: 40 74
[ 91] Order 108 Length 40 Maximal Subgroups: 71 75
[ 90] Order 80 Length 162 Maximal Subgroups: 7 53
[ 89] Order 72 Length 360 Maximal Subgroups: 48 59 61 62 63
[ 88] Order 72 Length 360 Maximal Subgroups: 34 70 71 72
[ 87] Order 48 Length 540 Maximal Subgroups: 37 58 64 66 68
[ 86] Order 48 Length 270 Maximal Subgroups: 41 58 60 67
[ 85] Order 48 Length 270 Maximal Subgroups: 40 54 59
[ 84] Order 48 Length 270 Maximal Subgroups: 38 53 60 65
[ 83] Order 48 Length 270 Maximal Subgroups: 39 57 60
[ 82] Order 32 Length 405 Maximal Subgroups: 53 55 56 57 58
[ 81] Order 32 Length 405 Maximal Subgroups: 55 56
[ 80] Order 32 Length 45 Maximal Subgroups: 54 55
---
[ 79] Order 81 Length 160 Maximal Subgroups: 50 51 52
[ 78] Order 60 Length 216 Maximal Subgroups: 17 25 36
[ 77] Order 60 Length 216 Maximal Subgroups: 18 25 35
[ 76] Order 54 Length 240 Maximal Subgroups: 43 44 45 48 50
[ 75] Order 54 Length 120 Maximal Subgroups: 42 46 47 50
[ 74] Order 54 Length 40 Maximal Subgroups: 45 51
[ 73] Order 36 Length 720 Maximal Subgroups: 37 38 44 47 48
[ 72] Order 36 Length 360 Maximal Subgroups: 13 42
[ 71] Order 36 Length 360 Maximal Subgroups: 41 42 46
[ 70] Order 36 Length 120 Maximal Subgroups: 37 42 43
[ 69] Order 24 Length 1080 Maximal Subgroups: 34 38 39 41
[ 68] Order 24 Length 540 Maximal Subgroups: 14 34 36
[ 67] Order 24 Length 540 Maximal Subgroups: 18 33 35
[ 66] Order 24 Length 540 Maximal Subgroups: 19 27 36
[ 65] Order 24 Length 540 Maximal Subgroups: 16 28 35
[ 64] Order 24 Length 540 Maximal Subgroups: 17 33 36
[ 63] Order 24 Length 360 Maximal Subgroups: 26 40
[ 62] Order 24 Length 360 Maximal Subgroups: 19 26
[ 61] Order 24 Length 360 Maximal Subgroups: 16 26
[ 60] Order 24 Length 270 Maximal Subgroups: 20 29 35
[ 59] Order 24 Length 90 Maximal Subgroups: 15 26
[ 58] Order 16 Length 810 Maximal Subgroups: 27 29 32 33 34
[ 57] Order 16 Length 810 Maximal Subgroups: 29 30 32
[ 56] Order 16 Length 405 Maximal Subgroups: 28 32
[ 55] Order 16 Length 405 Maximal Subgroups: 27 28 30 31
[ 54] Order 16 Length 270 Maximal Subgroups: 26 30 31
[ 53] Order 16 Length 27 Maximal Subgroups: 28 29
---
[ 52] Order 27 Length 320 Maximal Subgroups: 22 24
[ 51] Order 27 Length 40 Maximal Subgroups: 22
[ 50] Order 27 Length 40 Maximal Subgroups: 21 22 23
[ 49] Order 20 Length 1296 Maximal Subgroups: 13 25
[ 48] Order 18 Length 720 Maximal Subgroups: 15 16 19 23
[ 47] Order 18 Length 720 Maximal Subgroups: 17 20 23
[ 46] Order 18 Length 720 Maximal Subgroups: 18 20 21
[ 45] Order 18 Length 480 Maximal Subgroups: 14 15 22
[ 44] Order 18 Length 240 Maximal Subgroups: 14 16 23
[ 43] Order 18 Length 240 Maximal Subgroups: 14 19 21
[ 42] Order 18 Length 120 Maximal Subgroups: 17 18 21
[ 41] Order 12 Length 1080 Maximal Subgroups: 12 18 20
[ 40] Order 12 Length 1080 Maximal Subgroups: 8 15
[ 39] Order 12 Length 1080 Maximal Subgroups: 13 20
[ 38] Order 12 Length 1080 Maximal Subgroups: 9 16 20
[ 37] Order 12 Length 720 Maximal Subgroups: 9 14 17 19
[ 36] Order 12 Length 540 Maximal Subgroups: 6 12
[ 35] Order 12 Length 270 Maximal Subgroups: 5 10
[ 34] Order 8 Length 1620 Maximal Subgroups: 9 12 13
[ 33] Order 8 Length 1620 Maximal Subgroups: 10 12 13
[ 32] Order 8 Length 810 Maximal Subgroups: 11 13
[ 31] Order 8 Length 810 Maximal Subgroups: 8 11
[ 30] Order 8 Length 405 Maximal Subgroups: 8 11
[ 29] Order 8 Length 270 Maximal Subgroups: 9 10 11
[ 28] Order 8 Length 135 Maximal Subgroups: 10 11
[ 27] Order 8 Length 135 Maximal Subgroups: 11 12
[ 26] Order 8 Length 90 Maximal Subgroups: 8
---
[ 25] Order 10 Length 1296 Maximal Subgroups: 3 7
[ 24] Order 9 Length 960 Maximal Subgroups: 4
[ 23] Order 9 Length 240 Maximal Subgroups: 4 5 6
[ 22] Order 9 Length 160 Maximal Subgroups: 4 6
[ 21] Order 9 Length 120 Maximal Subgroups: 5 6
[ 20] Order 6 Length 1080 Maximal Subgroups: 3 5
[ 19] Order 6 Length 720 Maximal Subgroups: 2 6
[ 18] Order 6 Length 720 Maximal Subgroups: 3 5
[ 17] Order 6 Length 720 Maximal Subgroups: 3 6
[ 16] Order 6 Length 720 Maximal Subgroups: 2 5
[ 15] Order 6 Length 360 Maximal Subgroups: 2 4
[ 14] Order 6 Length 240 Maximal Subgroups: 2 6
[ 13] Order 4 Length 1620 Maximal Subgroups: 3
[ 12] Order 4 Length 540 Maximal Subgroups: 3
[ 11] Order 4 Length 405 Maximal Subgroups: 2 3
[ 10] Order 4 Length 270 Maximal Subgroups: 3
[ 9] Order 4 Length 270 Maximal Subgroups: 2 3
[ 8] Order 4 Length 270 Maximal Subgroups: 2
---
[ 7] Order 5 Length 1296 Maximal Subgroups: 1
[ 6] Order 3 Length 240 Maximal Subgroups: 1
[ 5] Order 3 Length 120 Maximal Subgroups: 1
[ 4] Order 3 Length 40 Maximal Subgroups: 1
[ 3] Order 2 Length 270 Maximal Subgroups: 1
[ 2] Order 2 Length 45 Maximal Subgroups: 1 --The involution fixing a K3 surface
---
[ 1] Order 1 Length 1 Maximal Subgroups:
Concretely, they are:
2: the group name is C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
3: the group name is C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2
Generators:
[ 1 0 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 0 0 1]
[ 0 0 0 1 0]
------------------------------
4: the group name is C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
------------------------------
5: the group name is C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3]
[1/3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3 -2/3 1/3 1/3*zeta_3]
------------------------------
6: the group name is C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
7: the group name is C5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 5
Generators:
[-1/3 2/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3 1/3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3]
------------------------------
8: the group name is C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
------------------------------
9: the group name is C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
10: the group name is C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 -2/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3]
------------------------------
11: the group name is C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
------------------------------
12: the group name is C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
13: the group name is C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2
Generators:
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[ -1 0 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -1 0 0]
[ 0 -zeta_3 0 0 0]
------------------------------
14: the group name is S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
------------------------------
15: the group name is C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 -zeta_3 - 1]
------------------------------
16: the group name is C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
------------------------------
17: the group name is S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) 2/3 -1/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 2/3*zeta_3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3 -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 2/3]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
18: the group name is S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*zeta_3 1/3 1/3 1/3 -2/3*zeta_3]
[1/3*zeta_3 1/3 1/3 -2/3 1/3*zeta_3]
[1/3*zeta_3 1/3 -2/3 1/3 1/3*zeta_3]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[1/3 1/3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
------------------------------
19: the group name is C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
------------------------------
20: the group name is C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3]
------------------------------
21: the group name is C3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^2
Generators:
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
22: the group name is C3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^2
Generators:
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
23: the group name is C3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^2
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
24: the group name is C9, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^2
Generators:
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 -1/3*zeta_3 2/3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3]
------------------------------
25: the group name is D5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 5
Generators:
[1/3 -2/3 -2/3*zeta_3 -2/3*zeta_3 -2/3*zeta_3]
[-1/3 2/3 -1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 2/3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 -1/3 2/3]
[1/3*(-2*zeta_3 - 1) 0 1/3*(4*zeta_3 + 2) 0 0]
[1/3*(-zeta_3 - 2) 0 1/3*(-zeta_3 - 2) 0 0]
[0 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
------------------------------
26: the group name is Q8, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 4) 0 0]
[0 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 0 0]
[0 1/3*(zeta_3 + 2) 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1)]
[0 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
27: the group name is C2^3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
------------------------------
28: the group name is C2^3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 -1/3 -1/3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2)]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3*zeta_3 -1/3 -1/3]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3 -1/3 -1/3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3 1/3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
------------------------------
29: the group name is C2^3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
------------------------------
30: the group name is C2*C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 -2/3*zeta_3 -2/3 -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 -
2)]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 +
1)]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3 -1/3*zeta_3 -1/3 2/3*zeta_3 -1/3*zeta_3]
------------------------------
31: the group name is D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[1/3 -2/3*zeta_3 -2/3 -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 +
1)]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 -
2)]
[-1/3 2/3*zeta_3 -1/3 -1/3*zeta_3 -1/3*zeta_3]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 zeta_3 0 0]
[ 0 zeta_3 0 0 0]
------------------------------
32: the group name is C2*C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 2/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 -1/3*zeta_3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3 -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
------------------------------
33: the group name is D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 2/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 -1/3*zeta_3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3 -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3]
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
------------------------------
34: the group name is D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
------------------------------
35: the group name is A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[1/3*(-2*zeta_3 - 1) 0 1/3*(4*zeta_3 + 2) 0 0]
[0 1/3*(zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2)]
[1/3*(-zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 0 0]
[0 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
[ 1/3 -2/3 -2/3 -2/3 -2/3]
[-1/3 2/3 -1/3 -1/3 -1/3]
[-1/3 -1/3 -1/3 -1/3 2/3]
[-1/3 -1/3 -1/3 2/3 -1/3]
[-1/3 -1/3 2/3 -1/3 -1/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3]
------------------------------
36: the group name is A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
------------------------------
37: the group name is D6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3 -2/3 -2/3 -2/3 -2/3]
[-1/3 2/3 -1/3 -1/3 -1/3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)
1/3*(zeta_3 + 1)]
[-1/3 -1/3 -1/3 -1/3 2/3]
------------------------------
38: the group name is C2*C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
------------------------------
39: the group name is C3:C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 zeta_3 + 1]
[ 0 0 0 -1 0]
[ 0 zeta_3 + 1 0 0 0]
[ 0 0 zeta_3 + 1 0 0]
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1)]
------------------------------
40: the group name is C12, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 2/3*zeta_3 -1/3 -1/3*zeta_3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 4) 0 0 0]
[1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[0 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
41: the group name is D6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1)]
------------------------------
42: the group name is C3:S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[1 0 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[1/3 -2/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3]
[-1/3 2/3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3*zeta_3 1/3*(zeta_3 + 1)]
[-1/3 -1/3 -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
------------------------------
43: the group name is C3*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[0 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2)]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
------------------------------
44: the group name is C3*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
[ 1 0 0 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
------------------------------
45: the group name is C3*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
46: the group name is C3*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3 1/3*zeta_3]
[1/3 -2/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3]
[-1/3 2/3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3*zeta_3 1/3*(zeta_3 + 1)]
[-1/3 -1/3 -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3]
------------------------------
47: the group name is C3*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 1 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
[ 1 0 0 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
------------------------------
48: the group name is C3*C6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^2
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[1/3*(2*zeta_3 + 1) 1/3*(-4*zeta_3 - 2) 0 0 0]
[1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2)]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
49: the group name is F5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 5
Generators:
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[ 1/3 -2/3 -2/3 -2/3 -2/3]
[-1/3 2/3 -1/3 -1/3 -1/3]
[-1/3 -1/3 -1/3 2/3 -1/3]
[-1/3 -1/3 2/3 -1/3 -1/3]
[-1/3 -1/3 -1/3 -1/3 2/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3 -2/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1)]
[1/3 1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
------------------------------
50: the group name is C3^3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
------------------------------
51: the group name is He3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3 -2/3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
52: the group name is C9:C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^3
Generators:
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2)]
[0 0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2)]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 -1/3*zeta_3 2/3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 2/3*zeta_3 -1/3]
------------------------------
53: the group name is C2^4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
[ -1 0 0 0 0]
[ 0 0 0 0 zeta_3 + 1]
[ 0 0 -1 0 0]
[ 0 0 0 -1 0]
[ 0 -zeta_3 0 0 0]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3 1/3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*zeta_3 1/3 1/3]
------------------------------
54: the group name is D4:C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
[1/3*(2*zeta_3 + 1) 1/3*(-4*zeta_3 - 2) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0 0 0]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
------------------------------
55: the group name is C2*D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 -2/3*zeta_3 -2/3 -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 -
2)]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 +
1)]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3 -1/3*zeta_3 -1/3 2/3*zeta_3 -1/3*zeta_3]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 zeta_3 0 0]
[ 0 zeta_3 0 0 0]
------------------------------
56: the group name is C2^2:C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ -1 0 0 0 0]
[ 0 0 0 0 zeta_3 + 1]
[ 0 zeta_3 + 1 0 0 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 +
2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 -
1)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 -
1)]
[1/3 -2/3*zeta_3 1/3 1/3*zeta_3 1/3*zeta_3]
------------------------------
57: the group name is C2^2:C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 -2/3*zeta_3 -2/3 -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 -
2)]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 +
1)]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3 -1/3*zeta_3 -1/3 2/3*zeta_3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3 -2/3]
------------------------------
58: the group name is C2*D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
------------------------------
59: the group name is SL(2,3), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[1/3*(2*zeta_3 + 1) 0 1/3*(-4*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(-zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
60: the group name is C2*A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*zeta_3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3 1/3*(-zeta_3 - 1)]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) 2/3 -1/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 2/3*zeta_3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3 -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 2/3]
------------------------------
61: the group name is SL(2,3), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 4) 0 0 0]
[1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 0 0 0]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(-4*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(-zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
62: the group name is SL(2,3), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3]
[1/3 1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(2*zeta_3 + 1) 0 1/3*(-4*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(-zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
63: the group name is C3*Q8, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(-4*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(-zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 + 2) 0 1/3*(-2*zeta_3 - 1) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
------------------------------
64: the group name is S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 zeta_3 + 1 0 0 0]
[ 0 0 0 -1 0]
[1/3 -2/3 -2/3 -2/3 -2/3]
[-1/3 2/3 -1/3 -1/3 -1/3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)
1/3*(zeta_3 + 1)]
[-1/3 -1/3 -1/3 -1/3 2/3]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
------------------------------
65: the group name is C2*A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3 1/3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*zeta_3 1/3 1/3]
------------------------------
66: the group name is C2*A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[1/3 -2/3 -2/3 -2/3 -2/3]
[-1/3 2/3 -1/3 -1/3 -1/3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)
1/3*(zeta_3 + 1)]
[-1/3 -1/3 -1/3 -1/3 2/3]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
------------------------------
67: the group name is S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -1]
[ 0 0 zeta_3 + 1 0 0]
[-1/3 2/3*zeta_3 2/3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*zeta_3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3 1/3*(-zeta_3 - 1)]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) 2/3 -1/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 2/3*zeta_3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3 -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 2/3]
------------------------------
68: the group name is S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
69: the group name is C3:D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1)]
------------------------------
70: the group name is S3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^2
Generators:
[-1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -1]
[1 0 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
71: the group name is S3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^2
Generators:
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[1 0 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
72: the group name is C3:S3.C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^2
Generators:
[-1 0 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -1]
[ 0 -1 0 0 0]
[ 0 0 0 -1 0]
[1 0 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[0 0 1 0 0]
[0 1 0 0 0]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
73: the group name is C6*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^2
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
74: the group name is C3^2:S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
75: the group name is C3*C3:S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 -1/3*zeta_3 2/3]
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3*(2*zeta_3 + 2) -2/3 -2/3*zeta_3 -2/3]
[-1/3*zeta_3 2/3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) 2/3 -1/3*zeta_3 -1/3]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
------------------------------
76: the group name is C3^2*S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
77: the group name is A5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3 * 5
Generators:
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3 -1/3 -1/3*zeta_3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
------------------------------
78: the group name is A5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3 * 5
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 2/3 2/3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3]
[1/3 1/3*(2*zeta_3 + 2) 1/3 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 1]
------------------------------
79: the group name is C3wrC3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 3^4
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
80: the group name is Q8:C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5
Generators:
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 -1/3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1) -1/3]
------------------------------
81: the group name is C2^2.D4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5
Generators:
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 -2/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
------------------------------
82: the group name is C2^2wrC2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 zeta_3 0 0]
[ 0 zeta_3 0 0 0]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 +
2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 -
1)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 -
1)]
[1/3 -2/3*zeta_3 1/3 1/3*zeta_3 1/3*zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 -1 0]
[ 0 0 zeta_3 + 1 0 0]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 -2/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2)]
[-1/3 -1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 2/3 -1/3*zeta_3 -1/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
83: the group name is A4:C4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3
Generators:
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 4) 0 0]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 1/3*(zeta_3 + 2) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
[1/3*(-zeta_3 - 2) 0 1/3*(-zeta_3 + 1) 0 0]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 -1 0]
[ 0 0 zeta_3 + 1 0 0]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1)]
[1/3 -2/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1)]
[1/3 1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3 1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[ 1 0 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 -2/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2)]
[-1/3 -1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 2/3 -1/3*zeta_3 -1/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
84: the group name is C2^2*A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*zeta_3 1/3 1/3]
[-1/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3]
[1/3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
85: the group name is SL(2,3):C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3
Generators:
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[1/3*(2*zeta_3 + 1) 0 0 0 1/3*(2*zeta_3 + 4)]
[0 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[1/3*(zeta_3 - 1) 0 0 0 1/3*(-2*zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 0 0 0 1/3*(2*zeta_3 - 2)]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[1/3*(zeta_3 + 2) 0 0 0 1/3*(-2*zeta_3 - 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
86: the group name is C2*S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3
Generators:
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*zeta_3]
[1/3 -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3 -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*zeta_3]
[ 1 0 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 zeta_3 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[1/3 -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 -1/3 -1/3*zeta_3 2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 2/3 -1/3*zeta_3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 -1/3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3 -1/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
------------------------------
87: the group name is C2*S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 2/3 2/3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3]
[1/3 1/3*(2*zeta_3 + 2) 1/3 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[1 0 0 0 0]
[0 0 1 0 0]
[0 1 0 0 0]
[0 0 0 0 1]
[0 0 0 1 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
88: the group name is S3wrC2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^2
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[-1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -1]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 -2/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*zeta_3 1/3]
[1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1)]
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
------------------------------
89: the group name is C3*SL(2,3), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^2
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 -2/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3 -1/3*zeta_3]
[-1/3 2/3 -1/3 -1/3*zeta_3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3]
[-1/3 -1/3 -1/3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
------------------------------
90: the group name is C2^4:C5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 5
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*zeta_3 1/3 -2/3]
[1/3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*zeta_3 -2/3 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 -1 0]
[ 0 0 zeta_3 + 1 0 0]
[-1 0 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -1]
[1/3 -2/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2)]
[-1/3 2/3 -1/3*zeta_3 -1/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3]
[1/3 -2/3*zeta_3 -2/3 -2/3*zeta_3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) 2/3 -1/3]
[-1/3 -1/3*zeta_3 2/3 -1/3*zeta_3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3 -1/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3 2/3]
------------------------------
91: the group name is C3^3:C2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^3
Generators:
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
------------------------------
92: the group name is C3^2:S3.C2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^3
Generators:
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3 -1/3*zeta_3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 2/3 -1/3*zeta_3 -1/3]
[-1/3*zeta_3 -1/3 -1/3 -1/3*zeta_3 2/3]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 4) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 0 0]
[0 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
------------------------------
93: the group name is C3*S3^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
------------------------------
94: the group name is C3^2:(C3:C4), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 zeta_3 + 1]
[ 0 0 0 -1 0]
[ 0 zeta_3 + 1 0 0 0]
[ 0 0 zeta_3 + 1 0 0]
[ 1 0 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1)]
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
------------------------------
95: the group name is S5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3 * 5
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 -2/3]
[ -1 0 0 0 0]
[ 0 0 0 0 zeta_3 + 1]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -zeta_3 0 0 0]
------------------------------
96: the group name is S5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3 * 5
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
------------------------------
97: the group name is C3wrS3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2 * 3^4
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
------------------------------
98: the group name is C2wrC2^2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6
Generators:
[-1 0 0 0 0]
[ 0 0 0 0 -1]
[ 0 0 -1 0 0]
[ 0 0 0 -1 0]
[ 0 -1 0 0 0]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 -1/3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2) -2/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 -1/3 -1/3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2)]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3*zeta_3 -1/3 -1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
99: the group name is C2^3:A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 3
Generators:
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[ 0 0 0 0 zeta_3]
[-1/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3*zeta_3]
[1/3*zeta_3 1/3 1/3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*zeta_3 1/3 1/3]
[1/3*(2*zeta_3 + 1) 0 0 0 1/3*(-4*zeta_3 - 2)]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 0]
[0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[1/3*(-2*zeta_3 - 1) 0 0 0 1/3*(-2*zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 - 2) 0 0 0]
[1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 0 0 0]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 0 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[1/3*(2*zeta_3 + 1) 1/3*(-4*zeta_3 - 2) 0 0 0]
[1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0 0 0]
[0 0 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1)]
[0 0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
100: the group name is C2^3:A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 3
Generators:
[ 1 0 0 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 -1/3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2) -2/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 -1/3 -1/3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2)]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3*zeta_3 -1/3 -1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
101: the group name is Q8.A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 3
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[1/3*(2*zeta_3 + 1) 0 0 0 1/3*(2*zeta_3 - 2)]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[1/3*(zeta_3 + 2) 0 0 0 1/3*(-2*zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 0 0 0 1/3*(-4*zeta_3 - 2)]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 0]
[0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 + 1) 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0]
[1/3*(-2*zeta_3 - 1) 0 0 0 1/3*(-2*zeta_3 - 1)]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3 -1/3 -1/3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
102: the group name is GL(2,Z/4), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 3
Generators:
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 4) 0 0]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 1/3*(zeta_3 + 2) 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1)]
[1/3*(-zeta_3 - 2) 0 1/3*(-zeta_3 + 1) 0 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3 2/3 -1/3*zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 -1 0]
[ 0 0 zeta_3 + 1 0 0]
[-1 0 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3 -2/3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
------------------------------
103: the group name is C2^4:D5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 5
Generators:
[-1/3 1/3*(-2*zeta_3 - 2) 2/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 -2/3 1/3*zeta_3 1/3 1/3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3 1/3*zeta_3 -2/3 1/3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 + 2) 0 0]
[1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 + 1) 0 0]
[0 1/3*(zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
[0 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2)]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 -1 0]
[ 0 0 zeta_3 + 1 0 0]
[-1 0 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -1]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3 -2/3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
------------------------------
104: the group name is SU(3,2), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^3
Generators:
[1/3 -2/3*zeta_3 -2/3*zeta_3 -2/3 -2/3*zeta_3]
[-1/3 -1/3*zeta_3 2/3*zeta_3 -1/3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 -
2)]
[1/3*(zeta_3 + 1) 2/3 -1/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[1/3 -2/3 -2/3*zeta_3 -2/3*zeta_3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 -1/3 2/3]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 +
1)]
[-1/3 2/3 -1/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3]
[-1/3 -1/3 2/3*zeta_3 -1/3*zeta_3 -1/3*zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 0 zeta_3]
[ 0 0 1 0 0]
[ 0 0 0 -zeta_3 - 1 0]
[1/3 1/3*(2*zeta_3 + 2) -2/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 2/3 -1/3*zeta_3 -1/3 -1/3]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 2/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 -1/3*zeta_3 -1/3 2/3]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
------------------------------
105: the group name is S3^2:S3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^3
Generators:
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 -1 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 0 zeta_3 + 1 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
106: the group name is C3^3:C2^2:C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^2 * 3^4
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 zeta_3]
[ 0 0 -zeta_3 - 1 0 0]
[ 1 0 0 0 0]
[ 0 0 0 0 -zeta_3 - 1]
[ 0 0 0 1 0]
[ 0 0 1 0 0]
[ 0 zeta_3 0 0 0]
[ 1 0 0 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 -zeta_3 - 1 0 0]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 2/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 -1/3 2/3]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3]
[1/3 -2/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3]
[-1/3 -1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
------------------------------
107: the group name is A6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^2 * 5
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*zeta_3 -2/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3 1/3]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3]
[-1/3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3]
------------------------------
108: the group name is C2^3:S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6 * 3
Generators:
[-1 0 0 0 0]
[ 0 0 0 0 -1]
[ 0 0 -1 0 0]
[ 0 0 0 -1 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[1/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2) -2/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 -2/3*zeta_3 -2/3*zeta_3 -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 1/3*(zeta_3 + 1) 2/3]
[1/3*(zeta_3 + 1) -1/3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 2/3 -1/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 2/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3 1/3 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
109: the group name is C2wrA4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6 * 3
Generators:
[ -1 0 0 0 0]
[ 0 0 0 0 -zeta_3]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 -1 0 0 0]
[ 1 0 0 0 0]
[ 0 -zeta_3 - 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 -zeta_3 - 1]
[1/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2) -2/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 -2/3*zeta_3 -2/3*zeta_3 -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 1/3*(zeta_3 + 1) 2/3]
[1/3*(zeta_3 + 1) -1/3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 2/3 -1/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 2/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3 1/3 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
110: the group name is SL(2,3):A4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^5 * 3^2
Generators:
[ 1 0 0 0 0]
[ 0 1 0 0 0]
[ 0 0 zeta_3 0 0]
[ 0 0 0 zeta_3 0]
[ 0 0 0 0 zeta_3]
[ 1 0 0 0 0]
[ 0 zeta_3 0 0 0]
[ 0 0 1 0 0]
[ 0 0 0 1 0]
[ 0 0 0 0 -zeta_3 - 1]
[1/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2) -2/3]
[1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[-1/3 -1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3 2/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3]
[1/3 -2/3*zeta_3 -2/3*zeta_3 -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3 -1/3 1/3*(zeta_3 + 1) 2/3]
[1/3*(zeta_3 + 1) -1/3 2/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[1/3*(zeta_3 + 1) 2/3 -1/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 2/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3 1/3 1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3]
[1/3 1/3 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3]
[1/3*(-zeta_3 - 1) 1/3 -2/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
111: the group name is SU(3,2).C3, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^4
Generators:
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*(2*zeta_3 + 2) -2/3 -2/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3*zeta_3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3]
[-1/3 2/3 1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3]
[1/3*(2*zeta_3 + 1) 0 0 1/3*(2*zeta_3 + 4) 0]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 1/3*(2*zeta_3 + 1)]
[1/3*(zeta_3 - 1) 0 0 1/3*(-2*zeta_3 - 1) 0]
[0 1/3*(-zeta_3 - 2) 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1)]
[0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2) 0 1/3*(-zeta_3 - 2)]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3 2/3]
[1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*zeta_3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1)]
[-1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3 2/3 -1/3]
[-1/3 1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3*zeta_3]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1)]
[1/3*(-2*zeta_3 - 1) 1/3*(4*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 + 1) 0 0 0]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1)]
[0 0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1)]
------------------------------
112: the group name is C3^3.S4, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^3 * 3^4
Generators:
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3 2/3*zeta_3]
[1/3 -2/3 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*zeta_3 -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3 1/3 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3 1/3*(zeta_3 + 1)]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 1/3*(zeta_3 + 1) 2/3*zeta_3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1)]
[-1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1)]
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 -2/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3 1/3*zeta_3]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3]
[-1/3 2/3*zeta_3 2/3*zeta_3 2/3*zeta_3 2/3]
[1/3*(-zeta_3 - 1) 1/3 1/3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3 1/3*(2*zeta_3 + 2)]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3 1/3*(-zeta_3 - 1)]
[1/3 1/3*zeta_3 -2/3*zeta_3 1/3*zeta_3 1/3]
[1/3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 -2/3 -2/3]
[-1/3*zeta_3 2/3 1/3*(zeta_3 + 1) -1/3*zeta_3 -1/3*zeta_3]
[-1/3*zeta_3 -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3 -1/3]
[-1/3*zeta_3 -1/3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3*zeta_3]
[1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 - 2) 0 0]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(2*zeta_3 + 1) 1/3*(-zeta_3 - 2)]
[1/3*(zeta_3 - 1) 0 1/3*(zeta_3 + 2) 0 0]
[0 1/3*(-zeta_3 - 2) 0 1/3*(2*zeta_3 + 1) 1/3*(2*zeta_3 + 1)]
[0 1/3*(2*zeta_3 + 1) 0 1/3*(-zeta_3 - 2) 1/3*(2*zeta_3 + 1)]
[-1/3 2/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 -2/3*zeta_3 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*zeta_3]
------------------------------
113: the group name is S6, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^4 * 3^2 * 5
Generators:
[-1/3 2/3*zeta_3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*zeta_3 1/3*(2*zeta_3 + 2) 1/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 1/3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*zeta_3 -2/3 1/3*zeta_3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 -zeta_3 0]
[ 0 0 zeta_3 + 1 0 0]
[ 0 0 0 0 -1]
------------------------------
114: the group name is C2.A4wrC2, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6 * 3^2
Generators:
[-1/3 2/3*zeta_3 2/3*zeta_3 2/3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3 1/3*(-zeta_3 - 1) 1/3]
[1/3*(-zeta_3 - 1) 1/3 -2/3 1/3*(-zeta_3 - 1) 1/3]
[1/3 1/3*zeta_3 1/3*zeta_3 -2/3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3 1/3*(-zeta_3 - 1) -2/3]
[1/3*(-2*zeta_3 - 1) 0 0 0 1/3*(4*zeta_3 + 2)]
[0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2) 0]
[0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0]
[0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0]
[1/3*(-zeta_3 + 1) 0 0 0 1/3*(-zeta_3 + 1)]
[1/3 -2/3 -2/3*zeta_3 -2/3 1/3*(2*zeta_3 + 2)]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(zeta_3 + 1) -1/3*zeta_3 2/3]
[-1/3*zeta_3 -1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3 -1/3]
[1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) -1/3 1/3*(-2*zeta_3 - 2) -1/3*zeta_3]
[1/3*(zeta_3 + 1) 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1) -1/3*zeta_3]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3 2/3]
[1/3*zeta_3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3]
[1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3 1/3]
[-1/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3 2/3]
[1/3 1/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[1/3*zeta_3 1/3*zeta_3 1/3 1/3*(2*zeta_3 + 2) 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3 -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3 1/3]
[1/3 -2/3*zeta_3 1/3*(2*zeta_3 + 2) -2/3*zeta_3 1/3*(2*zeta_3 + 2)]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 -1/3 2/3*zeta_3]
[-1/3*zeta_3 1/3*(zeta_3 + 1) 2/3 1/3*(zeta_3 + 1) -1/3]
[1/3*(zeta_3 + 1) -1/3 -1/3*zeta_3 2/3 -1/3*zeta_3]
[-1/3*zeta_3 1/3*(-2*zeta_3 - 2) -1/3 1/3*(zeta_3 + 1) -1/3]
[-1/3 1/3*(-2*zeta_3 - 2) 2/3 1/3*(-2*zeta_3 - 2) 1/3*(-2*zeta_3 - 2)]
[1/3*zeta_3 1/3 1/3*zeta_3 1/3 -2/3]
[1/3 1/3*(-zeta_3 - 1) 1/3 1/3*(2*zeta_3 + 2) 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3 -2/3*zeta_3 1/3 1/3]
[1/3*zeta_3 -2/3 1/3*zeta_3 1/3 1/3]
[ -1 0 0 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 zeta_3 + 1 0]
[ 0 0 -zeta_3 0 0]
[ 0 0 0 0 -1]
------------------------------
115: the group name is C2^4.A5, the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6 * 3 * 5
Generators:
[1/3*(-2*zeta_3 - 1) 0 0 1/3*(4*zeta_3 + 2) 0]
[1/3*(2*zeta_3 + 1) 0 0 1/3*(2*zeta_3 + 1) 0]
[0 1/3*(zeta_3 - 1) 1/3*(zeta_3 - 1) 0 1/3*(zeta_3 - 1)]
[0 1/3*(-2*zeta_3 - 1) 1/3*(zeta_3 + 2) 0 1/3*(zeta_3 - 1)]
[0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 - 1)]
[-1/3 2/3 2/3 1/3*(-2*zeta_3 - 2) 2/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[1/3*zeta_3 1/3*zeta_3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) 1/3*(2*zeta_3 + 2) 1/3*zeta_3 1/3]
[1/3*zeta_3 -2/3*zeta_3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[-1/3 2/3*zeta_3 2/3 2/3*zeta_3 2/3*zeta_3]
[1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3 1/3]
[1/3 1/3*zeta_3 -2/3 1/3*zeta_3 1/3*zeta_3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) -2/3 1/3]
[1/3*(-zeta_3 - 1) 1/3 1/3*(-zeta_3 - 1) 1/3 -2/3]
[-1/3 2/3 2/3*zeta_3 2/3 1/3*(-2*zeta_3 - 2)]
[1/3 -2/3 1/3*zeta_3 1/3 1/3*(-zeta_3 - 1)]
[1/3*(-zeta_3 - 1) 1/3*(-zeta_3 - 1) -2/3 1/3*(-zeta_3 - 1) 1/3*zeta_3]
[1/3 1/3 1/3*zeta_3 -2/3 1/3*(-zeta_3 - 1)]
[1/3*zeta_3 1/3*zeta_3 1/3*(-zeta_3 - 1) 1/3*zeta_3 -2/3]
[-1 0 0 0 0]
[ 0 0 0 -1 0]
[ 0 0 -1 0 0]
[ 0 -1 0 0 0]
[ 0 0 0 0 -1]
[1/3 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) 1/3*(2*zeta_3 + 2) -2/3]
[-1/3*zeta_3 -1/3 -1/3 2/3 -1/3*zeta_3]
[-1/3*zeta_3 -1/3 2/3 -1/3 -1/3*zeta_3]
[-1/3*zeta_3 2/3 -1/3 -1/3 -1/3*zeta_3]
[-1/3 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 1/3*(zeta_3 + 1) 2/3]
------------------------------
116: the group name is C(2,3), the generators are:
MatrixGroup(5, Cyclotomic Field of order 3 and degree 2) of order 2^6 * 3^4 * 5
Generators:
[1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 + 2) 0 0 0]
[1/3*(-zeta_3 + 1) 1/3*(-zeta_3 - 2) 0 0 0]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1)]
[0 0 1/3*(zeta_3 + 2) 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2)]
[0 0 1/3*(zeta_3 - 1) 1/3*(zeta_3 + 2) 1/3*(zeta_3 + 2)]
[1/3*(-2*zeta_3 - 1) 0 0 1/3*(-2*zeta_3 + 2) 0]
[0 1/3*(-2*zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 + 2)]
[0 1/3*(zeta_3 - 1) 1/3*(-2*zeta_3 - 1) 0 1/3*(zeta_3 - 1)]
[1/3*(2*zeta_3 + 1) 0 0 1/3*(-zeta_3 + 1) 0]
[0 1/3*(zeta_3 + 2) 1/3*(-2*zeta_3 - 1) 0 1/3*(-2*zeta_3 - 1)]
------------------------------