Database - gps_gmodules (Galois groups)

Formats: - HTML - YAML - JSON - 2026-04-20T08:03:28.706102 - next page

Query: /api/gps_gmodules/?_offset=0

Column	Type
complete	smallint
dim	smallint
gens	jsonb
index	smallint
n	smallint
name	text
t	smallint

0. id: 1
   {'complete': 1, 'dim': 1, 'gens': [['(1,2)', [[1]]]], 'index': 0, 'n': 2, 'name': 'Triv', 't': 1}
1. id: 2
   {'dim': 1, 'gens': [['(1,2)', [[-1]]]], 'index': 1, 'n': 2, 'name': 'Sign', 't': 1}
2. id: 3
   {'dim': 2, 'gens': [['(1,2)', [[0, 1], [1, 0]]]], 'index': 2, 'n': 2, 'name': '$L$', 't': 1}
3. id: 4
   {'complete': 1, 'dim': 1, 'gens': [['(1,2,3)', [[1]]]], 'index': 0, 'n': 3, 'name': 'Triv', 't': 1}
4. id: 5
   {'dim': 2, 'gens': [['(1,2,3)', [[0, 1], [-1, -1]]]], 'index': 1, 'n': 3, 'name': '$J$', 't': 1}
5. id: 6
   {'dim': 3, 'gens': [['(1,2,3)', [[0, 1, 0], [0, 0, 1], [1, 0, 0]]]], 'index': 2, 'n': 3, 'name': '$R$', 't': 1}
6. id: 7
   {'complete': 1, 'dim': 1, 'gens': [['(1,2,3)', [[1]]], ['(1,2)', [[1]]]], 'index': 0, 'n': 3, 'name': 'Triv', 't': 2}
7. id: 8
   {'dim': 1, 'gens': [['(1,2,3)', [[1]]], ['(1,2)', [[-1]]]], 'index': 1, 'n': 3, 'name': 'Sign', 't': 2}
8. id: 9
   {'dim': 2, 'gens': [['(1,2,3)', [[1, 0], [0, 1]]], ['(1,2)', [[0, 1], [1, 0]]]], 'index': 2, 'n': 3, 'name': '$L$', 't': 2}
9. id: 10
   {'dim': 2, 'gens': [['(1,2,3)', [[0, 1], [-1, -1]]], ['(1,2)', [[1, 0], [-1, -1]]]], 'index': 3, 'n': 3, 'name': '$A$', 't': 2}
10. id: 11
    {'dim': 2, 'gens': [['(1,2,3)', [[0, 1], [-1, -1]]], ['(1,2)', [[-1, 0], [1, 1]]]], 'index': 4, 'n': 3, 'name': "$A'$", 't': 2}
11. id: 12
    {'dim': 3, 'gens': [['(1,2,3)', [[0, 1, 0], [-1, -1, 0], [1, 0, 1]]], ['(1,2)', [[1, 0, 0], [-1, -1, 0], [-1, 0, -1]]]], 'index': 5, 'n': 3, 'name': '$(A,\\textrm{Sign})$', 't': 2}
12. id: 13
    {'dim': 3, 'gens': [['(1,2,3)', [[0, 1, 0], [-1, -1, 0], [1, 0, 1]]], ['(1,2)', [[-1, 0, 0], [1, 1, 0], [1, 0, 1]]]], 'index': 6, 'n': 3, 'name': "$(A',\\textrm{Triv})$", 't': 2}
13. id: 14
    {'dim': 4, 'gens': [['(1,2,3)', [[0, 1, 0, 0], [-1, -1, 0, 0], [-1, 0, 1, 0], [1, 0, 0, 1]]], ['(1,2)', [[1, 0, 0, 0], [-1, -1, 0, 0], [1, 0, 0, 1], [-1, 0, 1, 0]]]], 'index': 7, 'n': 3, 'name': '$(A,L)$', 't': 2}
14. id: 15
    {'dim': 4, 'gens': [['(1,2,3)', [[0, 1, 0, 0], [-1, -1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]], ['(1,2)', [[-1, 0, 0, 0], [1, 1, 0, 0], [1, 0, 0, 1], [1, 0, 1, 0]]]], 'index': 8, 'n': 3, 'name': "$(A',L)$", 't': 2}
15. id: 16
    {'dim': 6, 'gens': [['(1,2,3)', [[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]]], ['(1,2)', [[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]]]], 'index': 9, 'n': 3, 'name': "$(A+A',L)$", 't': 2}
16. id: 17
    {'complete': 1, 'dim': 1, 'gens': [['(1,2,3,4)', [[1]]]], 'index': 0, 'n': 4, 'name': 'Triv', 't': 1}
17. id: 18
    {'complete': -1, 'dim': 1, 'gens': [['(1,2,3,4)', [[-1]]]], 'index': 1, 'n': 4, 'name': '$B$', 't': 1}
18. id: 19
    {'complete': -1, 'dim': 2, 'gens': [['(1,2,3,4)', [[0, -1], [1, 0]]]], 'index': 2, 'n': 4, 'name': '$C$', 't': 1}
19. id: 20
    {'complete': -1, 'dim': 2, 'gens': [['(1,2,3,4)', [[0, 1], [1, 0]]]], 'index': 3, 'n': 4, 'name': '$E$', 't': 1}
20. id: 21
    {'complete': -1, 'dim': 3, 'gens': [['(1,2,3,4)', [[1, 0, 1], [0, 0, -1], [0, 1, 0]]]], 'index': 4, 'n': 4, 'name': '$(C,\\text{Triv})$', 't': 1}
21. id: 22
    {'complete': -1, 'dim': 3, 'gens': [['(1,2,3,4)', [[-1, 0, 1], [0, 0, -1], [0, 1, 0]]]], 'index': 5, 'n': 4, 'name': '$(C,B)$', 't': 1}
22. id: 23
    {'complete': -1, 'dim': 4, 'gens': [['(1,2,3,4)', [[0, 1, 0, 0], [1, 0, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0]]]], 'index': 6, 'n': 4, 'name': '$(C,E)$', 't': 1}
23. id: 24
    {'complete': -1, 'dim': 4, 'gens': [['(1,2,3,4)', [[0, 1, 0, 1], [1, 0, 0, -1], [0, 0, 0, -1], [0, 0, 1, 0]]]], 'index': 7, 'n': 4, 'name': "$(C,E)'$", 't': 1}
24. id: 25
    {'complete': -1, 'dim': 4, 'gens': [['(1,2,3,4)', [[1, 0, 0, 1], [0, -1, 0, 1], [0, 0, 0, -1], [0, 0, 1, 0]]]], 'index': 8, 'n': 4, 'name': '$(C,\\text{Triv}+B)$', 't': 1}
25. id: 26
    {'complete': 0, 'dim': 1, 'gens': [['(1,2)(3,4)', [[1]]], ['(1,4)(2,3)', [[1]]]], 'index': 0, 'n': 4, 'name': 'Triv', 't': 2}
26. id: 27
    {'dim': 1, 'gens': [['(1,2)(3,4)', [[1]]], ['(1,4)(2,3)', [[-1]]]], 'index': 1, 'n': 4, 'name': '$A_1$', 't': 2}
27. id: 28
    {'dim': 1, 'gens': [['(1,2)(3,4)', [[-1]]], ['(1,4)(2,3)', [[1]]]], 'index': 2, 'n': 4, 'name': '$A_2$', 't': 2}
28. id: 29
    {'dim': 1, 'gens': [['(1,2)(3,4)', [[-1]]], ['(1,4)(2,3)', [[-1]]]], 'index': 3, 'n': 4, 'name': '$A_3$', 't': 2}
29. id: 30
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[-1, 0], [0, -1]]], ['(1,4)(2,3)', [[0, 1], [1, 0]]]], 'index': 4, 'n': 4, 'name': '$B_1$', 't': 2}
30. id: 31
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, 1], [1, 0]]], ['(1,4)(2,3)', [[-1, 0], [0, -1]]]], 'index': 5, 'n': 4, 'name': '$B_2$', 't': 2}
31. id: 32
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, 1], [1, 0]]], ['(1,4)(2,3)', [[0, -1], [-1, 0]]]], 'index': 6, 'n': 4, 'name': '$B_3$', 't': 2}
32. id: 33
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[1, 0], [0, 1]]], ['(1,4)(2,3)', [[0, 1], [1, 0]]]], 'index': 7, 'n': 4, 'name': '$A_2B_1$', 't': 2}
33. id: 34
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[1, 0], [0, 1]]], ['(1,4)(2,3)', [[0, -1], [-1, 0]]]], 'index': 8, 'n': 4, 'name': '$A_3B_1$', 't': 2}
34. id: 35
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, 1], [1, 0]]], ['(1,4)(2,3)', [[1, 0], [0, 1]]]], 'index': 9, 'n': 4, 'name': '$A_1B_2$', 't': 2}
35. id: 36
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, -1], [-1, 0]]], ['(1,4)(2,3)', [[1, 0], [0, 1]]]], 'index': 10, 'n': 4, 'name': '$A_3B_2$', 't': 2}
36. id: 37
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, 1], [1, 0]]], ['(1,4)(2,3)', [[0, 1], [1, 0]]]], 'index': 11, 'n': 4, 'name': '$A_1B_3$', 't': 2}
37. id: 38
    {'dim': 2, 'gens': [['(1,2)(3,4)', [[0, -1], [-1, 0]]], ['(1,4)(2,3)', [[0, -1], [-1, 0]]]], 'index': 12, 'n': 4, 'name': '$A_2B_3$', 't': 2}
38. id: 39
    {'dim': 3, 'gens': [['(1,2)(3,4)', [[0, -1, 1], [0, -1, 0], [1, -1, 0]]], ['(1,4)(2,3)', [[0, 1, -1], [1, 0, -1], [0, 0, -1]]]], 'index': 13, 'n': 4, 'name': '$J$', 't': 2}
39. id: 40
    {'dim': 3, 'gens': [['(1,2)(3,4)', [[0, 0, 1], [-1, -1, -1], [1, 0, 0]]], ['(1,4)(2,3)', [[0, 1, 0], [1, 0, 0], [-1, -1, -1]]]], 'index': 14, 'n': 4, 'name': "$J'$", 't': 2}
40. id: 41
    {'complete': 1, 'dim': 1, 'gens': [['(1,2,3,4,5)', [[1]]]], 'index': 0, 'n': 5, 'name': 'Triv', 't': 1}
41. id: 42
    {'dim': 4, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]]]], 'index': 1, 'n': 5, 'name': '$J$', 't': 1}
42. id: 43
    {'dim': 5, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [1, 0, 0, 0, 0]]]], 'index': 2, 'n': 5, 'name': '$R$', 't': 1}
43. id: 44
    {'complete': 1, 'dim': 1, 'gens': [['(1,2,3,4,5)', [[1]]], ['(2,5)(3,4)', [[1]]]], 'index': 0, 'n': 5, 'name': 'Triv', 't': 2}
44. id: 45
    {'complete': -1, 'dim': 1, 'gens': [['(1,2,3,4,5)', [[1]]], ['(2,5)(3,4)', [[-1]]]], 'index': 1, 'n': 5, 'name': 'Sign', 't': 2}
45. id: 46
    {'complete': -1, 'dim': 2, 'gens': [['(1,2,3,4,5)', [[1, 0], [0, 1]]], ['(2,5)(3,4)', [[0, 1], [1, 0]]]], 'index': 2, 'n': 5, 'name': '$L$', 't': 2}
46. id: 47
    {'complete': -1, 'dim': 4, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]]], ['(2,5)(3,4)', [[1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0]]]], 'index': 3, 'n': 5, 'name': '$A$', 't': 2}
47. id: 48
    {'complete': -1, 'dim': 4, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]]], ['(2,5)(3,4)', [[-1, 0, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1], [0, 0, -1, 0]]]], 'index': 4, 'n': 5, 'name': "$A'$", 't': 2}
48. id: 49
    {'complete': -1, 'dim': 5, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [-1, -1, -1, -1, 0], [1, 0, 0, 0, 1]]], ['(2,5)(3,4)', [[1, 0, 0, 0, 0], [-1, -1, -1, -1, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [-1, 0, 0, 0, -1]]]], 'index': 5, 'n': 5, 'name': '$(A,\\textrm{Sign})$', 't': 2}
49. id: 50
    {'complete': -1, 'dim': 5, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [-1, -1, -1, -1, 0], [1, 0, 0, 0, 1]]], ['(2,5)(3,4)', [[-1, 0, 0, 0, 0], [1, 1, 1, 1, 0], [0, 0, 0, -1, 0], [0, 0, -1, 0, 0], [1, 0, 0, 0, 1]]]], 'index': 6, 'n': 5, 'name': "$(A',\\textrm{Triv})$", 't': 2}
50. id: 51
    {'complete': -1, 'dim': 6, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, 0, 0], [-1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1]]], ['(2,5)(3,4)', [[1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 1, 0]]]], 'index': 7, 'n': 5, 'name': '$(A,L)$', 't': 2}
51. id: 52
    {'complete': -1, 'dim': 6, 'gens': [['(1,2,3,4,5)', [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, 0, 0], [1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1]]], ['(2,5)(3,4)', [[-1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0]]]], 'index': 8, 'n': 5, 'name': "$(A',L)$", 't': 2}
52. id: 53
    {'complete': -1, 'dim': 10, 'gens': [['(1,2,3,4,5)', [[0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]]], ['(2,5)(3,4)', [[0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]]], 'index': 9, 'n': 5, 'name': "$(A+A',L)$", 't': 2}
53. id: 54
    {'complete': 1, 'dim': 1, 'gens': [['(1,3,5)(2,4,6)', [[1]]], ['(1,2)(3,6)(4,5)', [[1]]]], 'index': 0, 'n': 6, 'name': 'Triv', 't': 2}
54. id: 55
    {'dim': 1, 'gens': [['(1,3,5)(2,4,6)', [[1]]], ['(1,2)(3,6)(4,5)', [[-1]]]], 'index': 1, 'n': 6, 'name': 'Sign', 't': 2}
55. id: 56
    {'dim': 2, 'gens': [['(1,3,5)(2,4,6)', [[1, 0], [0, 1]]], ['(1,2)(3,6)(4,5)', [[0, 1], [1, 0]]]], 'index': 2, 'n': 6, 'name': '$L$', 't': 2}
56. id: 57
    {'dim': 2, 'gens': [['(1,3,5)(2,4,6)', [[0, 1], [-1, -1]]], ['(1,2)(3,6)(4,5)', [[1, 0], [-1, -1]]]], 'index': 3, 'n': 6, 'name': '$A$', 't': 2}
57. id: 58
    {'dim': 2, 'gens': [['(1,3,5)(2,4,6)', [[0, 1], [-1, -1]]], ['(1,2)(3,6)(4,5)', [[-1, 0], [1, 1]]]], 'index': 4, 'n': 6, 'name': "$A'$", 't': 2}
58. id: 59
    {'dim': 3, 'gens': [['(1,3,5)(2,4,6)', [[0, 1, 0], [-1, -1, 0], [1, 0, 1]]], ['(1,2)(3,6)(4,5)', [[1, 0, 0], [-1, -1, 0], [-1, 0, -1]]]], 'index': 5, 'n': 6, 'name': '$(A,\\textrm{Sign})$', 't': 2}
59. id: 60
    {'dim': 3, 'gens': [['(1,3,5)(2,4,6)', [[0, 1, 0], [-1, -1, 0], [1, 0, 1]]], ['(1,2)(3,6)(4,5)', [[-1, 0, 0], [1, 1, 0], [1, 0, 1]]]], 'index': 6, 'n': 6, 'name': "$(A',\\textrm{Triv})$", 't': 2}
60. id: 61
    {'dim': 4, 'gens': [['(1,3,5)(2,4,6)', [[0, 1, 0, 0], [-1, -1, 0, 0], [-1, 0, 1, 0], [1, 0, 0, 1]]], ['(1,2)(3,6)(4,5)', [[1, 0, 0, 0], [-1, -1, 0, 0], [1, 0, 0, 1], [-1, 0, 1, 0]]]], 'index': 7, 'n': 6, 'name': '$(A,L)$', 't': 2}
61. id: 62
    {'dim': 4, 'gens': [['(1,3,5)(2,4,6)', [[0, 1, 0, 0], [-1, -1, 0, 0], [1, 0, 1, 0], [1, 0, 0, 1]]], ['(1,2)(3,6)(4,5)', [[-1, 0, 0, 0], [1, 1, 0, 0], [1, 0, 0, 1], [1, 0, 1, 0]]]], 'index': 8, 'n': 6, 'name': "$(A',L)$", 't': 2}
62. id: 63
    {'dim': 6, 'gens': [['(1,3,5)(2,4,6)', [[0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]]], ['(1,2)(3,6)(4,5)', [[0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 1, 0]]]], 'index': 9, 'n': 6, 'name': "$(A+A',L)$", 't': 2}
63. id: 64
    {'complete': 1, 'dim': 1, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[1]]]], 'index': 0, 'n': 10, 'name': 'Triv', 't': 2}
64. id: 65
    {'complete': 1, 'dim': 1, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[-1]]]], 'index': 1, 'n': 10, 'name': 'Sign', 't': 2}
65. id: 66
    {'complete': 1, 'dim': 2, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[1, 0], [0, 1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[0, 1], [1, 0]]]], 'index': 2, 'n': 10, 'name': '$L$', 't': 2}
66. id: 67
    {'complete': 1, 'dim': 4, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[1, 0, 0, 0], [-1, -1, -1, -1], [0, 0, 0, 1], [0, 0, 1, 0]]]], 'index': 3, 'n': 10, 'name': '$A$', 't': 2}
67. id: 68
    {'complete': 1, 'dim': 4, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1], [-1, -1, -1, -1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[-1, 0, 0, 0], [1, 1, 1, 1], [0, 0, 0, -1], [0, 0, -1, 0]]]], 'index': 4, 'n': 10, 'name': "$A'$", 't': 2}
68. id: 69
    {'complete': 1, 'dim': 5, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [-1, -1, -1, -1, 0], [1, 0, 0, 0, 1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[1, 0, 0, 0, 0], [-1, -1, -1, -1, 0], [0, 0, 0, 1, 0], [0, 0, 1, 0, 0], [-1, 0, 0, 0, -1]]]], 'index': 5, 'n': 10, 'name': '$(A,\\textrm{Sign})$', 't': 2}
69. id: 70
    {'complete': 1, 'dim': 5, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [-1, -1, -1, -1, 0], [1, 0, 0, 0, 1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[-1, 0, 0, 0, 0], [1, 1, 1, 1, 0], [0, 0, 0, -1, 0], [0, 0, -1, 0, 0], [1, 0, 0, 0, 1]]]], 'index': 6, 'n': 10, 'name': "$(A',\\textrm{Triv})$", 't': 2}
70. id: 71
    {'complete': 1, 'dim': 6, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, 0, 0], [-1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[1, 0, 0, 0, 0, 0], [-1, -1, -1, -1, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 1, 0, 0, 0], [1, 0, 0, 0, 0, 1], [-1, 0, 0, 0, 1, 0]]]], 'index': 7, 'n': 10, 'name': '$(A,L)$', 't': 2}
71. id: 72
    {'complete': 1, 'dim': 6, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [-1, -1, -1, -1, 0, 0], [1, 0, 0, 0, 1, 0], [1, 0, 0, 0, 0, 1]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[-1, 0, 0, 0, 0, 0], [1, 1, 1, 1, 0, 0], [0, 0, 0, -1, 0, 0], [0, 0, -1, 0, 0, 0], [1, 0, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0]]]], 'index': 8, 'n': 10, 'name': "$(A',L)$", 't': 2}
72. id: 73
    {'complete': 1, 'dim': 10, 'gens': [['( 1, 3, 5, 7, 9)( 2, 4, 6, 8,10)', [[0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0]]], ['(1,4)(2,3)(5,10)(6,9)(7,8) ', [[0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 0, 0]]]], 'index': 9, 'n': 10, 'name': "$(A+A',L)$", 't': 2}