Database - gps_families ((description not yet updated on this server))

Formats: - HTML - YAML - JSON - 2025-11-28T00:15:17.912912 - next page

Query: /api/gps_families/?_offset=0

Column	Type
family	text
input	text
knowl	text
magma_cmd	text
name	text
priority	smallint
tex_name	text

0. family: C
   {'family': 'C', 'input': '^C(?P<n>\\d+)$', 'knowl': 'cyclic', 'magma_cmd': 'CyclicGroup(n)', 'name': 'Cyclic', 'priority': 1, 'tex_name': 'C_{{{n}}}'}
1. family: S
   {'family': 'S', 'input': '^S(?P<n>\\d+)$', 'knowl': 'symmetric', 'magma_cmd': 'Sym(n)', 'name': 'Symmetric', 'priority': 2, 'tex_name': 'S_{{{n}}}'}
2. family: D
   {'family': 'D', 'input': '^D(?P<n>\\d+)$', 'knowl': 'dihedral', 'magma_cmd': 'DihedralGroup(n)', 'name': 'Dihedral', 'priority': 3, 'tex_name': 'D_{{{n}}}'}
3. family: A
   {'family': 'A', 'input': '^A(?P<n>\\d+)$', 'knowl': 'alternating', 'magma_cmd': 'AlternatingGroup(n)', 'name': 'Alternating', 'priority': 4, 'tex_name': 'A_{{{n}}}'}
4. family: Q
   {'family': 'Q', 'input': '^Q(?P<n>\\d+)$', 'knowl': 'generalized_quaternion', 'magma_cmd': 'Group("Qn")', 'name': '(Generalized) Quaternion', 'priority': 5, 'tex_name': 'Q_{{{n}}}'}
5. family: F
   {'family': 'F', 'input': '^F(?P<n>\\d+)$', 'knowl': 'frobenius', 'magma_cmd': 'Group("Fn")', 'name': 'Frobenius', 'priority': 6, 'tex_name': 'F_{{{n}}}'}
6. family: SD
   {'family': 'SD', 'input': '^SD(?P<n>\\d+)$', 'knowl': 'semi_dihedral', 'magma_cmd': 'Group("SDn")', 'name': 'Semi-dihedral', 'priority': 7, 'tex_name': '\\SD_{{{n}}}'}
7. family: OD
   {'family': 'OD', 'input': '^OD(?P<n>\\d+)$', 'knowl': 'other_dihedral', 'magma_cmd': 'Group("ODn")', 'name': 'Other-dihedral', 'priority': 8, 'tex_name': '\\OD_{{{n}}}'}
8. family: He
   {'family': 'He', 'input': '^He(?P<n>\\d+)$', 'knowl': 'heisenberg', 'magma_cmd': 'Group("Hep")', 'name': 'Heisenberg', 'priority': 9, 'tex_name': '\\He_{{{n}}}'}
9. family: Dic
   {'family': 'Dic', 'input': '^Dic(?P<n>\\d+)$', 'knowl': 'dicyclic', 'magma_cmd': 'DicyclicGroup(n)', 'name': 'Dicyclic', 'priority': 10, 'tex_name': '\\Dic_{{{n}}}'}
10. family: Sporadic
    {'family': 'Sporadic', 'input': '^(?P<fam>Ru|McL|He|J\\d|Co\\d|HS|M\\d\\d)$', 'knowl': 'sporadic', 'magma_cmd': 'Group("fam")', 'name': 'Sporadic', 'priority': 11, 'tex_name': '{fam}'}
11. family: GL
    {'family': 'GL', 'input': '^GL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'general_linear', 'magma_cmd': 'GL(n,q)', 'name': 'General linear', 'priority': 12, 'tex_name': '\\GL({n},{q})'}
12. family: SL
    {'family': 'SL', 'input': '^SL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'special_linear', 'magma_cmd': 'SL(n,q)', 'name': 'Special linear', 'priority': 13, 'tex_name': '\\SL({n},{q})'}
13. family: PSL
    {'family': 'PSL', 'input': '^PSL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'special_linear', 'magma_cmd': 'PSL(n,q)', 'name': 'Projective special linear', 'priority': 14, 'tex_name': '\\PSL({n},{q})'}
14. family: PGL
    {'family': 'PGL', 'input': '^PGL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'general_linear', 'magma_cmd': 'PGL(n,q)', 'name': 'Projective general linear', 'priority': 15, 'tex_name': '\\PGL({n},{q})'}
15. family: Sp
    {'family': 'Sp', 'input': '^Sp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'Sp(n,q)', 'name': 'Symplectic', 'priority': 16, 'tex_name': '\\Sp({n},{q})'}
16. family: SO
    {'family': 'SO', 'input': '^SO\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'SO(n,q)', 'name': 'Special orthogonal', 'priority': 17, 'tex_name': '\\SO({n},{q})'}
17. family: SU
    {'family': 'SU', 'input': '^SU\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'SU(n,q)', 'name': 'Special unitary', 'priority': 18, 'tex_name': '\\SU({n},{q})'}
18. family: PSp
    {'family': 'PSp', 'input': '^PSp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'PSp(n,q)', 'name': 'Projective symplectic', 'priority': 19, 'tex_name': '\\PSp({n},{q})'}
19. family: PSO
    {'family': 'PSO', 'input': '^PSO\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PSO(n,q)', 'name': 'Projective special orthogonal', 'priority': 20, 'tex_name': '\\PSO({n},{q})'}
20. family: PSU
    {'family': 'PSU', 'input': '^PSU\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'PSU(n,q)', 'name': 'Projective special unitary', 'priority': 21, 'tex_name': '\\PSU({n},{q})'}
21. family: SOPlus
    {'family': 'SOPlus', 'input': '^SOPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'SOPlus(n,q)', 'name': 'Special orthogonal (plus)', 'priority': 22, 'tex_name': '\\SOPlus({n},{q})'}
22. family: SOMinus
    {'family': 'SOMinus', 'input': '^SOMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'SOMinus(n,q)', 'name': 'Special orthogonal (minus)', 'priority': 23, 'tex_name': '\\SOMinus({n},{q})'}
23. family: Orth
    {'family': 'Orth', 'input': '^Orth\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'GO(n,q)', 'name': 'General orthogonal', 'priority': 24, 'tex_name': '\\Orth({n},{q})'}
24. family: OrthPlus
    {'family': 'OrthPlus', 'input': '^OrthPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'GOPlus(n,q)', 'name': 'General orthogonal (plus)', 'priority': 25, 'tex_name': '\\OrthPlus({n},{q})'}
25. family: OrthMinus
    {'family': 'OrthMinus', 'input': '^OrthMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'GOMinus(n,q)', 'name': 'General orthogonal (minus)', 'priority': 26, 'tex_name': '\\OrthMinus({n},{q})'}
26. family: Unitary
    {'family': 'Unitary', 'input': '^Unitary\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'GU(n,q)', 'name': 'General unitary', 'priority': 27, 'tex_name': '\\Unitary({n},{q})'}
27. family: Omega
    {'family': 'Omega', 'input': '^Omega\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'Omega(n,q)', 'name': 'Omega', 'priority': 28, 'tex_name': '\\Omega({n},{q})'}
28. family: OmegaPlus
    {'family': 'OmegaPlus', 'input': '^OmegaPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'OmegaPlus(n,q)', 'name': 'Omega (plus)', 'priority': 29, 'tex_name': '\\OmegaPlus({n},{q})'}
29. family: OmegaMinus
    {'family': 'OmegaMinus', 'input': '^OmegaMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'OmegaMinus(n,q)', 'name': 'Omega (minus)', 'priority': 30, 'tex_name': '\\OmegaMinus({n},{q})'}
30. family: PSOPlus
    {'family': 'PSOPlus', 'input': '^PSOPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PSOPlus(n,q)', 'name': 'Projective special orthogonal (plus)', 'priority': 31, 'tex_name': '\\PSOPlus({n},{q})'}
31. family: PSOMinus
    {'family': 'PSOMinus', 'input': '^PSOMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PSOMinus(n,q)', 'name': 'Projective special orthogonal (minus)', 'priority': 32, 'tex_name': '\\PSOMinus({n},{q})'}
32. family: PO
    {'family': 'PO', 'input': '^PO\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PGO(n,q)', 'name': 'Projective orthogonal', 'priority': 33, 'tex_name': '\\PO({n},{q})'}
33. family: POPlus
    {'family': 'POPlus', 'input': '^POPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PGOPlus(n,q)', 'name': 'Projective orthogonal (plus)', 'priority': 34, 'tex_name': '\\POPlus({n},{q})'}
34. family: POMinus
    {'family': 'POMinus', 'input': '^POMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'PGOMinus(n,q)', 'name': 'Projective orthogonal (minus)', 'priority': 35, 'tex_name': '\\POMinus({n},{q})'}
35. family: PU
    {'family': 'PU', 'input': '^PU\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'PGU(n,q)', 'name': 'Projective unitary', 'priority': 36, 'tex_name': '\\PU({n},{q})'}
36. family: POmega
    {'family': 'POmega', 'input': '^POmega\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'POmega(n,q)', 'name': 'Projective omega', 'priority': 37, 'tex_name': '\\POmega({n},{q})'}
37. family: POmegaPlus
    {'family': 'POmegaPlus', 'input': '^POmegaPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'POmegaPlus(n,q)', 'name': 'Projective omega (plus)', 'priority': 38, 'tex_name': '\\POmegaPlus({n},{q})'}
38. family: POmegaMinus
    {'family': 'POmegaMinus', 'input': '^POmegaMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'POmegaMinus(n,q)', 'name': 'Projective omega (minus)', 'priority': 39, 'tex_name': '\\POmegaMinus({n},{q})'}
39. family: Spin
    {'family': 'Spin', 'input': '^Spin\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'Spin(n,q)', 'name': 'Spin', 'priority': 40, 'tex_name': '\\Spin({n},{q})'}
40. family: SpinPlus
    {'family': 'SpinPlus', 'input': '^SpinPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'SpinPlus(n,q)', 'name': 'Spin (plus)', 'priority': 41, 'tex_name': '\\SpinPlus({n},{q})'}
41. family: SpinMinus
    {'family': 'SpinMinus', 'input': '^SpinMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'SpinMinus(n,q)', 'name': 'Spin (minus)', 'priority': 42, 'tex_name': '\\SpinMinus({n},{q})'}
42. family: GSp
    {'family': 'GSp', 'input': '^GSp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'CSp(n,q)', 'name': 'Conformal symplectic', 'priority': 43, 'tex_name': '\\GSp({n},{q})'}
43. family: GSO
    {'family': 'GSO', 'input': '^GSO\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'CSO(n,q)', 'name': 'Conformal special orthgonal', 'priority': 44, 'tex_name': '\\GSO({n},{q})'}
44. family: GSOPlus
    {'family': 'GSOPlus', 'input': '^GSOPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'CSOPlus(n,q)', 'name': 'Conformal special orthgonal (plus)', 'priority': 45, 'tex_name': '\\GSOPlus({n},{q})'}
45. family: GSOMinus
    {'family': 'GSOMinus', 'input': '^GSOMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'CSOMinus(n,q)', 'name': 'Conformal special orthgonal (minus)', 'priority': 46, 'tex_name': '\\GSOMinus({n},{q})'}
46. family: GSU
    {'family': 'GSU', 'input': '^GSU\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'CSU(n,q)', 'name': 'Conformal special unitary', 'priority': 47, 'tex_name': '\\GSU({n},{q})'}
47. family: GOrth
    {'family': 'GOrth', 'input': '^GOrth\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'CO(n,q)', 'name': 'Conformal orthgonal', 'priority': 48, 'tex_name': '\\GOrth({n},{q})'}
48. family: GOrthPlus
    {'family': 'GOrthPlus', 'input': '^GOrthPlus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'COPlus(n,q)', 'name': 'Conformal orthgonal (plus)', 'priority': 49, 'tex_name': '\\GOrthPlus({n},{q})'}
49. family: GOrthMinus
    {'family': 'GOrthMinus', 'input': '^GOrthMinus\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'orthogonal', 'magma_cmd': 'COMinus(n,q)', 'name': 'Conformal orthgonal (minus)', 'priority': 50, 'tex_name': '\\GOrthMinus({n},{q})'}
50. family: GUnitary
    {'family': 'GUnitary', 'input': '^GUnitary\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'CU(n,q)', 'name': 'Conformal unitary', 'priority': 51, 'tex_name': '\\GUnitary({n},{q})'}
51. family: PGammaL
    {'family': 'PGammaL', 'input': '^PGammaL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'general_linear', 'magma_cmd': 'PGammaL(n,q)', 'name': 'Projective general linear automorphism', 'priority': 52, 'tex_name': '\\PGammaL({n},{q})'}
52. family: PSigmaL
    {'family': 'PSigmaL', 'input': '^PSigmaL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'special_linear', 'magma_cmd': 'PSigmaL(n,q)', 'name': 'Projective special linear automorphism', 'priority': 53, 'tex_name': '\\PSigmaL({n},{q})'}
53. family: PSigmaSp
    {'family': 'PSigmaSp', 'input': '^PSigmaSp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'PSigmaSp(n,q)', 'name': 'Projective symplectic automorphism', 'priority': 54, 'tex_name': '\\PSigmaSp({n},{q})'}
54. family: PGammaU
    {'family': 'PGammaU', 'input': '^PGammaU\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'unitary', 'magma_cmd': 'PGammaU(n,q)', 'name': 'Projective unitary automorphism group', 'priority': 55, 'tex_name': '\\PGammaU({n},{q})'}
55. family: AGL
    {'family': 'AGL', 'input': '^AGL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'general_linear', 'magma_cmd': 'AGL(n,q)', 'name': 'Affine general linear', 'priority': 56, 'tex_name': '\\AGL({n},{q})'}
56. family: ASL
    {'family': 'ASL', 'input': '^ASL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'special_linear', 'magma_cmd': 'ASL(n,q)', 'name': 'Affine special linear', 'priority': 57, 'tex_name': '\\ASL({n},{q})'}
57. family: ASp
    {'family': 'ASp', 'input': '^ASp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'ASp(n,q)', 'name': 'Affine symplectic', 'priority': 58, 'tex_name': '\\ASp({n},{q})'}
58. family: AGammaL
    {'family': 'AGammaL', 'input': '^AGammaL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'general_linear', 'magma_cmd': 'AGammaL(n,q)', 'name': 'Affine general linear automorphism', 'priority': 59, 'tex_name': '\\AGammaL({n},{q})'}
59. family: ASigmaL
    {'family': 'ASigmaL', 'input': '^ASigmaL\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'special_linear', 'magma_cmd': 'ASigmaL(n,q)', 'name': 'Affine special linear automorphism', 'priority': 60, 'tex_name': '\\ASigmaL({n},{q})'}
60. family: ASigmaSp
    {'family': 'ASigmaSp', 'input': '^ASigmaSp\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'symplectic', 'magma_cmd': 'ASigmaSp(n,q)', 'name': 'Affine symplectic automorphism', 'priority': 61, 'tex_name': '\\ASigmaSp({n},{q})'}
61. family: Chev
    {'family': 'Chev', 'input': '^(?P<fam>[A-G])\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'chevalley', 'magma_cmd': 'ChevalleyGroup("fam",n,q)', 'name': 'Chevalley', 'priority': 62, 'tex_name': '{fam}({n},{q})'}
62. family: TwistChev
    {'family': 'TwistChev', 'input': '^(?P<twist>\\d)(?P<fam>[A-G])\\((?P<n>\\d+),\\s*(?P<q>\\d+)\\)$', 'knowl': 'chevalley', 'magma_cmd': 'ChevalleyGroup("twistfam",n,q)', 'name': 'Twisted Chevalley', 'priority': 63, 'tex_name': '{{}}^{twist}{fam}({n},{q})'}
63. family: Cox
    {'family': 'Cox', 'input': '^W\\((?P<fam>[A-G])(?P<n>\\d+)\\)$', 'knowl': 'coxeter', 'magma_cmd': 'CoxeterGroup("famn")', 'name': 'Coxeter', 'priority': 64, 'tex_name': 'W({fam}_{{{n}}})'}
64. family: CoxH
    {'family': 'CoxH', 'input': '^H(?P<n>\\d+)$', 'knowl': 'coxeter', 'magma_cmd': 'CoxeterGroup("Hn")', 'name': 'Coxeter', 'priority': 65, 'tex_name': 'H_{{{n}}}'}
65. family: CoxI
    {'family': 'CoxI', 'input': '^I2\\((?P<n>\\d+)\\)$', 'knowl': 'coxeter', 'magma_cmd': 'CoxeterGroup("I2(n)")', 'name': 'Coxeter', 'priority': 66, 'tex_name': 'I_2({n})'}