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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '21424936845312000.a', 'ambient_counter': 1, 'ambient_order': 21424936845312000, 'ambient_tex': 'C_2^{14}.A_{15}.C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '21424936845312000.a.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.A', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '357082280755200.a', 'subgroup_hash': None, 'subgroup_order': 357082280755200, 'subgroup_tex': 'C_2^{13}.A_{14}', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '21424936845312000.a', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 15, 'diagramx': None, 'generators': [10904380712583390659848003902, 6267305527, 33520991652580466869383230640, 10904380711674627413973542999, 51090942171709440001, 161504506673953307468351303, 15537113151013350346878727, 367927, 25903229687484157595831, 10936805991851337059042748846, 121645100408832001, 10888895353647678324129861712, 25852016738884976640001, 380757047527589041, 25852017095886523473217, 10904406563691366305216681647, 10904380711674626106338653422, 40284726, 5046, 7, 135554325004095508007110276439, 121, 15537113272657189584782782, 15511210165333087762601527, 33714572248839061349519909040, 10904406563574243391684319705, 10904622428046959251070445943, 10904568527102609586203832366, 357001369769527, 22599887143563661407248517544, 10904946191091802623894237648, 15511261134630159026548553, 1313941673526, 10904406563691366299039732526], 'label': '21424936845312000.a.60.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '60.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[169027437061552855663639221263, 259510313868443265998495889048], [11114955452171860192171722953, 158460769005737849059531847758], [271253350863662127244804379663, 158428721603269099032576042648], [203306779267385953032241844824, 304758940978611199895851774793], [123858577928377126215368087753, 194145917910672156712007758], [169027355010133562895145664767, 259510313868442157090632976057], [169027437061419159036207704111, 226037122594934998245372616440], [169027383109517922338557673039, 304678957514623097183903888657], [169027436954504075147597807423, 259622668981191918452200404168], [169027437275769877483633073711, 226037122701982686604795594008], [146443115236791170137018665743, 259445733281482055002512273048], [203307211257313979054450960783, 259510447624529871514476777288], [203306913025006115375186612825, 304759128687242271465661459913], [146443115238458423578261672463, 259477996599512580143028522648], [169027462913569594548655777937, 248621444418024558150299792934], [169027462913691239649024698297, 259510313868442910311068160974], [169027462862478652376906058377, 259510313919533852482777595934], [169027437061674145076659879103, 259510313868443265998456335128], [158138567560043561324934397583, 259510339771550947048955311128], [169027437010461912184255055423, 259525825129577540463864059928], [169027462862478652370679400457, 259510313919533852482777233048], [169027437010583558592338250382, 259510313919534208170205691928], [169027437061674145076619594382, 259510313868442910311067792928], [158138593463151242381620840343, 259510313868443265998495889048], [169027437061552499976251042063, 259525825078486596984479894088], [169027437010461913491929418376, 259510313919534208170205691928], [169027437061552855663639221263, 259510313868443265998495889048], [169027437061552855663679137943, 248621444418024913837727888928], [293708564930246384009005729608, 11162837561002859517072549817]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 714164561510400, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 91, 1, 2], [2, 1001, 1, 2], [2, 3003, 1, 2], [2, 12012, 1, 2], [2, 540540, 1, 2], [2, 2522520, 1, 2], [2, 5045040, 1, 2], [2, 60540480, 1, 2], [2, 75675600, 1, 2], [3, 2912, 1, 1], [3, 1921920, 1, 1], [3, 287006720, 1, 1], [3, 5740134400, 1, 1], [4, 12012, 1, 2], [4, 240240, 1, 2], [4, 540540, 1, 2], [4, 2522520, 1, 2], [4, 2882880, 1, 2], [4, 4324320, 1, 2], [4, 5045040, 1, 2], [4, 6054048, 1, 1], [4, 30270240, 1, 2], [4, 34594560, 1, 2], [4, 60540480, 1, 2], [4, 75675600, 1, 2], [4, 121080960, 1, 6], [4, 242161920, 1, 4], [4, 302702400, 1, 1], 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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[8954748183442760514331687560360, 128244990840029274031844212995126], [8988189191359902086605790642329, 146560956444017080717218763178281], [63755281805504210430011554440360, 228519718553383837291697094910086], [8841826762033765605458501042329, 146640404779807481445247336874161], [9010886220271223719884799694950, 164865952491310583261523318735775], [8954748183443138257170030831216, 128245038614556073041433223427823], [8954748183442248324435228497406, 128244926313395493773634805720326], [8954748183442248324435228532432, 128244926313395103234418206860158], [8954748183442760514385289008680, 128267575161852363944620215017526], [8954748183442248324475726728360, 128244926313395493772125902693166], [8988221374716267655198402267560, 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