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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '23310331287699456000.a', 'ambient_counter': 1, 'ambient_order': 23310331287699456000, 'ambient_tex': 'C_2^{17}.A_{17}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '23310331287699456000.a.65280.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '65280.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': 65280, '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': '23310331287699456000.a', 'aut_centralizer_order': None, 'aut_label': '65280.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': 680, 'diagramx': None, 'generators': [53518199143762091944, 271076468422337457651480816288, 126, 33505454590398397518220476847, 1308063461329, 25852017095953494531414, 15537062060446413767224734, 10904406563569364203438080000, 33473245384060327688628816305, 51090942171709802880, 10904406563691366305216681647, 10904380711678040632319192104, 10904406564716145120492109735, 367920, 39916801, 10904406512478422037956058655, 10904812435136986945108214089, 357001369406767, 51091310331988380721, 15511261134630159023293423, 144644388828976360097654110, 15537062060425564658472550, 11179319267052346075391572543, 7, 5046, 1307714284807, 6227020806, 15511210043330985984362880, 25852016738884976640001], 'label': '23310331287699456000.a.65280.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '65280.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '65280.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': [[161256991192629962386157031602192250839, 169982502151411696756321093645915850742], [179174922519892719092455952472462526096, 187646431156593692869591723278019474265], [232768888103407129180635335408943414358, 250653607446534227931154585429479144822], [178963141271958085376021578314863806096, 187807485432212189156987826732692299864], [161257009485930639088988661692519312225, 169753515737574483707059167405125604065], [161282190214312120536727480907879346503, 169940318104939564638295966053979850591], [161256826552923818001332904885040016214, 169753515918571691675288855237948860662], [161282199665850803499857156454416232959, 169982511602950325767415835867371198656], [161256781124835383557274973927278049216, 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'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 34, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'Perm': {'d': 34, 'gens': [161256991192629962386157031602192250839, 169982502151411696756321093645915850742]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 194400, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^{17}.A_{17}', 'transitive_degree': 34, 'wreath_data': None, 'wreath_product': None}
