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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '283500000000.b', 'ambient_counter': 2, 'ambient_order': 283500000000, 'ambient_tex': 'C_5^8.A_9.C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '283500000000.b.360._.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.P', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, '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': '787500000.b', 'subgroup_hash': None, 'subgroup_order': 787500000, 'subgroup_tex': 'C_5^6.(D_5\\times S_7)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '283500000000.b', 'aut_centralizer_order': None, 'aut_label': None, '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': 360, 'diagramx': None, 'generators': [8097050863174614716208057958400450845423198246073758823, 62762714095992133411201514368005637419369899610, 5376991927420340974664125084836466133976740845883087366, 2720125505846697950625581218161303721986039712948608064, 10633086299153795072174538611107085996083094949601891770, 486580401635328033, 348713981376, 816570, 9157944981056696130163779129690, 2481793735357390803148833], 'label': '283500000000.b.360._.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '360.P', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360._.P', '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': '4.2', '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': [[6682911996507263661228681012902757895583, 2701870020620051659550394602090568509464], [3337644886358540974898194886379229007335, 4562816088750697928604832712695764380760], [6682912023947214676283570584998151861766, 5743747440560490574968862980174517430913], [6110339322779497554639318870061987987135, 1180931425107379019179228562479862440920], [6682912005632136908154540491970239615903, 2701870038902062009660136221679626800600], [6682911996507263661228681012902757895583, 2432687183594019094530038137221191299800], [6379522150647587620396714562277660372479, 2701870011462109160287433829342940105656], [6682912005632136908154642929669314918943, 2701870020620051659550394602090567299800], [6379522150647586973023129497875547655589, 1520938824461635096159920163422563069400], [6682911988580166701323993303764395769509, 2701870020620051659550394602090568751353], [6682911996507263661228937819225843207646, 2701870020620051659550394602090568751353], [6682911996507263661228553676803500979103, 2701870020620051659550394602090568751353], [7291270483570865495697170652168709639615, 1520938824461636387585921156408803459896], [6987083030288832451105384944501405254309, 2129297345661441847920830200419515747160]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 6300000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 105, 1], [2, 2625, 1], [2, 13125, 1], [2, 65625, 1], [2, 78125, 1], [2, 328125, 2], [3, 1750, 1], [3, 175000, 1], [4, 26250, 1], [4, 393750, 1], [4, 1968750, 1], [4, 3281250, 1], [5, 2, 2], [5, 14, 10], [5, 42, 12], [5, 70, 10], [5, 84, 14], [5, 140, 2], [5, 210, 32], [5, 280, 14], [5, 420, 24], [5, 840, 31], [5, 1260, 12], [5, 1680, 2], [5, 2520, 4], [5, 315000, 1], [5, 630000, 4], [5, 1260000, 4], [6, 52500, 1], [6, 131250, 1], [6, 656250, 1], [6, 2625000, 1], [6, 5468750, 1], [6, 6562500, 1], [6, 13125000, 1], [6, 21875000, 1], [7, 11250000, 1], [10, 210, 12], [10, 1050, 50], [10, 2100, 52], [10, 3150, 2], [10, 4200, 74], [10, 5250, 14], [10, 6300, 74], [10, 10500, 24], [10, 12600, 51], [10, 15750, 52], [10, 25200, 2], [10, 26250, 12], [10, 31500, 128], [10, 63000, 48], [10, 78750, 52], [10, 157500, 24], [10, 393750, 2], [10, 525000, 2], [10, 656250, 2], [10, 787500, 2], [10, 1312500, 4], [10, 1575000, 4], [10, 2625000, 1], [10, 3150000, 2], [10, 7875000, 1], [10, 15750000, 2], [10, 39375000, 1], [12, 1312500, 1], [12, 6562500, 1], [14, 56250000, 1], [15, 3500, 12], [15, 10500, 2], [15, 14000, 50], [15, 21000, 26], [15, 42000, 75], [15, 84000, 12], [15, 350000, 14], [15, 700000, 24], [20, 52500, 12], [20, 157500, 52], [20, 315000, 24], [20, 787500, 62], [20, 3937500, 4], [20, 6562500, 2], [20, 7875000, 4], [25, 630000, 10], [25, 1260000, 20], [30, 105000, 64], [30, 210000, 124], [30, 262500, 14], [30, 525000, 24], [30, 2625000, 4], [30, 5250000, 13], [30, 13125000, 2], [30, 26250000, 2], [35, 22500000, 2], [50, 3150000, 10], [60, 2625000, 12], [60, 13125000, 2]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '787500000.b', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '2520.a'], 'composition_length': 10, 'conjugacy_classes_known': False, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 105, 1, 1], [2, 2625, 1, 1], [2, 13125, 1, 1], [2, 65625, 1, 1], [2, 78125, 1, 1], [2, 328125, 1, 2], [3, 1750, 1, 1], [3, 175000, 1, 1], [4, 26250, 1, 1], [4, 393750, 1, 1], [4, 1968750, 1, 1], [4, 3281250, 1, 1], [5, 2, 2, 1], [5, 14, 2, 5], [5, 42, 2, 6], [5, 70, 2, 5], [5, 84, 2, 7], [5, 140, 2, 1], [5, 210, 2, 16], [5, 280, 2, 7], [5, 420, 2, 12], [5, 840, 1, 1], [5, 840, 2, 15], [5, 1260, 2, 6], [5, 1680, 2, 1], [5, 2520, 2, 2], [5, 315000, 1, 1], [5, 630000, 2, 2], [5, 1260000, 2, 2], [6, 52500, 1, 1], [6, 131250, 1, 1], [6, 656250, 1, 1], [6, 2625000, 1, 1], [6, 5468750, 1, 1], [6, 6562500, 1, 1], [6, 13125000, 1, 1], [6, 21875000, 1, 1], [7, 11250000, 1, 1], [10, 210, 2, 6], [10, 1050, 2, 25], [10, 2100, 2, 26], [10, 3150, 2, 1], [10, 4200, 2, 37], [10, 5250, 2, 7], [10, 6300, 2, 37], [10, 10500, 2, 12], [10, 12600, 1, 1], [10, 12600, 2, 25], [10, 15750, 2, 26], [10, 25200, 2, 1], [10, 26250, 2, 6], [10, 31500, 2, 64], [10, 63000, 2, 24], [10, 78750, 2, 26], [10, 157500, 2, 12], [10, 393750, 2, 1], [10, 525000, 2, 1], [10, 656250, 2, 1], [10, 787500, 2, 1], [10, 1312500, 2, 2], [10, 1575000, 1, 2], [10, 1575000, 2, 1], [10, 2625000, 1, 1], [10, 3150000, 2, 1], [10, 7875000, 1, 1], [10, 15750000, 2, 1], [10, 39375000, 1, 1], [12, 1312500, 1, 1], [12, 6562500, 1, 1], [14, 56250000, 1, 1], [15, 3500, 2, 6], [15, 10500, 2, 1], [15, 14000, 2, 25], [15, 21000, 2, 13], [15, 42000, 1, 1], [15, 42000, 2, 37], [15, 84000, 2, 6], [15, 350000, 2, 7], [15, 700000, 2, 12], [20, 52500, 2, 6], [20, 157500, 2, 26], [20, 315000, 2, 12], [20, 787500, 2, 31], [20, 3937500, 2, 2], [20, 6562500, 2, 1], [20, 7875000, 2, 2], [25, 630000, 2, 5], [25, 1260000, 2, 10], [30, 105000, 2, 32], [30, 210000, 2, 62], [30, 262500, 2, 7], [30, 525000, 2, 12], [30, 2625000, 2, 2], [30, 5250000, 1, 1], [30, 5250000, 2, 6], [30, 13125000, 2, 1], [30, 26250000, 2, 1], [35, 22500000, 2, 1], [50, 3150000, 2, 5], [60, 2625000, 2, 6], [60, 13125000, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 2100, 'exponents_of_order': [8, 5, 2, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '787500000.b', 'hash': 1180469327369231408, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_5^6.(D_5\\times S_7)', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '787500000.b', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C5^6.(D5*S7)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 1576, 'number_divisions': 806, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 787500000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 815855], [3, 176750], [4, 5670000], [5, 7953124], [6, 50496250], [7, 11250000], [10, 121981020], [12, 7875000], [14, 56250000], [15, 27167000], [20, 125580000], [25, 31500000], [30, 206535000], [35, 45000000], [50, 31500000], [60, 57750000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 8, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'Perm': {'d': 35, 'gens': [6682911996507263661228681012902757895583, 2701870020620051659550394602090568509464]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 1008, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^6.(D_5\\times S_7)', 'transitive_degree': 35, 'wreath_data': None, 'wreath_product': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', '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': [[73380145261083409942653202531481749403166990239335120679, 18977622742846982189529560028304581919126958627160732775], [81787873316601383768025658203031559070427713592415465606, 18977622929113762240335838932686924022393734824832096549], [2661115499570749016519761921150815744405886305895120679, 108989134001080787386779952700196464277192044763480732775], [59779514573416500116652507095471053658688962921466441023, 68187242880154311630703410692121330014163641031000732775], [81787873170098451663149452856408302790051726569362665549, 40985981525754045971416191572510328782757948388551776549], [95388503941506318921871446961900447294289978821752737189, 18977622991919676830292992392194695200126918541324947135], [73380145365758663833803310570817064591490427184067049606, 18977622742846979720224905327384593691189513683196646949], [95388503941506318921871446961890192232508830365866163749, 18977622742846978807644685718851912350984287625910291135], [95388503941506318921871630121061948179704977166095695429, 18977622742846979720224905327384593689905259575358099103], [116902095278041962811983377274940841126076242895513558983, 18977622742846979720224905327384593691419287882670748806], [70664268414532797247901724915704027538692234364801641549, 18977622866351046623404990922248214962174475113986023006], [78820328969957601962455191060768211485802096412578002086, 18977622803503470945981026010565315584792561159996469766], [73380145261083409942653202531481749403166990239335120679, 13784720192288826233404655929592255685185863891121206439], [68187242649868766445198636257182134214678340873907414983, 18977622782569173879991656297150790993116698063267010509], [73380145261083409942653211688617122851138892616494295079, 24417806491442622217327535358004276971850257616817864909], [70664268374810605219061578103745139218794464055115781286, 18977622824438510514319360902818018781926831321771862989], [68187242608041092186727674764264697799097580323050114599, 18977622742846982189529560028304581919229396767396510823], [73380145200426922062945498970721903153040939812765066215, 18977622782569173879991638015142275201701643436782646406], [73380145240149113484224730774388528799738150000594723783, 18977622742846982458712406211473063280677565817189225606], [73380145261083409942653185479513481473772780776162635655, 18977622742846983066273285852717246513479649742344227783], [70664268374810604949878748972547512061835657281430325735, 18977622761675796687510055359705922798730926590926474279]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 567000000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 180, 1, 1], [2, 9450, 1, 1], [2, 157500, 1, 1], [2, 390625, 1, 1], [2, 590625, 1, 2], [2, 2812500, 1, 1], [2, 3937500, 1, 1], [2, 5906250, 1, 1], [3, 4200, 1, 1], [3, 2100000, 1, 1], [3, 35000000, 1, 1], [4, 94500, 1, 1], [4, 4725000, 1, 1], [4, 35437500, 1, 2], [4, 59062500, 1, 1], [4, 118125000, 1, 1], [4, 177187500, 1, 2], [5, 18, 2, 1], [5, 72, 2, 2], [5, 144, 2, 1], [5, 168, 2, 1], [5, 252, 2, 1], [5, 504, 2, 3], [5, 630, 2, 1], [5, 756, 2, 1], [5, 1008, 2, 4], [5, 1260, 2, 1], [5, 1512, 2, 1], [5, 1680, 2, 1], [5, 2520, 2, 3], [5, 3024, 1, 1], [5, 3024, 2, 3], [5, 5040, 2, 3], [5, 7560, 2, 3], [5, 10080, 2, 4], [5, 15120, 2, 3], [5, 22680, 1, 1], [5, 30240, 2, 1], [5, 1890000, 1, 1], [5, 11340000, 2, 1], [5, 15120000, 2, 1], [5, 22680000, 2, 1], [5, 45360000, 1, 1], [5, 45360000, 2, 1], [6, 315000, 1, 1], [6, 4725000, 1, 1], [6, 7875000, 1, 2], [6, 31500000, 1, 2], [6, 65625000, 1, 1], [6, 118125000, 1, 1], [6, 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