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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3557376.a', 'ambient_counter': 1, 'ambient_order': 3557376, 'ambient_tex': 'C_{18528}.C_{192}', 'central': False, 'central_factor': True, 'centralizer_order': None, 'characteristic': False, 'core_order': 74112, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3557376.a.48._.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.BB', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{48}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '74112.a', 'subgroup_hash': None, 'subgroup_order': 74112, 'subgroup_tex': 'C_2\\times F_{193}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3557376.a', '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': 1, 'diagramx': None, 'generators': [18432, 1090950, 1778688, 1731, 64, 460896, 2255628, 824856, 1133616], 'label': '3557376.a.48._.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '48.BB', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48._.BB', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '384.563', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [192, 386], 'aut_gens': [[1, 192], [1, 44352], [44353, 192]], 'aut_group': '74112.a', 'aut_hash': 8990877608545953376, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 74112, 'aut_permdeg': 579, 'aut_perms': [163639633665277581841672839242556825352719149330919277691365020878334261066083920520185634692233801725036561999139526248981581890932787747018619617650197093672906892400103877771873552633610729033777271711856614257776959708520959894174161764708974031248222966952319127139811738969747200265073213345569757840876672405464400171382573571995233689984002831815706307095550501550984872702838311405068500356800614590608636590401285763373841545490505924990012295143846254311306766264824212511862905267713945360990889799476066102327115952860782547862871373119760175940817761300092603029026611640220708303145640560661905219201027974100582039096808564157428213754700082531269925594073845881251211618807878616415545004373855952720707748747652135527776528423960131290454564643954118604336608956205704117544404361137590494843000099140836568944967703760965615716171133863704521178516836390863041625966399241047955182401578242240386285514063688964983618805999029602189840521166114441022236023705317659194731874475858819708153847479291289527588083984805550824093033570072409308294869259753884925398967579971441867581195527073498048940092566520665882665542845639426092447964375301412237943761187932576128218637822226025559368390113953993504227041570226448070134416586824781369107009448414926816853633564561182545258773719652445247776448506123309518411354689504349223720, 621484067438359433187044768590508994743357151055436631732325391747888146276241330140504588362462103548985162182657023813604978817442797773082439929990956627344480149668738221549470358621288875763313721775012318186669681433446016341318280135271467197479812334544377387744632398484003334692234042993890892833662969691921712159950921626335533366792507023098097614768345298723899387688675685326704812129891269169206685476053385247551316813193063010782132896801259959369209681141574131072325348732767914065241576733575000597585123029250865825812852147794647795583350374632741316645400942944518810068204797187184081558524568213250414560725909391723879846826186039753324999229123780056136510757401239678239067732366578332497129858216009362259857529266347301251213396165296501318987246964778187066481266166494275297986672766949571848234337659433336847269071917426878622562043902125815803628674728747855419729319287859177972829553067720835780001789137135623796015275410416849048733175331850938483969144185751484025774837740190021319498167218506215361911539211946759223631453016633955391716937081928048394668935720962713456455350804464814766573509923068955748737114677556822804984374611575949535401912315434249293106868125339542472799468012446451600127169502639402986400964295877189025745422884020972957140802905809048975844927696511991795836518400000000000000], 'aut_phi_ratio': 3.015625, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 193, 1, 2], [4, 193, 1, 4], [6, 193, 1, 6], [8, 193, 1, 8], [12, 193, 1, 8], [16, 193, 1, 16], [24, 193, 1, 16], [32, 193, 1, 32], [48, 193, 1, 32], [64, 193, 2, 32], [96, 193, 1, 64], [192, 193, 2, 64], [193, 192, 1, 1], [386, 192, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times F_{193}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 193, 2], [3, 193, 2], [4, 193, 4], [6, 193, 6], [8, 193, 8], [12, 193, 8], [16, 193, 16], [24, 193, 16], [32, 193, 32], [48, 193, 32], [64, 193, 64], [96, 193, 64], [192, 193, 128], [193, 192, 1], [386, 192, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '37056.a', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '193.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['37056.a', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 193, 2, 1], [4, 193, 2, 2], [6, 193, 2, 3], [8, 193, 4, 2], [12, 193, 4, 2], [16, 193, 8, 2], [24, 193, 8, 2], [32, 193, 16, 2], [48, 193, 16, 2], [64, 193, 32, 2], [96, 193, 32, 2], [192, 193, 64, 2], [193, 192, 1, 1], [386, 192, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24576, 'exponent': 37056, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[192, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '74112.a', 'hash': 8990877608545953376, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 37056, 'inner_gen_orders': [192, 193], 'inner_gens': [[1, 44352], [29953, 192]], 'inner_hash': 1432757702296672986, 'inner_nilpotent': False, 'inner_order': 37056, 'inner_split': True, 'inner_tex': 'F_{193}', 'inner_used': [1, 2], 'irrC_degree': 192, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 192, 'irrep_stats': [[1, 384], [192, 2]], 'label': '74112.a', 'linC_count': 1, 'linC_degree': 192, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 192, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*F193', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 290, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 386, 'number_divisions': 30, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 80, 'number_subgroups': 7376, 'old_label': None, 'order': 74112, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 387], [3, 386], [4, 772], [6, 1158], [8, 1544], [12, 1544], [16, 3088], [24, 3088], [32, 6176], [48, 6176], [64, 12352], [96, 12352], [192, 24704], [193, 192], [386, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[37057, 73920]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 195, 'pgroup': 0, 'primary_abelian_invariants': [2, 64, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [8, 4], [16, 4], [32, 4], [64, 2], [192, 2]], 'representations': {'PC': {'code': '16679903266470323573040266711220953322760442179764000467049147910076701497912001905929615475842751539906223023435403560068726766211263', 'gens': [1, 8], 'pres': [9, -2, -2, -2, -2, -2, -2, -3, -2, -193, 18, 46, 74, 102, 130, 158, 3193351, 642832, 542617, 572002, 279115, 47140, 65077, 214, 1181960, 1446353, 1220858, 536579, 252764, 106001, 52550]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [201293672, 7189251, 1380299136]}, 'Perm': {'d': 195, 'gens': [139894816057469266527134691583056328931585515720972896885897577281684605832010741226784597360844130293899462493912358984502490078390261617684812368932833354519283692579744723338986184549282693118464901915303817352845970381194181112263420292603826488046060977856800410845628514774304103730299583767508450518600560122776532224814264219680941526673976585965413015, 13497361010984908776456863530964577017778314147923647507881442621445994787150913732934309838355322408380861442917377584339967736104611770946642331822375908242865503257958215743832646502994063510997637146703658456866946493807610847221269603320064578465007548330903540377828345762079960956355939695873675391746681148041281993136131754340827363315803931263987002360, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 192], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times F_{193}', 'transitive_degree': 386, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '18432.b', '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': [[1, 192], [876481, 1429440], [3069121, 3456960], [57985, 2080704], [2142913, 1063488], [888385, 1160256], [393793, 1965120]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 113836032, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 96.5, '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, 1, 1], [2, 193, 2], [3, 1, 2], [3, 193, 6], [4, 1, 2], [4, 193, 10], [6, 1, 2], [6, 193, 22], [8, 1, 4], [8, 193, 44], [12, 1, 4], [12, 193, 92], [16, 1, 8], [16, 193, 184], [24, 1, 8], [24, 193, 376], [32, 1, 16], [32, 193, 752], [48, 1, 16], [48, 193, 1520], [64, 193, 1024], [96, 1, 32], [96, 193, 6112], [192, 193, 8192], [193, 192, 1], [386, 192, 1], [579, 192, 2], [772, 192, 2], [1158, 192, 2], [1544, 192, 4], [2316, 192, 4], [3088, 192, 8], [4632, 192, 8], [6176, 192, 16], [9264, 192, 16], [18528, 192, 32]], 'center_label': '96.2', 'center_order': 96, 'central_product': None, 'central_quotient': '37056.a', 'commutator_count': None, 'commutator_label': '193.1', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 14, 'conjugacy_classes_known': False, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 1, 2, 1], [3, 193, 2, 3], [4, 1, 2, 1], [4, 193, 2, 5], [6, 1, 2, 1], [6, 193, 2, 11], [8, 1, 4, 1], [8, 193, 4, 11], [12, 1, 4, 1], [12, 193, 4, 23], [16, 1, 8, 1], [16, 193, 8, 23], [24, 1, 8, 1], [24, 193, 8, 47], [32, 1, 16, 1], [32, 193, 16, 47], [48, 1, 16, 1], [48, 193, 16, 95], [64, 193, 32, 32], [96, 1, 32, 1], [96, 193, 32, 191], [192, 193, 64, 128], [193, 192, 1, 1], [386, 192, 1, 1], [579, 192, 2, 1], [772, 192, 2, 1], [1158, 192, 2, 1], [1544, 192, 4, 1], [2316, 192, 4, 1], [3088, 192, 8, 1], [4632, 192, 8, 1], [6176, 192, 16, 1], [9264, 192, 16, 1], [18528, 192, 32, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 37056, 'exponents_of_order': [11, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': None, 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '222336.a', 'hash': 4558118773988019320, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [192, 193], 'inner_gens': [[1, 995520], [2562049, 192]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 37056, 'inner_split': None, 'inner_tex': 'F_{193}', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '3557376.a', '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': True, 'metacyclic': True, 'monomial': True, 'name': 'C18528.C192', 'ngens': 14, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 4, 0, 7, 0, 0, 12, 0, 15, 1, 0, 0, 28, 0, 31, 3, 0, 60, 0, 63, 7, 0, 124, 63, 15, 0, 252, 31, 31, 252, 15, 63, 124, 7, 63, 60, 3, 31, 28, 1, 15, 12, 7, 4, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 138, 'number_conjugacy_classes': 18528, 'number_divisions': 642, 'number_normal_subgroups': 1452, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 3557376, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 387], [3, 1160], [4, 1932], [6, 4248], [8, 8496], [12, 17760], [16, 35520], [24, 72576], [32, 145152], [48, 293376], [64, 197632], [96, 1179648], [192, 1581056], [193, 192], [386, 192], [579, 384], [772, 384], [1158, 384], [1544, 768], [2316, 768], [3088, 1536], [4632, 1536], [6176, 3072], [9264, 3072], [18528, 6144]], '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': 3072, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [32, 64, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '182054418431007814350628784113035127425923799998549626324737447559099474473500212095784854959685208198956508708925754548976768011429404512891574259881681671221516751393913168065686356563808892270973000037766487093761654031433869714286538508197012735365514548618076002727100258032622909305370828966937134972730735153736039736031801992112423270146020575514718706769132929262778706691501037447094141129207654048030198545299388335059695198597258946583347266060671', 'gens': [1, 8], 'pres': [14, -2, -2, -2, -2, -2, -2, -3, -2, -2, -2, -2, -2, -3, -193, 28, 71, 114, 157, 200, 243, 111498247, 1042965, 50582819, 6711985, 12903807, 1613549, 871339, 329, 250871048, 2346646, 1753956, 15101906, 1019152, 3630390, 1960400, 372, 59458569, 5214743, 3897637, 33559731, 2264705, 8067439, 4356333, 415, 130808842, 11472408, 8574758, 5351860, 4982274, 628400, 1023886, 458, 285401099, 25030681, 18708519, 11676725, 10870339, 1370961, 2233823, 501, 618369036, 54233114, 40535080, 25299510, 23552324, 2970322, 4839840, 726, 603316237, 175214619, 130959401, 81736759, 32514117, 9596243, 4741729]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 35945286, 999278948]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [96, 192], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 256, 'supersolvable': True, 'sylow_subgroups_known': False, 'tex_name': 'C_{18528}.C_{192}', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '48.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 4], 'aut_gens': [[1], [17], [7], [37]], 'aut_group': '16.10', 'aut_hash': 10, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 8, 'aut_perms': [120, 5040, 5049], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [16, 1, 8, 1], [24, 1, 8, 1], [48, 1, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 1, 2], [6, 1, 2], [8, 1, 4], [12, 1, 4], [16, 1, 8], [24, 1, 8], [48, 1, 16]], 'center_label': '48.2', 'center_order': 48, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [8, 1, 4, 1], [12, 1, 4, 1], [16, 1, 8, 1], [24, 1, 8, 1], [48, 1, 16, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 48, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 16]], 'familial': True, 'frattini_label': '8.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 2, 'irrep_stats': [[1, 48]], 'label': '48.2', 'linC_count': 16, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 2, 'linQ_dim': 10, 'linQ_dim_count': 2, 'linR_count': 8, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C48', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 48, 'number_divisions': 10, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [8, 4], [12, 4], [16, 8], [24, 8], [48, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[17], [7], [37]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [120, 5040, 5049], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [16, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 2], [16, 1]], 'representations': {'PC': {'code': 61763224033, 'gens': [1], 'pres': [5, -2, -2, -2, -2, -3, 10, 26, 42, 58]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [2204]}, 'Perm': {'d': 19, 'gens': [101282746544179200, 4, 47039662393456320, 19918769973905760, 6423384156578664]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [48], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{48}', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
