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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '74112.g', 'ambient_counter': 7, 'ambient_order': 74112, 'ambient_tex': 'D_{193}:C_{192}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 386, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '74112.g.192.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '192.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{192}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '386.1', 'subgroup_hash': 1, 'subgroup_order': 386, 'subgroup_tex': 'D_{193}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '74112.g', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6176.a1.a1', 'complements': ['386.b1.a1', '386.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.b1', '96.a1.a1'], 'contains': ['384.a1.a1', '37056.b1.b1'], 'core': '192.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9371, 7030, 8776, 1726, 1110, 1365, 1627, 883], 'generators': [12272, 384], 'label': '74112.g.192.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '192.b1.b1', 'normal_contained_in': ['64.b1.b1', '96.a1.a1'], 'normal_contains': ['384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.b1', 'projective_image': '74112.g', 'quotient_action_image': '32.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '192.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6176.247'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [192, 193], 'aut_gens': [[1, 2], [1, 76], [89, 2]], 'aut_group': '37056.a', 'aut_hash': 1432757702296672986, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 37056, 'aut_permdeg': 193, 'aut_perms': [39053339670721327572543569039395005031096653245802774324204298263788953285647090763476541643345676324473056783378543774660072842471514711015868302482279618194714261105949788702112347134548908091797187306612050281053946057960581089182560863568602379974419627409015496038525465690691519350455551181816446171767151758025418672254963521648341121096265656543605694, 26050449041681162492548710440995937563664756826005913227073023112753247056788313513984546803542232538805426739439663986532672315593722655010746107170273261490771004561083259209978481997137743019238691910286438957865896173872775082918816828123307684233145679874600070754892101626552617092219781602671854206488611070839026500642814134865081246962631311266645171], 'aut_phi_ratio': 193.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [193, 2, 96, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{193}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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, 193, 1], [193, 2, 96]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '386.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '193.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [193, 2, 96, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 386, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 193], 'faithful_reps': [[2, 1, 96]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '386.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 386, 'inner_gen_orders': [2, 193], 'inner_gens': [[1, 384], [5, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 386, 'inner_split': False, 'inner_tex': 'D_{193}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 96]], 'label': '386.1', 'linC_count': 96, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 96, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D193', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 98, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 196, 'old_label': None, 'order': 386, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 193], [193, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 96, 'outer_gen_orders': [96], 'outer_gen_pows': [1], 'outer_gens': [[1, 90]], 'outer_group': '96.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 35, 'outer_perms': [304187744744822368938255957323620940307], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{96}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 193, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [192, 1]], 'representations': {'PC': {'code': 28238015, 'gens': [1, 2], 'pres': [2, -2, -193, 1537]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1380298945]}, 'Perm': {'d': 193, 'gens': [354996793146960497053355363383973425965094809743694491885455534984190204750249968830591340591162785093141951525209177997501478084577063512837513105442388103085116949108248219929177667335850225156399124325817472036634653562449665740610033707601842063277098323069015230061026956365247457276593902258859903874498559999999999999999999999999999999999999999999999, 68159384284216415434244229769722897785298203470789342442007462716964519312047994015473537393503254737883254692840162175520283792238796194464802516244938515792342454228783658226402112128483243230028631870556954631033853483990335822197126471859553676149202878029250924171717175622127511797106029233701101543903723520000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{193}', 'transitive_degree': 193, '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': '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': [16, 192, 192, 192, 48], 'aut_gens': [[1, 32], [42049, 20576], [49089, 35872], [42529, 2336], [20769, 35872], [14721, 38944]], 'aut_group': None, 'aut_hash': 2047870114700848400, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 592896, 'aut_permdeg': 774, 'aut_perms': 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'aut_phi_ratio': 24.125, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 2, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 193, 1, 2], [6, 1, 2, 1], [6, 193, 4, 1], [8, 193, 1, 4], [8, 193, 2, 2], [12, 1, 4, 1], [12, 193, 2, 2], [16, 193, 1, 8], [16, 193, 2, 4], [24, 193, 2, 4], [24, 193, 4, 2], [32, 193, 2, 16], [48, 193, 2, 8], [48, 193, 4, 4], [64, 193, 4, 16], [96, 193, 4, 16], [192, 193, 8, 16], [193, 32, 6, 1], [386, 32, 6, 1], [579, 32, 12, 1], [772, 32, 12, 1], [1158, 32, 12, 1], [2316, 32, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{386}.C_{96}.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', '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, 1, 2], [4, 1, 2], [4, 193, 2], [6, 1, 2], [6, 193, 4], [8, 193, 8], [12, 1, 4], [12, 193, 4], [16, 193, 16], [24, 193, 16], [32, 193, 32], [48, 193, 32], [64, 193, 64], [96, 193, 64], [192, 193, 128], [193, 32, 6], [386, 32, 6], [579, 32, 12], [772, 32, 12], [1158, 32, 12], [2316, 32, 24]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '6176.247', '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': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['24704.21814', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 1, 2, 1], [4, 1, 2, 1], [4, 193, 2, 1], [6, 1, 2, 1], [6, 193, 2, 2], [8, 193, 4, 2], [12, 1, 4, 1], [12, 193, 4, 1], [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, 32, 6, 1], [386, 32, 6, 1], [579, 32, 12, 1], [772, 32, 12, 1], [1158, 32, 12, 1], [2316, 32, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3072, 'exponent': 37056, 'exponents_of_order': [7, 1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[32, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '37056.r', 'hash': 6586773659675919904, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6176, 'inner_gen_orders': [32, 193], 'inner_gens': [[1, 6944], [67201, 32]], 'inner_hash': 247, 'inner_nilpotent': False, 'inner_order': 6176, 'inner_split': False, 'inner_tex': 'C_{193}:C_{32}', 'inner_used': [1, 2], 'irrC_degree': 32, 'irrQ_degree': 768, 'irrQ_dim': 768, 'irrR_degree': 64, 'irrep_stats': [[1, 384], [32, 72]], 'label': '74112.g', 'linC_count': 24, 'linC_degree': 32, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 226, 'linQ_degree_count': 16, 'linQ_dim': 226, 'linQ_dim_count': 16, 'linR_count': 768, 'linR_degree': 34, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D193:C192', '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': 118, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 456, 'number_divisions': 34, 'number_normal_subgroups': 46, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 80, 'number_subgroups': 6608, 'old_label': None, 'order': 74112, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 387], [3, 2], [4, 388], [6, 774], [8, 1544], [12, 776], [16, 3088], [24, 3088], [32, 6176], [48, 6176], [64, 12352], [96, 12352], [192, 24704], [193, 192], [386, 192], [579, 384], [772, 384], [1158, 384], [2316, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [0, 5, 5, 61782], 'outer_gens': [[24705, 37024], [61761, 39328], [6177, 59488], [6177, 25888]], 'outer_group': '96.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 11, 'outer_perms': [2424, 1680, 40320, 11612164], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}:C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 260, '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], [384, 3], [768, 1]], 'representations': {'PC': {'code': '365644094072947909894236552328535569515916202899457241062082746986993595775394582645118793487688647782911948228437052420822502342088632839277002784515931219220230046079', 'gens': [1, 6], 'pres': [9, -2, -2, -2, -2, -2, -2, -2, -3, -193, 18, 46, 74, 102, 34780, 374981, 664430, 337415, 184280, 41621, 158, 874950, 1550319, 787272, 429945, 97062, 186, 1999879, 875536, 465433, 315682, 221803, 286, 746504, 2954897, 70010, 314963, 373292]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1006468143, 64701556]}, 'Perm': {'d': 260, 'gens': [14845286375451794187549058706076011061126241263109602856314650407918283614350873888563207346615447013224354468990533812343270799015556647556189472144596813951556254664023927520818327727351953438375301288335022290489917858127270383666487806715296278532196442714167850865697835507750861081546040136052497789221246936886977956170130476552198803949466557440955029103119148999612000438314038752876079836319387868488516107098642505531293953376520930832220886389634906046730532750160216955962511059048202240000000000000000, 171524956777218344906295377373569570087762386517359592377726532303122536359252947798762469585345530270727824782053991494377159740892842370800708584401864734221148838924691593740403350700529159934418962183375175926430399312725081359694887973335308378657343007109070469543549887994001184691548858666013402981619287319075578068153196885362769857052594489248541435356544734700482274900542242000598204753807342804465139998295374178068052073126228696315436395830808893071262570145815968027479768889298448501253103768984, 228845238607050044888128047258240248409125599860769090121938918889539905911282805399878329908925433669152220524336995064314921468459188395879757330213406897829109162510371139686656746650791571253432241827938468608171773105113021859635674899199361525223294373014247950197247462545131599170970182271502121935874903528237517425069168928138970188994969636015725089892961942515383472789524462034831576671833410592076455309102026290127876012099021400198569829282259681841557537120957197727194754019520431717333108348163]}}, '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': 'D_{193}:C_{192}', 'transitive_degree': 37056, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '192.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 16, 'aut_gen_orders': [2, 2, 16], 'aut_gens': [[1], [65], [127], [133]], 'aut_group': '64.183', 'aut_hash': 183, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 64, 'aut_permdeg': 20, 'aut_perms': [355687428096000, 121652215820507520, 121648016789608890], '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], [32, 1, 16, 1], [48, 1, 16, 1], [64, 1, 32, 1], [96, 1, 32, 1], [192, 1, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_{16}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '64.183', 'autcent_hash': 183, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{16}', '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], [32, 1, 16], [48, 1, 16], [64, 1, 32], [96, 1, 32], [192, 1, 64]], 'center_label': '192.2', 'center_order': 192, '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', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.1', 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], [32, 1, 16, 1], [48, 1, 16, 1], [64, 1, 32, 1], [96, 1, 32, 1], [192, 1, 64, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 192, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 64]], 'familial': True, 'frattini_label': '32.1', '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': 64, 'irrQ_dim': 64, 'irrR_degree': 2, 'irrep_stats': [[1, 192]], 'label': '192.2', 'linC_count': 64, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 34, 'linQ_degree_count': 2, 'linQ_dim': 34, 'linQ_dim_count': 2, 'linR_count': 32, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C192', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 192, 'number_divisions': 14, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 14, 'number_subgroups': 14, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [8, 4], [12, 4], [16, 8], [24, 8], [32, 16], [48, 16], [64, 32], [96, 32], [192, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 16, 'outer_gen_orders': [2, 2, 16], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[65], [127], [133]], 'outer_group': '64.183', 'outer_hash': 183, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 20, 'outer_perms': [355687428096000, 121652215820507520, 121648016789608890], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{16}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 67, 'pgroup': 0, 'primary_abelian_invariants': [64, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 2], [16, 2], [32, 2], [64, 1]], 'representations': {'PC': {'code': 4553336054269763133313, 'gens': [1], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 14, 36, 58, 80, 102, 124]}, 'GLFp': {'d': 2, 'p': 31, 'gens': [119074]}, 'Perm': {'d': 67, 'gens': [34812819462234954428607685341897082192301945708552738688865836491528209085355972467097600000000, 4, 17125731743961598921943674325579392227242124480672411041416803851981460023914660624295657472000, 8282187884824921168611668818381987555972846584752266182758164987540677113354309924032688179200, 3860415955256618126428729875983775624818504154288173718968029842331521501914651066812729456320, 1649530213841581475001430175259373643701598531447003215154104016101461640635225996085127825760, 544471857487925546941072384503952816534977960565454352280865841524404515036981945541028258664]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [192], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{192}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
