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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.26460', 'ambient_counter': 26460, 'ambient_order': 256, 'ambient_tex': 'C_2\\times Q_8\\times C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.26460.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.183', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.26460', 'aut_centralizer_order': 12288, 'aut_label': '64.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24576, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.c1', '32.d1'], 'contains': ['128.a1', '128.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7388, 7154, 7435, 7211], 'generators': [1015839, 557073], 'label': '256.26460.64.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.c1', '32.d1'], 'normal_contains': ['128.a1', '128.c1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '64.183', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.183', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '128.2136', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 12, 12, 4, 4, 4, 4], 'aut_gens': [[574447, 1015839, 754643, 295159], [245783, 1015839, 820045, 295159], [246295, 1015839, 295261, 574447], [229689, 492047, 229451, 835593], [311321, 491535, 229587, 819943], [508465, 1016351, 229963, 311833], [819943, 491535, 820181, 574447], [573935, 492047, 295365, 753961]], 'aut_group': None, 'aut_hash': 1681730677298827678, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 56, 'aut_perms': [303488974343477071632089385414683520519193966917133482692659122757410527694, 46981684916569234905295652960239739746669958994347858883964330768178718378, 609919866539837547248423028976045053291887590794987854428252400727396742722, 671697334189109041136478670600892173781804357678685369470880647548678353938, 212116743554012131156743495890279822612611382680180208620196745219185655065, 548271891609170266062935432104954470540783638071259048057914251054144751236, 193305192625617907490290387899859231747758522994968864407468903140463622297], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [4, 1, 2, 2], [4, 1, 4, 1], [4, 2, 12, 2], [8, 1, 4, 2], [8, 1, 8, 1], [8, 2, 24, 1], [16, 1, 32, 1], [16, 2, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.C_6.C_2.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 6168903709875402657, 'autcent_nilpotent': True, 'autcent_order': 8192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8.C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [4, 1, 8], [4, 2, 24], [8, 1, 16], [8, 2, 24], [16, 1, 32], [16, 2, 48]], 'center_label': '64.183', 'center_order': 64, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', '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', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 26460, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['2.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 1, 2, 4], [4, 2, 1, 12], [4, 2, 2, 6], [8, 1, 4, 4], [8, 2, 4, 6], [16, 1, 8, 4], [16, 2, 8, 6]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 26880, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '16.14', 'hash': 26460, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 1, 1, 2], 'inner_gens': [[574447, 1015839, 754643, 819943], [574447, 1015839, 754643, 295159], [574447, 1015839, 754643, 295159], [49663, 1015839, 754643, 295159]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [1, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 128], [2, 32]], 'label': '256.26460', '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': False, 'monomial': True, 'name': 'C2*Q8*C16', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 160, 'number_divisions': 50, 'number_normal_subgroups': 255, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 291, 'number_subgroups': 327, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 56], [8, 64], [16, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [4, 12, 12, 4, 4, 4, 4], 'outer_gen_pows': [32769, 32769, 32769, 32769, 32769, 32769, 32769], 'outer_gens': [[245783, 1015839, 820045, 295159], [246295, 1015839, 295261, 574447], [229689, 492047, 229451, 835593], [311321, 491535, 229587, 819943], [508465, 1016351, 229963, 311833], [819943, 491535, 820181, 574447], [573935, 492047, 295365, 753961]], 'outer_group': None, 'outer_hash': 8391963929860577020, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 256, 'outer_perms': [3443511276081426072318683951156216048702360980630742706319172440095780413227659006757814484591733188355866839862213239841266349594104726517935104699233494391109367272787528208305103534839547171261091406681491524284317360214057496903010928430728212815613862445454900086683110942524346410965465982185873349028260755958236926442343230449539672501350652316445232461611387057950497063459538433613261348396996217094830932136349738951647530892790588008153812809328062376370643307573052833067308176915239416989497, 6807554491844954367562666111241106366397493687890476930243490123440771269899206590279382431194491733521683310424849946761314532652373427568736564517710089042112979446258329354823846757804929076671788338815998677908607688398560747031496727847093872899647565005788847243486981717191527706403683706771651501787456448828251184754250659303505794516815087317185398596824207374773044631076698389727844130227123267358436716864297425973560613740294127167865768433627268040154164676116830795910421476119866013395343, 10171595046062580181556388826429684705454520596881218780254381372192854735675313286604556642898310854751058107519742185165988215457654418078953795667087820168927553156603782087221107527484326507402485056382433477694663006757474117378042101747468402898635358220436813417260549946591348807167561027111880502836915253599457755558429960334815910021523979922515284446175633746713299293399167610161816466529013632485986125107966706017924009787496298847767271439202931036592695196644941119514677101669021054722148, 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16899683932969828951664046043527920272905536330518325029271907378291199609186377376109951489549074970988461271820300489963456589559973826165405210879064115265363892972079542568935315390963724435108818775007479601358076544824299870432536508451182923549698809907490628066217076034339004052184745407290807818568121840532688326577201583663863561086392138370897444319350281422276786160141308318330187862528173310279333738921108698715475179825833450411357780182684479879569448966808732282207480023068507755088965, 20263727126814592576945784852428724432660345048890612155276718454046411504249285043441350295890951247153416394571695032309832305323917930428325661419207606117432331654571795143338188358803964098805010807297213735089450244954236882027622785119683416194120472330333399158865196291053848256903393920266481229425293514887389544592188490449898769054068553146792536103387127620568116288376148334905479605324178014224707504140137720535193304879198716509131067542302724768976684182569067378934042167995306957735335, 23627770363695137968448058815662543603277926859516520618955808323802220757694996228212085190352944437052042605767107526780076328107238032317193330265219490656842046809867273804460926191846307043082000961912960687810819992598862330086129528532916953465228117956526631810715251876079346333044127692624052878671549761910626309085067330293227425146950258246205461495620177553476604528730957986503604765422661601687602325075962581124787601483549600396881550115545895232040533653998883943270852663083549707627566], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4:C_3.C_2^4.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 16], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 10], [8, 10], [16, 2]], 'representations': {'PC': {'code': 37928829813726409396317, 'gens': [1, 2, 3, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1024, 66, 91, 116, 10758, 166]}, 'GLZN': {'d': 2, 'p': 42, 'gens': [2173837, 836411, 2936733, 2148581, 1906645, 1863823, 74971, 963157]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [32803, 491535, 1032787, 33041, 32905, 836105, 33281, 557073]}, 'Perm': {'d': 26, 'gens': [16858938128880799419206823, 32940072497586997509581284, 49144837215449145838406823, 49144837215450610216397284, 49144837215091956129792000, 49144837215096354106472734, 5800817303020, 2966658509284]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 16], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times Q_8\\times C_{16}', 'transitive_degree': 256, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '64.183', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 4, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [3, 2, 4], [1, 2, 28], [1, 2, 12], [2, 3, 5], [1, 34, 36], [33, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 36]], 'aut_group': '768.1090215', 'aut_hash': 1090215, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 768, 'aut_permdeg': 18, 'aut_perms': [85092497694055, 1, 819074715523560, 189743871462480, 2567105332778526, 1516205100373248, 361313303949726, 3677548499212488, 1200485585577960], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [4, 1, 2, 1], [4, 1, 6, 1], [8, 1, 4, 1], [8, 1, 12, 1], [16, 1, 32, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^3\\times C_4):S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '768.1090215', 'autcent_hash': 1090215, 'autcent_nilpotent': False, 'autcent_order': 768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '(C_2^3\\times C_4):S_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, 7], [4, 1, 8], [8, 1, 16], [16, 1, 32]], 'center_label': '64.183', 'center_order': 64, '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'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 183, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 1, 2, 4], [8, 1, 4, 4], [16, 1, 8, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 112, 'exponent': 16, 'exponents_of_order': [6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '8.5', 'hash': 183, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 64]], 'label': '64.183', 'linC_count': 14336, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 48, 'linQ_dim': 10, 'linQ_dim_count': 48, 'linR_count': 192, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C16', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 64, 'number_divisions': 20, 'number_normal_subgroups': 49, 'number_subgroup_autclasses': 19, 'number_subgroup_classes': 49, 'number_subgroups': 49, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 8], [8, 16], [16, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 4], [1, 2, 28], [1, 2, 12], [2, 3, 5], [1, 34, 36], [33, 2, 4], [1, 2, 5], [1, 2, 6], [1, 2, 36]], 'outer_group': '768.1090215', 'outer_hash': 1090215, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 18, 'outer_perms': [85092497694055, 1, 819074715523560, 189743871462480, 2567105332778526, 1516205100373248, 361313303949726, 3677548499212488, 1200485585577960], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '(C_2^3\\times C_4):S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 16], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 4], [8, 4]], 'representations': {'PC': {'code': 4433379356, 'gens': [1, 2, 3], 'pres': [6, -2, 2, 2, -2, -2, -2, 50, 69, 88]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [39958, 120406, 9269, 74096, 43861, 38503]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [14903, 28679, 36873, 37985, 4225, 39113]}, 'Perm': {'d': 20, 'gens': [20916435456000, 121645100408832000, 355687428096000, 9703614452976, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 16], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_{16}', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
