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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '111168.a', 'ambient_counter': 1, 'ambient_order': 111168, 'ambient_tex': 'C_3\\times F_{193}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 772, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '111168.a.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.30', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_{48}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '772.3', 'subgroup_hash': 3, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '111168.a', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '37056.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '72.a1.a1'], 'contains': ['288.a1.a1', '27792.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6442, 6503, 3594, 6536, 3632, 5680, 3421, 5369], 'generators': [48, 96, 576], 'label': '111168.a.144.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '48.b1.b1', '48.b1.c1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '111168.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '37056.a'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '4.1', '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, 4], [1, 152], [185, 4]], 'aut_group': '37056.a', 'aut_hash': 1432757702296672986, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 37056, 'aut_permdeg': 193, 'aut_perms': [61272615719092122982610759792821958511909420795915030513327860904014465224443192649858023561829774754724575809596473792993940652311140839199146488236748639901622727640038524534730385019296380851718009358861441590372291416486519026776577141721449963662140054630663223675078771382857152940789137320257093558707121259248681892514079655620055879690603186704865213, 67178041534197292754573192769075534499306560894306136346399659541289400771691323016075450188540940299285605655787420661850582830276745604837421215569555304537197493102123870592638680035936324156002700108062815653617883918810554489259986952039038637108435642740370315486728873544842651577588594479538393484894340859485078004918166755209647833450510758410840804], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [4, 193, 1, 2], [193, 4, 48, 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], [4, 193, 2], [193, 4, 48]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '772.3', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '193.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [4, 193, 2, 1], [193, 4, 48, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 772, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 193], 'faithful_reps': [[4, 1, 48]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '772.3', 'hash': 3, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 772, 'inner_gen_orders': [4, 193], 'inner_gens': [[1, 324], [453, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 772, 'inner_split': False, 'inner_tex': 'C_{193}:C_4', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [4, 48]], 'label': '772.3', 'linC_count': 48, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 48, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C193:C4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 52, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 390, 'old_label': None, 'order': 772, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 193], [4, 386], [193, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 48, 'outer_gen_orders': [48], 'outer_gen_pows': [3], 'outer_gens': [[1, 188]], 'outer_group': '48.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 19, 'outer_perms': [6780385526348307], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{48}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 193, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [192, 1]], 'representations': {'PC': {'code': 25796330568548543, 'gens': [1, 3], 'pres': [3, -2, -2, -193, 6, 2918, 3461]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1380299025]}, 'Perm': {'d': 193, 'gens': [205530080005009162641077000181173998501330573549047245928711810937437620041108049358630124279587601117259582474840406954063226566763978664766934694398300263047418002079469019967946929403052739356557842984556730718109007040998025472112703922643327049083031947536668765661973440413892556127813149520779681262570563738592931330822217591774976181127273350008373, 354996793146960497053355363383973425965094809743694491885455534984190204750249968830591340591162785093141951525209177997501478084577063512837513105442388103085116949108248219929177667335850225156399124325817472036634653562449665740610033707601842063277098323069015230061026956365247457276593902258859903874498559999999999999999999999999999999999999999999999, 68159384284216415434244229769722897785298203470789342442007462716964519312047994015473537393503254737883254692840162175520283792238796194464802516244938515792342454228783658226402112128483243230028631870556954631033853483990335822197126471859553676149202878029250924171717175622127511797106029233701101543903723520000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{193}:C_4', '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': '576.182', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [64, 192, 96], 'aut_gens': [[1, 192], [97153, 39552], [105793, 64320], [47809, 18816]], 'aut_group': None, 'aut_hash': 9034218873832238734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 222336, 'aut_permdeg': 579, 'aut_perms': [415332439196822892389352437816130401390738383370221364844878850607550778333990999776184605568421278475280244453511953039962181494122189821781883263316959201531902154435173394089394881934386442975626803816682013366274710639327603048148709203263335850956934513705677432612445360081946015157071655246361766139655035408612165506562077446916418628964643217990337766352996222601170027446653298548723903021005585090748174612486989215916127204701984643312424419565310829136987071596031819888738883484494631912286631467416080596207115760718910261030352200258429464228694285393933605670082097777061678748728778910376089906175830219538826740427819069543445641473111518135030865041383761505802995633042264157695385149095812910305730873962133804210048811778408408912044895041794289016373876993393003850343067915221826771638027998018289443816891858117689277909315562197355454440756908444550351612076844757970360026059982795028072217662618178674174347631582979577052959925128972855693498719179982748932220795907650991275021926868086525363090353655986424650695238183662501765618102081991333595375807675522468968658278057534484857352976226502006309087252976077697563757811289195230490163803952647899670731559865265643180967467213966712908123993183585039763847724928805148033274967628307145129222343322411324931038858051345174327003752114021781110525226462752885580313, 479014167272169279755996534749016869201360125409707869346777139173855325732973306407581827360637861416796628583967537605174750440755172951647611148360420886066818966625224493036121140593991361702574439173487931495542811324288522316193184742900760726240752065536218699257748196284431579881855064224518805697295732303159061258681671081176040188032548833476269580387262908306563250660702611019277068476953424205735136714001191742818540650758360743051137638423493431011048231585738140104365197692678118733943399624276121231952910352335809352534900979894500301522060798687180784338268714734310069283898407485255332153678510128023079965874650141745439653517794871949674493658599361325135322238631828400809628963234626171640799212597628544539653848153537551703888160925703847542959186641445837725502276602925122671623118778042891665514630761156855503193641295628483318460990688232589593362604657098181334407559208546438440116238131525874637673754413479433224759030646838233940605423973996483539483765545005350674521063200626975803892704173618464958000037145440102744057197009069087597840592403845425088701173293366696779715011794067656736491752480204104369899761052146486746011901145681350543544281549199692102699926114539513794074642925875249292216791419433139874592421827462737631936905234500848852439091584890275128310285682039693192033515132543417787127, 277760953236342837117292557174462821114287163390486698520044107397102630341828911334724634063986710842920444830955313299925385350983244268886021022315981237795549780737884741923651084913239180727343406296955777942433557918598624112300413804496960863368252179927543364492282896784532251429949042415925461844126162445734642961450965380443036076222027786381896161962090515095762416255165795351898158842639957857049238957473589440156894832176991940550709600986239377877538544743956803923387193193865066176949238129341122274150540946851597339194782674124160123517928207485441918334711385663320613461637191579989079478741038608798295078518503987684983548650849968716598703795924874995717040585144950493270494927740533175639582291434685719726656706800993299794242981898778028252854083548476628038358490539279012898734102971616777329387637325227448025943318834668524333064387760248758936069676844022436243570342772220747138128162070159407304816491385443347970526774849970968076693118499504812073473738620026244292676174046524243626716974721534065429730115396995305226243592090361756712031130218463359952789100999205852776151465902423211012566157221428957791334117857340426667880379703257574413329883898048665482750203385023283066989113542296839356503238609620710525212771820102003142672456708042283414397442459359716168084828115094291803017438146292553014690], 'aut_phi_ratio': 6.03125, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 3, 2], [4, 193, 1, 2], [6, 193, 2, 1], [6, 193, 3, 2], [8, 193, 1, 4], [12, 193, 2, 2], [12, 193, 3, 4], [16, 193, 1, 8], [24, 193, 2, 4], [24, 193, 3, 8], [32, 193, 1, 16], [48, 193, 2, 8], [48, 193, 3, 16], [64, 193, 1, 32], [96, 193, 2, 16], [96, 193, 3, 32], [192, 193, 2, 32], [192, 193, 3, 64], [193, 192, 1, 1], [579, 192, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{579}.C_{96}.C_2^2', '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': 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], [3, 1, 2], [3, 193, 6], [4, 193, 2], [6, 193, 8], [8, 193, 4], [12, 193, 16], [16, 193, 8], [24, 193, 32], [32, 193, 16], [48, 193, 64], [64, 193, 32], [96, 193, 128], [192, 193, 256], [193, 192, 1], [579, 192, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '37056.a', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['37056.a', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 193, 1, 1], [3, 1, 2, 1], [3, 193, 2, 3], [4, 193, 2, 1], [6, 193, 2, 4], [8, 193, 4, 1], [12, 193, 4, 4], [16, 193, 8, 1], [24, 193, 8, 4], [32, 193, 16, 1], [48, 193, 16, 4], [64, 193, 32, 1], [96, 193, 32, 4], [192, 193, 64, 4], [193, 192, 1, 1], [579, 192, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24576, 'exponent': 37056, 'exponents_of_order': [6, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[192, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '111168.a', 'hash': 2544430592072231885, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 37056, 'inner_gen_orders': [192, 193], 'inner_gens': [[1, 28416], [82945, 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': 384, 'irrQ_dim': 384, 'irrR_degree': None, 'irrep_stats': [[1, 576], [192, 3]], 'label': '111168.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': 'C3*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, 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': 258, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 579, 'number_divisions': 37, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 84, 'number_subgroups': 7764, 'old_label': None, 'order': 111168, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 193], [3, 1160], [4, 386], [6, 1544], [8, 772], [12, 3088], [16, 1544], [24, 6176], [32, 3088], [48, 12352], [64, 6176], [96, 24704], [192, 49408], [193, 192], [579, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[37057, 110976], [74113, 192]], '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': 196, 'pgroup': 0, 'primary_abelian_invariants': [64, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 5], [8, 5], [16, 5], [32, 5], [64, 4], [192, 1], [384, 1]], 'representations': {'PC': {'code': '43023836931081284013122713998333971413484062145605317493274726077956947008935476624168211114647392625691859060173537147616629038650528127', 'gens': [1, 8], 'pres': [9, -2, -2, -2, -2, -2, -2, -3, -3, -193, 18, 46, 74, 102, 130, 158, 2045959, 3324688, 1175065, 654946, 42379, 36772, 59893, 286, 6905096, 2216177, 1714634, 1084787, 142928, 123983, 61298]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [201293672, 7189251, 776418240]}, 'Perm': {'d': 196, 'gens': [26998242104082005447251696691331464774121971917348421755781267835361429941668435221333290080630207260549917888723056059763539993175776658074908879762949012617169070415501257720842862810632964336955359428101490488135920181880491972015344559396903845870899558118113549760267322033639158277229321994017930485074559887727912882386576752937183479668551985879937835304, 2631778338730623662950964945824670653980764756662906445448946890283312750222914027144913759101874195455749646321665281014480436912763364625294578572203894275170402936839769371092982389742011367078542571256093075126368574007362860032302134699363967331838336966533207438392507094484694472919274785125127394266993739467967407942441269210233369459195139463953392461104, 53651049977427163004782649094143068173087154853604693633795859769783469643879806996027569149175074794409538134264301490310872601961150471788286697107340058590630568151646039445332768032894779979465847323816958134956968491642077503940495849602428272197081574774182305031506649821005649262198902553255728399362769286478552688840974860927203438716481864507921529723]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 192], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times F_{193}', 'transitive_degree': 579, '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': '144.30', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 2, 12, 4, 4], 'aut_gens': [[1, 3], [2, 141], [2, 3], [97, 111], [98, 5], [97, 53]], 'aut_group': '384.17899', 'aut_hash': 17899, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 14, 'aut_perms': [1, 40723614, 128177527, 33265209600, 40451045040], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 8, 1], [4, 1, 2, 1], [6, 1, 8, 1], [8, 1, 4, 1], [12, 1, 16, 1], [16, 1, 8, 1], [24, 1, 32, 1], [48, 1, 64, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_4\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '384.17899', 'autcent_hash': 17899, 'autcent_nilpotent': False, 'autcent_order': 384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times C_4\\times \\GL(2,3)', '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, 1], [3, 1, 8], [4, 1, 2], [6, 1, 8], [8, 1, 4], [12, 1, 16], [16, 1, 8], [24, 1, 32], [48, 1, 64]], 'center_label': '144.30', 'center_order': 144, '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', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 30, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [4, 1, 2, 1], [6, 1, 2, 4], [8, 1, 4, 1], [12, 1, 4, 4], [16, 1, 8, 1], [24, 1, 8, 4], [48, 1, 16, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 24, 'exponent': 48, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '18.5', 'hash': 30, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 144]], 'label': '144.30', 'linC_count': 4608, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 24, 'linQ_dim': 12, 'linQ_dim_count': 24, 'linR_count': 1152, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C48', 'ngens': 6, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 144, 'number_divisions': 25, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 30, 'number_subgroups': 30, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 2], [6, 8], [8, 4], [12, 16], [16, 8], [24, 32], [48, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 12, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[2, 141], [2, 3], [97, 111], [98, 5], [97, 53]], 'outer_group': '384.17899', 'outer_hash': 17899, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 14, 'outer_perms': [1, 40723614, 128177527, 33265209600, 40451045040], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times C_4\\times \\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [16, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 5], [8, 5], [16, 4]], 'representations': {'PC': {'code': 204619489740705, 'gens': [1, 2], 'pres': [6, -3, -2, -2, -2, -2, -3, 31, 50, 69, 88]}, 'GLFp': {'d': 2, 'p': 97, 'gens': [10039467, 55673088]}, 'Perm': {'d': 22, 'gens': [801964354420054425600, 240, 4, 372746197194121497600, 158139739458985898880, 51212944273488041520]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 48], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{48}', 'transitive_degree': 144, 'wreath_data': None, 'wreath_product': False}
