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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '62208.g', 'ambient_counter': 7, 'ambient_order': 62208, 'ambient_tex': 'C_6^4:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '62208.g.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.ew', 'subgroup_hash': 3895397110574237554, 'subgroup_order': 5184, 'subgroup_tex': 'D_6:D_6:S_3^2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '62208.g', 'aut_centralizer_order': None, 'aut_label': '12.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.S'], 'contains': ['24.CU', '24.CV', '24.CX', '24.DA', '24.DF', '24.DN', '24.DX', '24.FV', '24.FW', '24.FX', '24.FY', '36.DD', '36.DE'], 'core': '192.A', 'coset_action_label': None, 'count': 6, 'diagramx': [7027, -1, 882, -1], 'generators': [3629527, 26064, 160834880721741271, 891796177002952230, 500811828009398834, 1110215538432000, 513993179411807950, 81, 79940904, 102270], 'label': '62208.g.12.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.S', 'old_label': '12.bc1', 'projective_image': '31104.ji', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BC', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 12, 12, 12, 4, 4, 6], 'aut_gens': [[1, 2, 8, 96, 288, 864], [2593, 1818, 392, 480, 384, 912], [2673, 1822, 856, 672, 768, 912], [869, 2662, 2376, 672, 576, 2656], [81, 1518, 184, 480, 384, 864], [2597, 3806, 1992, 480, 384, 2608], [53, 1482, 1848, 672, 768, 2624], [2593, 934, 8, 96, 288, 4320], [33, 38, 40, 192, 576, 864]], 'aut_group': None, 'aut_hash': 3931606577831760306, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 165888, 'aut_permdeg': 96, 'aut_perms': [290471523601896381688682823165133768076503236014231632615275223645363397027555425363471916445333989722373611134377654714832914563604332734384106642501, 594977535961283838643368738771864008443118297215542520010743489654694063043617296080933258035635326550104687188918229722848626363224959998195386334392, 124179105221112103836444180603160128635724903378514603384084054143078033410474892658377858446333491093607482055881691949569140258833120746070456892909, 242993622718716558260565414126075156895277978156987752968876635166250138809784065810328142223062575675382119512541612409761255186392218818257087419021, 403448630469763855818214078843272937688969777809184652549097613816243390739954450211447259778425600253952136674779135872474880887761103056089005988856, 230421337201770814683683621635679958681433003140328142369729852073371822170362902311197657740197191158639326894736602925116967856843050649708249045919, 289656019361846704078563667807401074093174584023026764806485660444006964234707370831131811199257016374961734450573646343242441123231412671189532934354, 442389853661432043086036006708135172968597955142326227484253249365443417905229484696036470680999916636483135609182570777251048386342881288557771021286], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 2, 1], [2, 36, 2, 1], [2, 81, 2, 1], [2, 108, 2, 1], [2, 162, 1, 1], [3, 2, 2, 1], [3, 4, 1, 3], [3, 8, 2, 3], [3, 16, 1, 1], [4, 18, 1, 4], [4, 36, 2, 1], [6, 2, 2, 1], [6, 4, 1, 3], [6, 4, 2, 3], [6, 8, 1, 1], [6, 8, 2, 3], [6, 8, 4, 2], [6, 16, 1, 1], [6, 16, 2, 2], [6, 24, 2, 1], [6, 24, 4, 2], [6, 24, 8, 2], [6, 72, 2, 2], [6, 144, 2, 1], [6, 216, 2, 1], [8, 108, 4, 1], [12, 36, 2, 3], [12, 72, 1, 5], [12, 72, 2, 2], [12, 144, 2, 1], [24, 216, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_2^6.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '10368.si', 'autcentquo_hash': 82513012810261405, 'autcentquo_nilpotent': False, 'autcentquo_order': 10368, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^4:C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 12, 2], [2, 36, 2], [2, 81, 2], [2, 108, 2], [2, 162, 1], [3, 2, 2], [3, 4, 3], [3, 8, 6], [3, 16, 1], [4, 18, 4], [4, 36, 2], [6, 2, 2], [6, 4, 9], [6, 8, 15], [6, 16, 5], [6, 24, 26], [6, 72, 4], [6, 144, 2], [6, 216, 2], [8, 108, 4], [12, 36, 6], [12, 72, 9], [12, 144, 2], [24, 216, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2592.fh', 'commutator_count': 1, 'commutator_label': '324.156', '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', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 127, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 2], [2, 36, 1, 2], [2, 81, 1, 2], [2, 108, 1, 2], [2, 162, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 8, 1, 6], [3, 16, 1, 1], [4, 18, 1, 4], [4, 36, 1, 2], [6, 2, 1, 2], [6, 4, 1, 9], [6, 8, 1, 15], [6, 16, 1, 5], [6, 24, 1, 26], [6, 72, 1, 4], [6, 144, 1, 2], [6, 216, 1, 2], [8, 108, 1, 4], [12, 36, 1, 4], [12, 36, 2, 1], [12, 72, 1, 9], [12, 144, 1, 2], [24, 216, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1240162560, 'exponent': 24, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2592.fh', 'hash': 3895397110574237554, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 6, 3, 3, 6], 'inner_gens': [[1, 54, 88, 96, 288, 864], [5, 2, 3480, 480, 288, 2608], [17, 1810, 8, 192, 576, 864], [1, 770, 200, 96, 288, 864], [1, 2, 584, 96, 288, 864], [1, 3538, 8, 96, 288, 864]], 'inner_hash': 1293884799352898782, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': False, 'inner_tex': 'C_2\\times S_3^2:S_3^2', 'inner_used': [1, 2, 3, 4, 6], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 20], [4, 30], [8, 48], [16, 6]], 'label': '5184.ew', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'D6:D6:S3^2', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 59, 'number_characteristic_subgroups': 41, 'number_conjugacy_classes': 120, 'number_divisions': 119, 'number_normal_subgroups': 145, 'number_subgroup_autclasses': 1500, 'number_subgroup_classes': 3977, 'number_subgroups': 112996, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 639], [3, 80], [4, 144], [6, 1872], [8, 432], [12, 1152], [24, 864]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 76, 0, 0], 'outer_gens': [[2645, 2598, 3528, 672, 576, 2672], [1, 2, 40, 192, 576, 4368], [2597, 2598, 3528, 192, 576, 2672], [53, 2666, 3528, 672, 768, 2656], [1, 50, 56, 192, 576, 864], [1, 2, 40, 96, 288, 4320]], 'outer_group': '64.264', 'outer_hash': 264, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [1275487, 373681, 1961646, 848928, 374407, 374406], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^3', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 20], [4, 30], [8, 46], [16, 7]], 'representations': {'PC': {'code': '584725553526340931498870462519829556465424594440768876745680703745643112801433083027477520351607158813', 'gens': [1, 2, 4, 7, 8, 9], 'pres': [10, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 1081, 51, 1562, 382, 3523, 69613, 423, 113, 4004, 44414, 1024, 144, 3845, 103695, 985, 16816, 1716, 5797, 117378, 97228, 268, 1619, 86429]}, 'Perm': {'d': 20, 'gens': [22237170278403, 385252637894623709, 249692574523493064, 121646421019957681, 249735727785942960]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6:D_6:S_3^2', 'transitive_degree': 24, '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 12, 12, 6, 12, 12, 6, 6], 'aut_gens': [[121666029505671646, 13934578108996513, 262500111643921201], [33143094115241242, 372488434646988083, 499744940165156910], [122734399464342725, 640282005901652856, 257898231186346905], [249713677940482542, 161526640542338253, 160794342856224801], [616471702915877473, 859008770439418816, 122042639647480424], [859049308381174042, 494053766919372083, 499744940165151864], [859049308344841938, 866143441827608284, 390904580940799110], [6423383754053058, 871519378296311736, 629296065402707665], [397662642071163965, 20276798793796536, 262500111680104231]], 'aut_group': '5000.cq', 'aut_hash': 2826640325681291568, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 497664, 'aut_permdeg': 188, 'aut_perms': [125457654667431215199442350209766634012035861755043617441784073305846305740736825358483955170873884413080248113457454278086191112372722642826691386027278280990812115878978055515852349830948292529955645739504922862404330343642926669653687259787386553605248813281134275746819956746942414603082385670057480802100660562948530336692061352166965668655726, 212552910029629157675382003059406384074700670301635827595232533572034109718477953284933657024294347647819229758529519647320750050864621229969148495925173254743890491809765563636072685288301441311048503956543738138399884641188397494029860336088865921208602408474879309743725810798630036006877667486708371225790966489210435347829589491653547869698988, 136237702078886906579707415194019317011262835793397808912275165674156902048759697426475488887773774397449957791350925180817802153929078971909332076274572000576934224696400477252123319771466094162668333926902353815176836903186392391453532038357916061935440566523619212253788864634244884584011774720463627064699235434798119819893533897819405866833044, 54218418158401064414105764522437830251616521291306553409677912774764111800958248138625807387108117800792736035209568934243386335734632504854194704947773315674192813326577727573429728460460665507789663335777616424312447910435049799164774789098956911707194857630248583522349514695700769179491704714318950942965884590621614084729874724381134672007959, 97324022449686234549120415299413868515657997276172325445747053952097857977923454016357150688986542591334872088038666654640242855381912991949246601974153684749275420641648429833463384308839517997240919631811265014997959021853011668776084065991091598108164188841902501611192044620848006676168947959106822052359432007855165115422621437856391533987194, 197312862605177913635987077821239483467636869714547870182403153487035906825746665176881004016080104461382434363301275392784635960479159599773211317848241838518753436914149735065379885808056092494063927595982477079615520655325307662790411045380317588731232854784223784946546309830130395660522382666921090974442502895027073635372213516573345129482685, 229295407848853240741087326275503152506995701426805037819204451390927345999752622155298697856241863203853269053628774443691207812507291180113527865544868192936152394353852729285704245002864192668973778289049541121224971826667357910343283417759305912519561060712262226407018492549499774522270304766861089795827475564036619914120831884632649347790199, 41596300800353385584735034043549846123948431853185473780762347662710269172921818120724065048480771912278329654229062739337983207633003721271191409209841169640988041828243581736735317388882225317287825566027053917471984619502869119496815320020341209115837708823056538236734047263022010330708621751295805684390211193883452125041043996754718286932086], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 2, 1], [2, 6, 1, 1], [2, 36, 2, 1], [2, 72, 1, 1], [2, 81, 2, 1], [2, 108, 1, 2], [2, 324, 2, 2], [2, 486, 1, 1], [2, 648, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 12, 1, 2], [3, 24, 1, 1], [3, 288, 1, 1], [3, 576, 1, 1], [4, 36, 2, 1], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 2], [4, 324, 2, 1], [4, 648, 1, 1], [4, 1296, 1, 2], [6, 2, 1, 1], [6, 6, 1, 1], [6, 8, 1, 1], [6, 8, 2, 3], [6, 8, 4, 1], [6, 12, 1, 6], [6, 12, 2, 1], [6, 24, 1, 6], [6, 24, 2, 6], [6, 24, 4, 3], [6, 48, 1, 2], [6, 48, 2, 2], [6, 72, 2, 3], [6, 72, 4, 1], [6, 144, 1, 3], [6, 144, 2, 5], [6, 144, 4, 2], [6, 216, 1, 2], [6, 288, 1, 1], [6, 288, 2, 1], [6, 432, 1, 3], [6, 576, 1, 1], [6, 576, 2, 1], [6, 648, 2, 1], [6, 1296, 1, 1], [6, 2592, 2, 2], [8, 1296, 1, 2], [9, 576, 1, 1], [9, 576, 2, 1], [12, 72, 2, 3], [12, 72, 4, 1], [12, 144, 1, 3], [12, 144, 2, 5], [12, 144, 4, 2], [12, 216, 1, 2], [12, 432, 1, 7], [12, 432, 2, 1], [12, 648, 2, 1], [12, 864, 1, 1], [12, 1296, 1, 1], [12, 2592, 1, 2], [18, 576, 1, 1], [18, 576, 2, 2], [18, 576, 4, 1], [24, 2592, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_5^4:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 219204698074101422, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_2^2\\times C_3^3:C_2^2).D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [2, 6, 1], [2, 36, 2], [2, 72, 1], [2, 81, 2], [2, 108, 2], [2, 324, 4], [2, 486, 1], [2, 648, 1], [3, 2, 1], [3, 6, 1], [3, 8, 3], [3, 12, 2], [3, 24, 1], [3, 288, 1], [3, 576, 1], [4, 36, 2], [4, 72, 1], [4, 108, 2], [4, 216, 2], [4, 324, 2], [4, 648, 1], [4, 1296, 2], [6, 2, 1], [6, 6, 1], [6, 8, 11], [6, 12, 8], [6, 24, 30], [6, 48, 6], [6, 72, 10], [6, 144, 21], [6, 216, 2], [6, 288, 3], [6, 432, 3], [6, 576, 3], [6, 648, 2], [6, 1296, 1], [6, 2592, 4], [8, 1296, 2], [9, 576, 3], [12, 72, 10], [12, 144, 21], [12, 216, 2], [12, 432, 9], [12, 648, 2], [12, 864, 1], [12, 1296, 1], [12, 2592, 2], [18, 576, 9], [24, 2592, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '31104.ji', 'commutator_count': 1, 'commutator_label': '7776.bj', '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', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 6, 1, 1], [2, 36, 1, 2], [2, 72, 1, 1], [2, 81, 1, 2], [2, 108, 1, 2], [2, 324, 1, 4], [2, 486, 1, 1], [2, 648, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 8, 1, 3], [3, 12, 1, 2], [3, 24, 1, 1], [3, 288, 1, 1], [3, 576, 1, 1], [4, 36, 1, 2], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 2], [4, 324, 1, 2], [4, 648, 1, 1], [4, 1296, 1, 2], [6, 2, 1, 1], [6, 6, 1, 1], [6, 8, 1, 11], [6, 12, 1, 8], [6, 24, 1, 30], [6, 48, 1, 6], [6, 72, 1, 10], [6, 144, 1, 21], [6, 216, 1, 2], [6, 288, 1, 3], [6, 432, 1, 3], [6, 576, 1, 3], [6, 648, 1, 2], [6, 1296, 1, 1], [6, 2592, 1, 4], [8, 1296, 1, 2], [9, 576, 1, 3], [12, 72, 1, 10], [12, 144, 1, 21], [12, 216, 1, 2], [12, 432, 1, 9], [12, 648, 1, 2], [12, 864, 1, 1], [12, 1296, 1, 1], [12, 2592, 1, 2], [18, 576, 1, 9], [24, 2592, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [8, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 4], [24, 1, 24], [48, 1, 2]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '7776.bl', 'hash': 3172442348882996740, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 12, 12], 'inner_gens': [[121666029505671646, 494053766919330418, 378179607849266310], [397662642071159013, 13934578108996513, 635638286131053339], [33143094078894041, 871519378332776616, 262500111643921201]], 'inner_hash': 1063518838656689817, 'inner_nilpotent': False, 'inner_order': 31104, 'inner_split': None, 'inner_tex': 'C_6^3:(S_3\\times S_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [6, 20], [8, 32], [12, 42], [16, 14], [24, 62], [48, 6]], 'label': '62208.g', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C6^4:(C2*S4)', 'ngens': 3, '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, 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': 131, 'number_characteristic_subgroups': 48, 'number_conjugacy_classes': 210, 'number_divisions': 210, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 13900, 'number_subgroup_classes': 30079, 'number_subgroups': 4039948, 'old_label': None, 'order': 62208, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 2967], [3, 944], [4, 4680], [6, 22224], [8, 2592], [9, 1728], [12, 16704], [18, 5184], [24, 5184]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [160834880801574871, 1110215538558000, 500811828009314551, 43647870], 'outer_gens': [[33143094115241242, 372488434646988083, 499744940165156910], [122734399464342725, 640282005901652856, 257898231186346905], [249713677940482542, 161526640542338253, 160794342856224801], [6423383754053058, 871519378296311736, 629296065402707665]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1328432193090, 2966618070835, 4483583802622, 8597469399120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [6, 20], [8, 32], [12, 42], [16, 14], [24, 62], [48, 6]], 'representations': {'PC': {'code': '310762935437346640212582807787892583022909974696645679282695997550644207276071186930972174629706119871785108113881692509488634446863275002997977309459940432580821313032830249384344336135925812065180791041724262221771786331929463898513875677301174221186010236953917055846540565', 'gens': [1, 2, 4, 6, 7, 10, 12], 'pres': [13, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 364416, 1251381, 66, 191258, 43683, 49312, 691889, 146, 1784644, 1555337, 744540, 2591, 36522, 101119, 39824, 789522, 2645389, 1088483, 215715, 102160, 7897, 266, 2703175, 1576244, 675825, 49966, 306, 4852232, 2830485, 1213090, 11279, 6336729, 2737822, 1584215, 496128, 7887, 386, 3541834, 1565015, 885492, 329521, 6952, 4942091, 2515992, 2156581, 147002, 61865, 466, 194700, 48697, 2044262, 48762]}, 'Perm': {'d': 20, 'gens': [121666029505671646, 13934578108996513, 262500111643921201]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^4:(C_2\\times S_4)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
