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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': None, 'characteristic': False, 'core_order': 648, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '62208.g.12.BR', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1', '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.cn', 'subgroup_hash': 5428266237022475929, 'subgroup_order': 5184, 'subgroup_tex': 'C_3\\times C_6^3.D_4', '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.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.D', '6.S', '6.T'], 'contains': ['24.CX', '24.DY', '24.ET', '24.FC', '24.FK', '36.EU', '36.EV'], 'core': '96.A', 'coset_action_label': None, 'count': 3, 'diagramx': [6183, -1, 2194, -1], 'generators': [712682530576024, 33479166347853338, 26064, 512549681269737606, 160834880721741271, 891796177002952230, 1110215538432000, 81, 79940904, 102270], 'label': '62208.g.12.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '12.br1', 'projective_image': '31104.ji', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BR', 'subgroup_fusion': None, 'weyl_group': '3456.ct'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', '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, 2, 12, 6, 4, 6, 2], 'aut_gens': [[1, 6, 36, 216, 864], [2201, 1014, 1836, 5094, 504], [1879, 1302, 2772, 4104, 864], [1469, 1830, 3204, 2808, 4320], [1763, 3030, 3996, 2142, 504], [1753, 3126, 1404, 2502, 576], [4501, 438, 4860, 5166, 504], [101, 4758, 36, 2376, 864], [4853, 1902, 180, 216, 4320]], 'aut_group': None, 'aut_hash': 2854184908137106426, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 27648, 'aut_permdeg': 98, 'aut_perms': [1948162423213822250601638823198841343514350508126157698409279441635100953522850357485284078088720020466729205888060751736081588159909226735002295330558936, 3844794302363394692754750739303987394511400118711458508038728679282671065654155723633496081626163962211407539345369327654771965229168406978597362616612167, 7396952566542420878685173254274795624225451456543838912027432653517271546477625097398458115338651567141603419533385735927112044975999749417142753944947351, 7191245809112170250041120847744240733852438164006944411167467707418636897100562205146489953276235740628651552641255530640405458488936550150388813506487405, 6669100240514760869396397796037835997691336299561471625609135477138402967970673449921244737946419678673450546349431979687583849401939165334793140246791350, 4389089258875882127487344588430647191283226414395782146547485901037824244889524384612942435081813634090672185912855952037830578909999209610995567186486920, 1048218123087830458218102025187116320701428347515596585796780212839974291426754092915494269438970732990098969399444210128118319247801920684622731357837778, 8474945748344659812898440345835942691338171795126305166365793355607393262989141824898898937847589622773604122270737630573847548728622130131180463494317149], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 1], [2, 36, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 3], [3, 4, 4, 1], [3, 8, 1, 1], [3, 8, 2, 1], [4, 12, 2, 1], [4, 18, 2, 1], [4, 36, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 4, 1, 4], [6, 4, 2, 9], [6, 4, 4, 4], [6, 8, 1, 4], [6, 8, 2, 8], [6, 8, 4, 5], [6, 8, 8, 1], [6, 24, 2, 3], [6, 24, 4, 3], [6, 24, 8, 1], [6, 36, 2, 1], [6, 36, 4, 1], [6, 72, 1, 1], [6, 72, 2, 2], [6, 72, 4, 1], [8, 216, 2, 1], [12, 12, 4, 2], [12, 12, 8, 1], [12, 18, 4, 1], [12, 24, 2, 1], [12, 24, 4, 2], [12, 24, 8, 1], [12, 36, 2, 1], [12, 36, 4, 2], [12, 72, 2, 1], [12, 72, 4, 1], [24, 216, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_2^6.C_2^4', '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': '1728.46671', 'autcentquo_hash': 46671, 'autcentquo_nilpotent': False, 'autcentquo_order': 1728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 24, 1], [2, 36, 3], [3, 1, 2], [3, 2, 3], [3, 4, 12], [3, 8, 3], [4, 12, 2], [4, 18, 2], [4, 36, 2], [6, 1, 2], [6, 2, 11], [6, 4, 38], [6, 8, 48], [6, 24, 26], [6, 36, 6], [6, 72, 9], [8, 216, 2], [12, 12, 16], [12, 18, 4], [12, 24, 18], [12, 36, 10], [12, 72, 6], [24, 216, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '864.4297', 'commutator_count': 1, 'commutator_label': '216.143', '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': 66, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['1728.33409', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 3], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 5], [3, 8, 1, 1], [3, 8, 2, 1], [4, 12, 1, 2], [4, 18, 1, 2], [4, 36, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 4, 1, 4], [6, 4, 2, 17], [6, 8, 1, 6], [6, 8, 2, 21], [6, 24, 2, 13], [6, 36, 2, 3], [6, 72, 1, 3], [6, 72, 2, 3], [8, 216, 1, 2], [12, 12, 2, 8], [12, 18, 2, 2], [12, 24, 1, 2], [12, 24, 2, 8], [12, 36, 1, 2], [12, 36, 2, 4], [12, 72, 1, 2], [12, 72, 2, 2], [24, 216, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1397760, 'exponent': 24, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 16], [8, 0, 12]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '1296.3570', 'hash': 5428266237022475929, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 6, 4, 6], 'inner_gens': [[1, 102, 4860, 5022, 504], [157, 6, 3204, 4104, 4320], [1441, 3102, 36, 648, 864], [3511, 2166, 468, 216, 4320], [1441, 1734, 36, 1944, 864]], 'inner_hash': 4297, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': '(S_3\\times D_6):D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 42], [4, 120], [8, 48]], 'label': '5184.cn', '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': True, 'name': 'C3*C6^3.D4', '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': 90, 'number_characteristic_subgroups': 62, 'number_conjugacy_classes': 234, 'number_divisions': 137, 'number_normal_subgroups': 94, 'number_subgroup_autclasses': 1471, 'number_subgroup_classes': 2309, 'number_subgroups': 23140, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 139], [3, 80], [4, 132], [6, 2048], [8, 432], [12, 1488], [24, 864]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1369, 1734, 180, 216, 4320], [1, 3054, 3060, 216, 864], [3529, 1734, 180, 3240, 4320], [1877, 30, 36, 216, 864], [4069, 4326, 180, 216, 4320]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 32], [8, 58], [16, 21]], 'representations': {'PC': {'code': '97435491889092661121535024863479483405649683051206037309238951071927107466260862836278957826479838545', 'gens': [1, 3, 5, 7, 9], 'pres': [10, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 20, 3062, 53022, 82, 963, 243004, 26724, 144, 207365, 1465, 351546, 128536, 47906, 1306, 206, 207367, 45368, 64828, 1868, 268, 14409, 57629, 1669]}, 'Perm': {'d': 20, 'gens': [269654229986294403, 263250542853542400, 134806842923599467]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_6^3.D_4', '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, 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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}
