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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '118206.b', 'ambient_counter': 2, 'ambient_order': 118206, 'ambient_tex': 'C_3\\times F_{199}', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 597, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '118206.b.198.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '198.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '198.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 198, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{198}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '597.1', 'subgroup_hash': 1, 'subgroup_order': 597, 'subgroup_tex': 'C_{199}:C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '118206.b', 'aut_centralizer_order': None, 'aut_label': '198.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '39402.a1.a1', 'complements': ['597.b1.a1', '597.b1.c1', '597.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '66.a1.a1', '99.b1.b1'], 'contains': ['594.a1.a1', '39402.b1.b1'], 'core': '198.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [953, 4495, 9424, 3566, 4156, 4685, 8436, 3593], 'generators': [21120, 594], 'label': '118206.b.198.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '198.b1.b1', 'normal_contained_in': ['18.b1.b1', '66.a1.a1', '99.b1.b1'], 'normal_contains': ['594.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '198.b1.b1', 'projective_image': '118206.b', 'quotient_action_image': '198.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '198.b1.b1', 'subgroup_fusion': None, 'weyl_group': '39402.d'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 39402, 'aut_gen_orders': [198, 199], 'aut_gens': [[1, 3], [433, 45], [247, 3]], 'aut_group': '39402.d', 'aut_hash': 6821401462869295210, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 39402, 'aut_permdeg': 199, 'aut_perms': [14249569701562140475043836670393341229874253545226482709932418980719581028612303626936167801928260941907504592272019702420706807227873780493824538866681227645585821651812131825888627299148578552329229919440378638579346964469404353335689579409493538593212218075490466385696404949057230989105940039905799207842333994452046373781576643182025103848921701906735125240652848694, 1951735416027101176815493477317094715357638335984710587729059925808176804935283484908620406744954782698394606059603004540970918220319684736134550402710988281163376063171236312303802348128904835709822214398249858647786503151635872558054372960958236280836390632445889326852210150646455215640402721788591978611241524172325885614644589923336546465682336146417690740281260341811], 'aut_phi_ratio': 99.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 199, 1, 2], [199, 3, 66, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{199}', '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': 39402, 'autcentquo_group': '39402.d', 'autcentquo_hash': 6821401462869295210, 'autcentquo_nilpotent': False, 'autcentquo_order': 39402, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{199}', 'cc_stats': [[1, 1, 1], [3, 199, 2], [199, 3, 66]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '597.1', 'commutator_count': 1, 'commutator_label': '199.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '199.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 199, 2, 1], [199, 3, 66, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8, 'exponent': 597, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 11, 199], 'factors_of_order': [3, 199], 'faithful_reps': [[3, 0, 66]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '597.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 597, 'inner_gen_orders': [3, 199], 'inner_gens': [[1, 318], [283, 3]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 597, 'inner_split': False, 'inner_tex': 'C_{199}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 198, 'irrQ_dim': 198, 'irrR_degree': 6, 'irrep_stats': [[1, 3], [3, 66]], 'label': '597.1', 'linC_count': 66, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 198, 'linQ_degree_count': 1, 'linQ_dim': 198, 'linQ_dim_count': 1, 'linR_count': 33, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C199:C3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 69, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 202, 'old_label': None, 'order': 597, 'order_factorization_type': 11, 'order_stats': [[1, 1], [3, 398], [199, 198]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 66, 'outer_gen_orders': [66], 'outer_gen_pows': [583], 'outer_gens': [[31, 9]], 'outer_group': '66.4', 'outer_hash': 4, 'outer_nilpotent': True, 'outer_order': 66, 'outer_permdeg': 16, 'outer_perms': [1314416678400], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{66}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 199, 'pgroup': 0, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [198, 1]], 'representations': {'PC': {'code': 16544483, 'gens': [1, 2], 'pres': [2, -3, -199, 1273]}, 'GLFp': {'d': 2, 'p': 199, 'gens': [7880799, 725015214]}, 'Perm': {'d': 199, 'gens': [10514629720867041060297939725809411292731935422172545620015302544657345240892822204479635453933526988432537113852801376984245945600630229642349947492373211292722139946788245686735296692698539810029810043372007914953367388474040589992273219153226888354542571492871965438761238245325362215669576234036813851507171978415524530217870189944607211455083807108513577209189585333, 3923473812518304515159997898456599053629068431710057943024096019657868620420951303975383121466657174196660502600655489658065660112262365497544258083936189104534312707025405447562929743992377995805211796974128105321334120176653326154496226130570342533708130878550370718460420962739339803124262230403056367502515385565160092467200000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{199}:C_3', 'transitive_degree': 199, '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': '594.20', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 39402, 'aut_gen_orders': [198, 22, 198], 'aut_gens': [[1, 198], [25543, 13464], [33463, 24750], [52471, 54252]], 'aut_group': None, 'aut_hash': 2208373850004692075, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 236412, 'aut_permdeg': 597, 'aut_perms': [45905969717789313423542045323874484700830724530266657392202381513338847248582402287155053166923729934198186163426939951839811077441920428168300753294379162435438786576169123234632249955388656200333171148632774696983728413529023822914096037248544001985162167975389382504154269338338006585757689215588354783755833436069306996702726078160751933001888080753449829675068050491174494545824772050114354303545450242100792508348684736007390295073289199365023237993606933306950467921877816544710398940800650844770509854231238582947399261065826082411886757751891682458605071910929667756083380586451089900967357514869950968503959893783289805029690261574948879983433113093195840970093284544315714093080574522872579265803279986405533681271566553590495761688374136904622491567128760570531267593078790693570658984428291016332676669381351011712229473206635044228101719313216000458092969336452736722403161169457663886918294700242180724372700353748536968999972198432915943185104880223370636593212447493082145985617620749597170388035711329999371552801180857894130934639221097952271003805840009918180487891328931165559883248717672153919417127242915874796969226336149328618088500488797483211682581369174840764657818619064321905186729639072994234027740554556957943798014621211873128774529716541087790434950032113713113051504174835244714741248101133168127376897586141814585943693868829162038698479823988575692761153931727080, 13285205691541514669759029574092199538247856464911462142275536389477756093198124268616440918786383101492530951069494740440207253671901983192272454689727263093284178233929233578889144749212779067709157908522797013553475364266141574355089331745881542845879341037189302013374385674543795332709080396601513808416482306446375284470538997833040647835744790530884574684230829457143013755839933830800161782923197759382570347258694512357371668453981774804412611960018080372936697158454948099543616234759088591958955890534860614184510133637924949983550927105035600664116094706430884019399796434075500221165972820166740333877402237505472289323907902808670674815004335337767648473892301672540014770106795253863336534564033564977598089717150462535477056626138048096974701015607247529979099797523184209840388668673762071592591092845714900219723245370684961110881809476550568836396618492222816016086757679500731060352087256644288198795402152681480041961741280760615875912726184934244375942364314687199658072811173135757256424278101234221688509305893364949065448553435563744257645685517876268162649358688065392026025783756850587228435557666288757599969052348975052687737238255085131936352662147457342342702520158980088904391895600886406070566865407964175716911940417212387086497799345539548967446011723738097590981637038789369032157246530463536043462955450918790892093702811188434565074511745868277117278619166033330, 44860379721712607805887808320895791982405838697581922534221652228645456029232406765673999235662889349171825676714582625848771022717626255594934283104857908329119437599787068929577576340671836951374207189362807951041773135188981262681185386189925572264852637415771287306391054277173309456332530669791620373087556989251578322752532732535986211155922682024200200594187054752866372666726712057967968502958020234411245453565876002537600661470823097848426166026308555579668741572900866829851142806601937950725795550192681621128742241687709015512153837732020453178660056387146868751783058156342824882296510138687199993395569176931324710854567423027760671686115458436413417608015609725704713353696091291841152446100116957368753803556218919857430610476336459113885093259356856711760378489961279750633207864317984200897638800841092408559797856425317442487644184534833368418354551941644335398409282002046609493037022627223007044776904838996454386608934907994323874267711446171050113910172047227434755817015622866669959287940859038477663098497004917609697039192572934407278689766216685945093349595385194716072182592472470484331359464958933605889704227910654557588036250801436035334729945362264363476781765599126068011180018022267410345628492450276221874329233015958004150743133946072361005114592899213855555263975903362128869230942594263324691987751992427950560985324434319242510431798707378050376653447059860538], 'aut_phi_ratio': 6.633333333333334, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 199, 1, 1], [3, 1, 2, 1], [3, 199, 1, 2], [3, 199, 2, 2], [6, 199, 1, 2], [6, 199, 2, 3], [9, 199, 3, 6], [11, 199, 1, 10], [18, 199, 3, 6], [22, 199, 1, 10], [33, 199, 1, 20], [33, 199, 2, 30], [66, 199, 1, 20], [66, 199, 2, 30], [99, 199, 3, 60], [198, 199, 3, 60], [199, 198, 1, 1], [597, 198, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{199}:(C_{11}:(C_{18}\\times 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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 39402, 'autcentquo_group': '39402.d', 'autcentquo_hash': 6821401462869295210, 'autcentquo_nilpotent': False, 'autcentquo_order': 39402, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{199}', 'cc_stats': [[1, 1, 1], [2, 199, 1], [3, 1, 2], [3, 199, 6], [6, 199, 8], [9, 199, 18], [11, 199, 10], [18, 199, 18], [22, 199, 10], [33, 199, 80], [66, 199, 80], [99, 199, 180], [198, 199, 180], [199, 198, 1], [597, 198, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '39402.d', 'commutator_count': 1, 'commutator_label': '199.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '11.1', '199.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['39402.d', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 199, 1, 1], [3, 1, 2, 1], [3, 199, 2, 3], [6, 199, 2, 4], [9, 199, 6, 3], [11, 199, 10, 1], [18, 199, 6, 3], [22, 199, 10, 1], [33, 199, 20, 4], [66, 199, 20, 4], [99, 199, 60, 3], [198, 199, 60, 3], [199, 198, 1, 1], [597, 198, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 25920, 'exponent': 39402, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 11, 199], 'factors_of_order': [2, 3, 11, 199], 'faithful_reps': [[198, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '118206.b', 'hash': 993549773098811332, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 39402, 'inner_gen_orders': [198, 199], 'inner_gens': [[1, 86328], [32077, 198]], 'inner_hash': 6821401462869295210, 'inner_nilpotent': False, 'inner_order': 39402, 'inner_split': True, 'inner_tex': 'F_{199}', 'inner_used': [1, 2], 'irrC_degree': 198, 'irrQ_degree': 396, 'irrQ_dim': 396, 'irrR_degree': None, 'irrep_stats': [[1, 594], [198, 3]], 'label': '118206.b', '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*F199', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 266, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 597, 'number_divisions': 34, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 80, 'number_subgroups': 7604, 'old_label': None, 'order': 118206, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 199], [3, 1196], [6, 1592], [9, 3582], [11, 1990], [18, 3582], [22, 1990], [33, 15920], [66, 15920], [99, 35820], [198, 35820], [199, 198], [597, 396]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[78805, 118008], [39403, 198]], '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': 202, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 9, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [6, 6], [10, 2], [20, 8], [60, 6], [198, 1], [396, 1]], 'representations': {'PC': {'code': '238659246580686050565389015627360277025947720797371306756695821870781064794743', 'gens': [1, 5], 'pres': [6, -2, -3, -3, -11, -3, -199, 12, 43, 68, 2589844, 742510, 312856, 20152, 118, 812597, 545303, 417005, 72491]}, 'GLFp': {'d': 2, 'p': 199, 'gens': [7880799, 1008716714, 725015214]}, 'Perm': {'d': 202, 'gens': [1617107125760524307766100365424199373010971604634639225606828417689585168323053353330077072011087644895861673386127722921844440215533147109943204670751965379014642136739140539745050865979379043606840365902069089296329276807637706001055845521129334678412362574408342890869574767270015764787465041502313767900651858237629569988745092874895192355775818958102217826757319360452563, 2409728899142544665694002617428431763699342373216762171439217176948816013893203935440411500988577433714435727611511524343568068758731540559311672140615088929784766255489056102979438836153563905451468293439068281052874898659916019410835019087556304920392130840485924635808963716032116321772421457756199845089703003598915957423708435679300320777307445046041544288858899497114083, 161675261840272413713656168254934723851818547888749537980209141527158143994532142410874015243118211155969703800450240243502807430740906227550703011269515180637950537540327182201746637127738428301787436940258064877062536671335551525418763876116108829399777583208675654656903869536546942154959627862239344794391430764502618263004589118004893647062516949149047611325598654549344480]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 198], '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_{199}', 'transitive_degree': 597, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '198.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 30, 'aut_gen_orders': [2, 30], 'aut_gens': [[1], [89], [79]], 'aut_group': '60.13', 'aut_hash': 13, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 60, 'aut_permdeg': 12, 'aut_perms': [362880, 40285473], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [9, 1, 6, 1], [11, 1, 10, 1], [18, 1, 6, 1], [22, 1, 10, 1], [33, 1, 20, 1], [66, 1, 20, 1], [99, 1, 60, 1], [198, 1, 60, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{30}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 30, 'autcent_group': '60.13', 'autcent_hash': 13, 'autcent_nilpotent': True, 'autcent_order': 60, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{30}', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [6, 1, 2], [9, 1, 6], [11, 1, 10], [18, 1, 6], [22, 1, 10], [33, 1, 20], [66, 1, 20], [99, 1, 60], [198, 1, 60]], 'center_label': '198.4', 'center_order': 198, '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', '3.1', '3.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [9, 1, 6, 1], [11, 1, 10, 1], [18, 1, 6, 1], [22, 1, 10, 1], [33, 1, 20, 1], [66, 1, 20, 1], [99, 1, 60, 1], [198, 1, 60, 1]], 'element_repr_type': 'PC', 'elementary': 66, 'eulerian_function': 1, 'exponent': 198, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[1, 0, 60]], 'familial': True, 'frattini_label': '3.1', 'frattini_quotient': '66.4', 'hash': 4, 'hyperelementary': 66, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': 2, 'irrep_stats': [[1, 198]], 'label': '198.4', 'linC_count': 60, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 3, 'linQ_dim': 16, 'linQ_dim_count': 3, 'linR_count': 30, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C198', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 198, 'number_divisions': 12, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 12, 'number_subgroups': 12, 'old_label': None, 'order': 198, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2], [9, 6], [11, 10], [18, 6], [22, 10], [33, 20], [66, 20], [99, 60], [198, 60]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 30], 'outer_gen_pows': [0, 0], 'outer_gens': [[89], [79]], 'outer_group': '60.13', 'outer_hash': 13, 'outer_nilpotent': True, 'outer_order': 60, 'outer_permdeg': 12, 'outer_perms': [362880, 40285473], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{30}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 9, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 2], [10, 2], [20, 2], [60, 2]], 'representations': {'PC': {'code': 212044870119, 'gens': [1], 'pres': [4, -2, -3, -3, -11, 8, 29, 46]}, 'GLFp': {'d': 2, 'p': 89, 'gens': [17197939]}, 'Perm': {'d': 22, 'gens': [51090942171709440000, 1013709170073600000, 36288000, 243332058851481600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [198], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{198}', 'transitive_degree': 198, 'wreath_data': None, 'wreath_product': False}
