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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.12236', 'ambient_counter': 12236, 'ambient_order': 1728, 'ambient_tex': '(C_4\\times \\He_3).\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.12236.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2254', 'subgroup_hash': 2254, 'subgroup_order': 864, 'subgroup_tex': 'C_{12}.F_9', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.12236', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.30150', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '18.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1342, 4838, 9110, 5574, 1795, 4688, 8495, 5430], 'generators': [2, 864, 688, 432, 8, 576, 1200, 4], 'label': '1728.12236.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '864.2195', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.520'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 12, 6, 12, 8], 'aut_gens': [[1, 8, 24, 72], [705, 16, 336, 72], [491, 608, 56, 504], [561, 296, 600, 504], [563, 304, 312, 360], [33, 56, 608, 360]], 'aut_group': None, 'aut_hash': 8011066568325907130, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 216, 'aut_perms': [3154773982508018882559147612054471998055102719592369668443680860947431437782785250511444142564879757831582712675914587329080245044753913652526367961527356875248272613953370926378396609829558077199891030424761221778582453163463878352929907730257139968582699648177799724465045234567301105040196671963894210571036564443180616828746185465780323857229563874753462951566348522457353343174336177299920381220524039362517, 6996566183089623573859273335516653336045671490720781832892989861239110346468983671735475230970093860064772782173051037505054899421571332006717700629441666055820652278540139152357806064435181594627793424645815920600581385876817706853868619903051960855579207227070119548466758624493583824395780747168513620868546831138758860209113243145404887461649395003802954513209524407254827331462297739535571202830587323170797, 4415358896263396153408187373880261912866223141309909530567456467298536251030549462802546953500266448848469762039656191330087381223917702219618505211528044022610699645803374911846714709966314307498390634621438647470991043755196898306811892781850285489582806382845705484669454381372631819006673741021861263932432509165911826628440233708541914087086358819297055993345143603554017884473755717832863902989935588782964, 4690613033232939962442415686885279525353371583868319586054553419945464232415636564895829272414166008781797997711292226550866281392782062475440067999068901408511338431960969136073360584507193567533236937128962404296633573692815784746092798849644007309497012300998695479583394879497089045881614199525637175042515701500645767717183262261978216679007839046670575014605792496213274606337261580266956218254974024299894, 4947057510773884639893542922673509225711987927978143499036211470139242604208986054528844041538605440349901604118411727136044664727407587124759965531067648668916974204714956444394501101786051021594782791474072935530713756228358047947978026492971114242369866637037306513013503062566348710023007100500914642195584309335863566384742918717194597735985285869794664389319518602906045578747622271114793216283695702408635], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 2, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 1, 2, 1], [4, 9, 2, 1], [6, 2, 1, 1], [6, 18, 2, 1], [6, 24, 1, 1], [8, 9, 4, 2], [12, 2, 2, 1], [12, 18, 2, 1], [12, 24, 2, 1], [16, 27, 8, 2], [24, 18, 4, 2]], 'aut_supersolvable': False, 'aut_tex': '\\He_3.(C_2\\times C_8:C_4).C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.520', 'autcentquo_hash': 520, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_3:\\SD_{16}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [3, 2, 1], [3, 24, 1], [4, 1, 2], [4, 9, 2], [6, 2, 1], [6, 18, 2], [6, 24, 1], [8, 9, 8], [12, 2, 2], [12, 18, 2], [12, 24, 2], [16, 27, 16], [24, 18, 8]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '216.86', 'commutator_count': 1, 'commutator_label': '27.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2254, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [3, 2, 1, 1], [3, 24, 1, 1], [4, 1, 2, 1], [4, 9, 2, 1], [6, 2, 1, 1], [6, 18, 1, 2], [6, 24, 1, 1], [8, 9, 4, 2], [12, 2, 2, 1], [12, 18, 2, 1], [12, 24, 2, 1], [16, 27, 8, 2], [24, 18, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 48, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 8]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '144.185', 'hash': 2254, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 3, 3, 3], 'inner_gens': [[1, 56, 32, 360], [25, 8, 312, 72], [305, 584, 24, 72], [577, 8, 24, 72]], 'inner_hash': 86, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': '\\He_3:C_8', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 48, 'irrR_degree': 12, 'irrep_stats': [[1, 32], [6, 16], [8, 4]], 'label': '864.2254', 'linC_count': 8, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 8, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C12.F9', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 52, 'number_divisions': 21, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 58, 'number_subgroups': 440, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 19], [3, 26], [4, 20], [6, 62], [8, 72], [12, 88], [16, 432], [24, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[649, 8, 24, 504], [649, 8, 24, 72], [219, 336, 592, 792]], 'outer_group': '16.13', 'outer_hash': 13, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [288, 21677, 27882], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 43, 'pgroup': 0, 'primary_abelian_invariants': [2, 16], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 2], [6, 4], [8, 4], [12, 2], [16, 1], [24, 2]], 'representations': {'PC': {'code': 1152109787603975832748622367541601137728660617746605849, 'gens': [1, 4, 5, 6], 'pres': [8, -2, -2, -2, -3, 3, -2, -2, -3, 16, 41, 2610, 1795, 9611, 2451, 1284, 11852, 500, 1588, 17285, 141, 40326, 166, 36871]}, 'Perm': {'d': 43, 'gens': [106315485001137316447675617041897396606339681140291, 3079510239250, 140384546595434250452522099129484907741308407665975, 174651029647902135611867992361101557008818031952535, 7265098885373, 1580554599125993585478570798177363263665698250752000, 3019929497670561600269187408673152774608156725248000, 4459228794837017176944008116507424009906872958976000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 16], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.F_9', 'transitive_degree': 144, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [12, 12, 4, 8, 8], 'aut_gens': [[1, 2, 16, 48, 144], [929, 754, 1168, 1200, 144], [1709, 1462, 624, 1184, 1008], [309, 774, 640, 688, 1008], [37, 370, 96, 80, 720], [1453, 402, 704, 1184, 720]], 'aut_group': None, 'aut_hash': 4225599256170198327, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 288, 'aut_perms': [464963900091594935424607327797031744954452481248853142622202000053441138308792094786404792404911412919063423775939004775809659373534934377617923102658315100717484160777248443840302361436163716924869216453270988507184790752824410588285591531754107476146061129444928566990020627370783586980514839390872922253844057643988294273821719192287698980209229766217250742860190523087713302408302154807798897408413261885341540381703218181050387411990936563661721349081677135245329194019107356287180407328162094905641602626273100417426489039602143709987060110168708909986772112171039008539582885546, 573993276770214604261822194688094286110681732218301215992051200943522804325643464307889069876739250362396452934874140664691836429262405899342365868302406521051133662981422572623495091951865339790131116795902766960917445765454919952578483596722703609062833094535895966683905808209854283998092159390290271483120128503192055281955730278040417919293023230229222975386596363743760900618485139097819855023051704916561442250121913529147480217369447505075936775776386669064724358549289574772825657369462372211232697045378218098756503333159216667730133145180213523802876093474244858012730522718, 39133669117259013966190787678069334823643997507720090879732609265554021390848245378885682536962369613096292148392081414737100893325663932144534627266908128580661630021392109953502172684400923592341246004273815680211390243230206904099382611534891687449021972532524310640462353327331268302482194265820646654664556576554415300651167848438226298634242883045117637000423306849930023741881529557921895740997131406109707198894077635888294346213095430048374264169672692866364846935941148193062334743018743859281479598474776742968031362505808598769512045263302108392735930242353796201983491948, 290968664042432357125821585286422859909014453868817329362396418681798054483764480099564755554135243671470529745765679653923490145705845693639875333614794245707300585400474468999544358235781470996027243851624768209677118619940722584193268700940163951264338269942912638062142055875599212532467653705425200623410054044205157111640885346997777126139297877598413523525535971933603481150655970218736178699678123637934125947328026986544063451949813236865209047063957429537699894853324723463587232283512732422220974004087710081044060943876253529509862677179270485041820888108938354164610056334, 378659006706924660826336355583996499069565419426370678570784840774927119123257333004288428152963615451433650238216805869837205430260566941437665078436077634860995537132321625993794287008802440710393141640716121806532070957255976756794103312872238129897616286181268912383406599040275300843257337341833471640867088364362241073673985660308611301583435459172755099937285775042825779492208277898548137586018820240803930882487310203769381510245589302976871428918024574898485198937330269112693400613742306349917464556622820149600208929646987523253700994947382094369693619055218182852190508357], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [2, 72, 2, 1], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 1, 2], [6, 24, 1, 1], [6, 144, 2, 1], [8, 18, 2, 2], [12, 4, 1, 1], [12, 36, 1, 1], [12, 48, 1, 1], [12, 72, 2, 2], [16, 54, 4, 2], [24, 36, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:S_3.C_2^4.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '1728.46113', 'autcentquo_hash': 46113, 'autcentquo_nilpotent': False, 'autcentquo_order': 1728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SU(3,2):C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [2, 72, 2], [3, 2, 1], [3, 24, 1], [4, 2, 1], [4, 18, 1], [4, 72, 2], [6, 2, 1], [6, 18, 2], [6, 24, 1], [6, 144, 2], [8, 18, 4], [12, 4, 1], [12, 36, 1], [12, 48, 1], [12, 72, 4], [16, 54, 8], [24, 36, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '864.2195', 'commutator_count': 1, 'commutator_label': '216.25', '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'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 12236, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [2, 72, 1, 2], [3, 2, 1, 1], [3, 24, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [4, 72, 2, 1], [6, 2, 1, 1], [6, 18, 1, 2], [6, 24, 1, 1], [6, 144, 1, 2], [8, 18, 2, 2], [12, 4, 1, 1], [12, 36, 1, 1], [12, 48, 1, 1], [12, 72, 4, 1], [16, 54, 8, 1], [24, 36, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 48, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 4]], 'familial': False, 'frattini_label': '12.2', 'frattini_quotient': '144.182', 'hash': 12236, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 8, 3, 3, 6], 'inner_gens': [[1, 1302, 80, 624, 1584], [1309, 2, 128, 1184, 720], [705, 1234, 16, 624, 144], [1153, 642, 1168, 48, 144], [289, 1154, 16, 48, 144]], 'inner_hash': 2195, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': '(C_2\\times \\He_3).\\SD_{16}', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 48, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 14], [6, 8], [8, 4], [12, 6], [16, 1]], 'label': '1728.12236', 'linC_count': 64, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': '(C4*He3).SD16', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 41, 'number_divisions': 26, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 125, 'number_subgroup_classes': 153, 'number_subgroups': 3513, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 163], [3, 26], [4, 164], [6, 350], [8, 72], [12, 376], [16, 432], [24, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [432, 0], 'outer_gens': [[433, 2, 16, 48, 144], [1, 434, 16, 48, 144]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 43, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 2], [6, 2], [8, 6], [12, 5], [16, 1], [24, 2]], 'representations': {'PC': {'code': 1527782808690746636509188454173786280571102744841675489645123823725605161967561503382553, 'gens': [1, 2, 5, 6, 7], 'pres': [9, -2, -2, -2, -2, -3, 3, -2, -2, -3, 23437, 46, 23654, 74, 31395, 3918, 3604, 2893, 922, 211, 33701, 31982, 16439, 8456, 2147, 99798, 22695, 186, 103687, 51856, 214, 93320, 46673]}, 'Perm': {'d': 43, 'gens': [103051769102521726361107864058747403149389484297274, 140586915037552063253734078109681513361997375312780, 174652063397549908043361945803818962866068440137126, 4497682605676, 208918857227046410725795775456009378596421386413676, 5901332335801, 1546306431198056630058652294838848897230869262336000, 3053381643260330370887589682026615822877776261120000, 4492680797991609120023789961411117769433838833664000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_4\\times \\He_3).\\SD_{16}', 'transitive_degree': 144, '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': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
