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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '200000000.dic', 'ambient_counter': 2239, 'ambient_order': 200000000, 'ambient_tex': 'C_5^8.C_4.C_4^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 390625, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 5, 'label': '200000000.dic.512.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '512.A', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '512.46623', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 512, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8^2:(C_2\\times C_4)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 390625, 'subgroup_tex': 'C_5^8', 'supersolvable': True, 'sylow': 5}
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gps_subgroup_data • Show schema
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{'ambient': '200000000.dic', 'aut_centralizer_order': None, 'aut_label': '512.a1', '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': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [93925681920, 35367047974958807818174464000064, 41869337511869071988640626592713391822231160416, 64, 348713164896, 608358513305777857350276378805912344993, 911748377415199097084042000040816844890, 20935041053440555707365996483631823159838507616], 'label': '200000000.dic.512.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[479908804524335552678681853619890572897438728370, 523376275566089973203773670003847480364349652576, 815364726432135254962900988820260040422125564290], [335469696594274642649474825090463225033906900503, 648477310385339896896652207396776594600576775596, 773536308794571602465929258872387527193325564200], [419251572084603960725409715640208911243934318733, 584584057538725488268965160616818583257081480395, 1596968255237236559915529939210096901062035760], [439126803837420627051207426855117758541989569984, 523376276442833708185323545787746132412725318433, 1596968255237209119963920237378209483040006490], [459510550762147640226865097606785581617240891626, 564695434312693822395947608526649975625902113366, 733277331584508626753595397319261181692366255455], [481463735770932016596718130411793374305141171223, 524422693966071599572884680874301864312270204093, 754707494565773962442568998804784852710125564290], [480954476879972223037053914122095822272603262810, 543802057728570716481465606873557146420962559223, 775105749222072279250564565618404086993172937039], [480445591207229700943529842651156842099508474906, 524973243499773085582978513876408817769414343046, 733773198107345481528339861860648450994925564290], [501338968399711266513925441037768012938851578196, 604967804463452438648110714193305528913360315616, 754707494565773962442568998804784852523833858690], [461079990295537920582418553457334851506265542413, 565245613346344249816214273881179922665728682816, 733773198107345481528339861860648450902478255490], [500843100713581178251800009940002175076697400909, 565245612469600505676725028001486508401779967296, 733773198715703993603270885003686029914205569160], [479908804255152723579746248504222863237422267629, 586138990234654833991798429084639096782880696896, 733773197803955635700927137918553644544750380744], [479908804828506568177434897307416096481550150450, 544311316011172033920437742946880183657502993210, 815364726432135254962900988820260040422124929250], [500843101286935058249606533514641653276974267533, 544311316280354880103606224308175072066962138880, 794471349239653663182593331815420230578925564296], [479908804828506577335377396570863449724656827533, 544311316011172033920437742946880183563657946880, 794471349239653663182593331815420230578925564296], [479908804524335552678681853620018955136191496429, 523376275566089973203773670003847480432846881370, 733773198107345481528339861860648450994925564264], [479908803950965236161509473463064043140296097363, 523376275835272819386942798738239764348052186913, 773536309098742636279760718163581385257709564200], [440144949277085526263543936038306291979283172333, 523376276747021178519327444584226078195446834464, 773536309098742627122624801822873823687405171113], [500843100982764024434968491301194583941423326029, 586138990234654798624750454125702854617928549696, 794471349239653663182593331815420230647422793090], [585629731075309764813308814826712970663772185690, 501338968096321428298637186814010914081658468364, 754707494565773962442568998805168994852253308290], [459510550762147622859118324189021592957182350770, 564695434312693813565074484237487997091638874976, 815364726432135254962900988820260040329678255490], [461079990599708919029201393737048114923609926509, 544311316887915750586906721333606006595852561120, 773536308794571602465926697223657919172884301976]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 3200000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1250, 1, 1], [2, 2500, 1, 1], [2, 10000, 1, 3], [2, 20000, 1, 1], [2, 390625, 1, 1], [4, 2500, 1, 1], [4, 125000, 1, 1], [4, 250000, 4, 1], [4, 500000, 1, 1], [4, 781250, 2, 1], [4, 1562500, 1, 2], [4, 6250000, 1, 1], [5, 16, 4, 1], [5, 32, 1, 1], [5, 32, 2, 1], [5, 32, 4, 3], [5, 64, 1, 1], [5, 64, 2, 1], [5, 64, 4, 3], [5, 128, 2, 2], [5, 128, 4, 1], [5, 256, 2, 2], [5, 256, 4, 21], [5, 256, 8, 11], [5, 512, 2, 3], [5, 512, 4, 30], [5, 512, 8, 44], [5, 512, 16, 12], [8, 5000, 1, 1], [8, 250000, 1, 1], [8, 3125000, 1, 1], [8, 3125000, 2, 3], [8, 6250000, 1, 1], [8, 6250000, 4, 1], [10, 10000, 4, 1], [10, 20000, 1, 1], [10, 20000, 2, 1], [10, 20000, 4, 4], [10, 40000, 1, 2], [10, 40000, 2, 1], [10, 40000, 4, 8], [10, 80000, 2, 6], [10, 80000, 4, 8], [10, 160000, 2, 2], [10, 160000, 4, 21], [10, 160000, 8, 11], [16, 12500000, 4, 1], [20, 20000, 2, 1], [20, 20000, 4, 1], [20, 40000, 2, 2], [20, 40000, 4, 4], [20, 40000, 8, 2], [20, 500000, 4, 1], [20, 1000000, 1, 1], [20, 1000000, 4, 1], [20, 1000000, 16, 1], [20, 2000000, 4, 2], [40, 40000, 2, 1], [40, 40000, 4, 3], [40, 40000, 8, 4], [40, 40000, 16, 2], [40, 1000000, 2, 1], [40, 1000000, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1250, 1], [2, 2500, 1], [2, 10000, 3], [2, 20000, 1], [2, 390625, 1], [4, 2500, 1], [4, 125000, 1], [4, 250000, 4], [4, 500000, 1], [4, 781250, 2], [4, 1562500, 2], [4, 6250000, 1], [5, 16, 4], [5, 32, 15], [5, 64, 15], [5, 128, 8], [5, 256, 176], [5, 512, 670], [8, 5000, 1], [8, 250000, 1], [8, 3125000, 7], [8, 6250000, 5], [10, 10000, 4], [10, 20000, 19], [10, 40000, 36], [10, 80000, 44], [10, 160000, 176], [16, 12500000, 4], [20, 20000, 6], [20, 40000, 36], [20, 500000, 4], [20, 1000000, 21], [20, 2000000, 8], [40, 40000, 78], [40, 1000000, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '200000000.dic', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 17, 'conjugacy_classes_known': False, 'counter': 2239, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1250, 1, 1], [2, 2500, 1, 1], [2, 10000, 1, 3], [2, 20000, 1, 1], [2, 390625, 1, 1], [4, 2500, 1, 1], [4, 125000, 1, 1], [4, 250000, 2, 2], [4, 500000, 1, 1], [4, 781250, 1, 2], [4, 1562500, 1, 2], [4, 6250000, 1, 1], [5, 16, 2, 2], [5, 32, 1, 3], [5, 32, 2, 6], [5, 64, 1, 3], [5, 64, 2, 6], [5, 128, 1, 4], [5, 128, 2, 2], [5, 256, 1, 4], [5, 256, 2, 86], [5, 512, 1, 22], [5, 512, 2, 324], [8, 5000, 1, 1], [8, 250000, 1, 1], [8, 3125000, 1, 7], [8, 6250000, 1, 1], [8, 6250000, 2, 2], [10, 10000, 2, 2], [10, 20000, 1, 3], [10, 20000, 2, 8], [10, 40000, 1, 4], [10, 40000, 2, 16], [10, 80000, 1, 12], [10, 80000, 2, 16], [10, 160000, 1, 4], [10, 160000, 2, 86], [16, 12500000, 2, 2], [20, 20000, 2, 3], [20, 40000, 1, 2], [20, 40000, 2, 9], [20, 40000, 4, 4], [20, 500000, 2, 2], [20, 1000000, 1, 1], [20, 1000000, 2, 2], [20, 1000000, 4, 4], [20, 2000000, 2, 4], [40, 40000, 2, 5], [40, 40000, 4, 9], [40, 40000, 8, 4], [40, 1000000, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 80, 'exponents_of_order': [9, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[16, 1, 32], [32, 0, 4], [32, 1, 68], [64, 0, 92], [64, 1, 76], [128, 0, 4], [128, 1, 28], [256, 1, 352], [512, 1, 670]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '200000000.dic', 'hash': 3543204675378884009, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 200000000, 'inner_split': None, 'inner_tex': 'C_5^8.C_4.C_4^2.D_4', 'inner_used': None, 'irrC_degree': 16, 'irrQ_degree': 32, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 6], [16, 32], [32, 72], [64, 168], [128, 32], [256, 352], [512, 670]], 'label': '200000000.dic', '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': 'C5^8.C4.C4^2.D4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 7, 0, 0, 11, 0, 15, 0, 11, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 256, 'number_characteristic_subgroups': 39, 'number_conjugacy_classes': 1364, 'number_divisions': 697, 'number_normal_subgroups': 61, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 200000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 444375], [4, 12565000], [5, 390624], [8, 53380000], [10, 33540000], [16, 50000000], [20, 40560000], [40, 9120000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '16.10', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 16, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [8, 6], [32, 28], [64, 38], [128, 42], [256, 35], [512, 198], [1024, 324]], 'representations': {'PC': {'code': '59678789861144143587249459458831923917789509172952880013475098840434571568681038806090311725112351100596384322587228349349307404175865104657795305212310410912158154275470228066257405969259980711721313546055858975859405142127825402822808634953288943146275920713601907558920515910526484883929534581394829077742983532599237922669532781184179456331172966100688217694940176909928936741525081013580029996912353099662320781599620550820509474875565175417055906291189223497192956284010292258106052640216847991406782097987267109065089960052888785947063199453522936869711304594857075280389942482991910019282784589498499538009977075719902456169543572661642126246086327355761643402583958754143938226117470083143886835226022101908443626458406239159568579021656976855789682175409495840179707565939013909946345623867044861584365844453747372496143034775324651132581693961843226448357118375064742825540536905789120835814590307941012799487', 'gens': [1, 3, 4, 5, 8, 11, 12, 13, 14, 15, 16, 17], 'pres': [17, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 34, 305967922, 5918, 730150393, 1915765260, 7735800227, 1655286756, 235663693, 360937526, 13672448564, 416141661, 3281366218, 2010494685, 242, 6342666821, 4382300278, 4258032471, 1941030272, 294, 15099001798, 7882411511, 1963147800, 2635593969, 4567602439, 1631939096, 33723689, 805161402, 1634990987, 493717628, 333202557, 398, 25488076616, 2148031897, 51398250, 3408884123, 998169628, 353453349, 400865618, 450, 29865600009, 61276186, 15645483, 43580, 3911437, 49338174, 5551, 10796859402, 1639472411, 1192276140, 3942067773, 290589102, 99137023, 30032, 47221369, 6780766, 21583448075, 1760784412, 58203693, 1929742142, 2382799, 979296, 163313, 12770530, 25510347, 70720012, 1026118941, 937718958, 23450815, 340382512, 1326097, 884114, 2210102285, 2894080030, 218960064, 257040081, 4760098, 4760115, 1785132, 1190149, 391694, 13749600031, 132600065, 2259300082, 43350099, 25500116, 8287633, 6375150, 6720323599, 4526080032, 2197760049, 4058240066, 152320083, 136000100, 136000117, 51000134, 34000151, 4733940240, 21732800033, 11999280050, 1572160067, 1820700084, 1228250101, 722500118, 234812635, 180625152]}, 'Perm': {'d': 40, 'gens': [479908804524335552678681853619890572897438728370, 523376275566089973203773670003847480364349652576, 815364726432135254962900988820260040422125564290]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 320, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^8.C_4.C_4^2.D_4', 'transitive_degree': 40, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 4, 4, 4, 2, 8, 4], 'aut_gens': [[1, 4, 8, 64], [19, 4, 72, 448], [385, 4, 136, 320], [353, 36, 488, 480], [209, 436, 280, 192], [417, 388, 8, 64], [421, 36, 280, 336], [481, 276, 8, 64], [385, 36, 296, 320]], 'aut_group': '8192.xo', 'aut_hash': 2168597184236359916, 'aut_nilpotency_class': 5, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 96, 'aut_perms': [93741476579761360608155174069961040087624194963323862163165722750288027753985207115164032743281286816910958221177343596290977995830057342403445701169, 20877430344528908280278972429867141921900560359593380488533823974144110910077774768255422920778371011008154844441020464820269045514940466652851825934, 501333087093278132460149858408242185556878112053935600169195269514396479183066419069941331099395843169562534496394779123393232439772675352700817538015, 146596812221985900086536214793545782484343348382921904956549512563588579786837440222213475525408016412320219855612208790578591510694096514533502668129, 511554319534872360802561596648689074672673559328731369870233010258839415469803081950888325051421166462325456132454341828772988134300199357341094974182, 840410690549992511421558659481651777376259373903528407600080120940352003263884209715373851778155778658402080224503090078564125495493999736897391453213, 197809455044917765051774933785953655247614693773662613033261802032889993306681102533927575155677793758426824442473432665862739619413568560232747106650, 10439878843727752031817340518193137965487436365495023745800327431936332516370808723699466109307103151926693450373518902177406819151162018813933657021], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 16, 1, 3], [2, 32, 1, 1], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 16, 1, 1], [4, 16, 4, 1], [4, 32, 1, 1], [8, 8, 2, 2], [8, 8, 4, 1], [8, 16, 2, 1], [8, 16, 4, 1], [16, 32, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2^2\\times D_4^2).C_2^5', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': None, 'autcentquo_hash': 8719009971623998540, 'autcentquo_nilpotent': True, 'autcentquo_order': 1024, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times C_2^6.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 16, 3], [2, 32, 1], [4, 2, 2], [4, 4, 3], [4, 8, 1], [4, 16, 5], [4, 32, 1], [8, 8, 8], [8, 16, 6], [16, 32, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '256.2416', 'commutator_count': 1, 'commutator_label': '32.3', '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', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46623, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 16, 1, 3], [2, 32, 1, 1], [4, 2, 1, 2], [4, 4, 1, 3], [4, 8, 1, 1], [4, 16, 1, 1], [4, 16, 2, 2], [4, 32, 1, 1], [8, 8, 1, 8], [8, 16, 1, 2], [8, 16, 2, 2], [16, 32, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 5376, 'exponent': 16, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 1, 4]], 'familial': False, 'frattini_label': '64.85', 'frattini_quotient': '8.5', 'hash': 46623, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [8, 2, 8, 4], 'inner_gens': [[1, 20, 360, 224], [49, 4, 56, 448], [225, 20, 8, 64], [417, 132, 8, 64]], 'inner_hash': 2416, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': False, 'inner_tex': 'C_4^2.(C_2\\times D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 12], [4, 4], [8, 6]], 'label': '512.46623', 'linC_count': 4, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C8^2:(C2*C4)', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [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': 21, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 38, 'number_divisions': 32, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': 261, 'number_subgroup_classes': 402, 'number_subgroups': 2026, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 87], [4, 136], [8, 160], [16, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [16, 0, 66, 32], 'outer_gens': [[435, 276, 8, 352], [33, 4, 8, 64], [421, 388, 408, 336], [147, 308, 136, 96]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [16703, 16, 15960, 6480], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 6], [8, 6]], 'representations': {'PC': {'code': '103449793541506701523162071180323865332143141845343598070169307', 'gens': [1, 3, 4, 7], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 18, 3754, 542, 2225, 12963, 732, 525, 102, 6484, 562, 130, 15557, 14118, 10095, 7080, 186, 27655, 6937, 214]}, 'Perm': {'d': 16, 'gens': [15316467690942, 15310288183680, 5612501687742, 6920263158463, 11657, 8402167094393, 1313941668480, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_8^2:(C_2\\times C_4)', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
