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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3362', 'ambient_counter': 3362, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 324, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3362.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1296.3362', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '10368.tp', 'aut_weyl_index': 16, 'centralizer': '108.a1', 'complements': ['324.b1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.d1'], 'contains': ['8.b1', '8.d1', '12.f1', '12.w1', '12.x1', '12.y1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5676, 6712, 5366, 5875], 'generators': [69, 432, 72, 36, 2, 24], 'label': '1296.3362.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.b1', '2.d1'], 'normal_contains': ['8.b1', '12.f1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '216.171', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 936, 'aut_gen_orders': [2, 3, 2, 13, 3, 2, 3], 'aut_gens': [[1, 6, 18, 54], [5, 6, 18, 54], [247, 6, 18, 54], [163, 6, 18, 54], [43, 126, 138, 60], [121, 6, 18, 54], [167, 228, 240, 54], [109, 6, 18, 54]], 'aut_group': '1213056.a', 'aut_hash': 4959825539050127108, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1213056, 'aut_permdeg': 56, 'aut_perms': [122277327209721826976174190080982897741416609791208325120000000000, 693683930174139448047287674951767296749959254574808780365840730786711787640, 90529944900064822463534912494463806154190826022229804845044084500716368098, 177406859188871659595252069726299319744016143474548816704932968546160063988, 387948124477343235140806277158207312842845001934945737981727023325018544056, 97229738763249481499541626230778633150035218036262375643859433304367059298, 51961620591852050441966487997880133370143645119309772864997368549552060856], 'aut_phi_ratio': 11232.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 2, 1], [3, 1, 2, 1], [3, 2, 13, 1], [3, 2, 26, 1], [6, 1, 2, 1], [6, 2, 13, 1], [6, 2, 26, 1], [6, 27, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.(C_2^2\\times \\GL(3,3))', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 936, 'autcentquo_group': '303264.a', 'autcentquo_hash': 8091482650397092313, 'autcentquo_nilpotent': False, 'autcentquo_order': 303264, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:\\GL(3,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 27, 2], [3, 1, 2], [3, 2, 39], [6, 1, 2], [6, 2, 39], [6, 27, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '54.14', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 174, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['54.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 1, 2], [3, 1, 2, 1], [3, 2, 1, 13], [3, 2, 2, 13], [6, 1, 2, 1], [6, 2, 1, 13], [6, 2, 2, 13], [6, 27, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4200, 'exponent': 6, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '324.174', 'hash': 174, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3, 3], 'inner_gens': [[1, 12, 36, 270], [13, 6, 18, 54], [37, 6, 18, 54], [109, 6, 18, 54]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 54, 'inner_split': True, 'inner_tex': 'C_3^2:S_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 12], [2, 78]], 'label': '324.174', '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': False, 'monomial': True, 'name': 'C3^3:D6', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 90, 'number_divisions': 60, 'number_normal_subgroups': 118, 'number_subgroup_autclasses': 38, 'number_subgroup_classes': 436, 'number_subgroups': 1528, 'old_label': None, 'order': 324, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 55], [3, 80], [6, 188]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 312, 'outer_gen_orders': [2, 2, 13], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 6, 18, 54], [167, 6, 114, 204], [1, 132, 156, 198]], 'outer_group': '22464.a', 'outer_hash': 5045075831251158205, 'outer_nilpotent': False, 'outer_order': 22464, 'outer_permdeg': 17, 'outer_perms': [7, 21371672494103, 44569364842920], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(3,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 30], [4, 26]], 'representations': {'PC': {'code': 241102895561545151581, 'gens': [1, 3, 4, 5], 'pres': [6, -2, -3, -3, -3, -2, -3, 12, 218, 867, 8104, 88, 7781]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [99161, 24505, 40831, 6083, 5941, 96397]}, 'Perm': {'d': 14, 'gens': [482635576, 3628800, 325, 348, 45708, 6706103475]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:D_6', 'transitive_degree': 108, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 12, 4, 24, 12, 6, 6], 'aut_gens': [[1, 6, 72, 216], [17, 498, 936, 360], [653, 714, 936, 252], [49, 1290, 504, 1224], [661, 1266, 576, 792], [689, 654, 576, 1116], [689, 510, 864, 360], [41, 834, 432, 1152]], 'aut_group': None, 'aut_hash': 3079928416082064686, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 165888, 'aut_permdeg': 50, 'aut_perms': [26374650243334902526501963181716039778636269475543482931719812582, 29685039337012060874870404309501130938985466191994363471844306399, 29247558843812527310423355831482082956755064575222660395928861689, 17084874201098765202549381207462257775599093224974670796858582619, 18781647240146058797293270497845939309146405637585701739549055754, 24707945108614878527822148073531247656571742179459315320800084187, 20637450225638680534591700978514300406698905100569839730690738105], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 54, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 2, 4, 1], [3, 2, 8, 1], [3, 4, 4, 1], [3, 4, 8, 1], [4, 18, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 2], [6, 2, 8, 2], [6, 2, 16, 1], [6, 4, 4, 1], [6, 4, 8, 2], [6, 4, 16, 1], [6, 6, 4, 1], [6, 6, 16, 1], [6, 6, 32, 1], [6, 54, 4, 1], [12, 18, 4, 2], [12, 18, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSU(3,2).C_6^2.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '2592.fv', 'autcentquo_hash': 9019849488891309561, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 54, 2], [3, 1, 2], [3, 2, 15], [3, 4, 12], [4, 18, 2], [6, 1, 6], [6, 2, 45], [6, 4, 36], [6, 6, 52], [6, 54, 4], [12, 18, 16]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '108.39', 'commutator_count': 1, 'commutator_label': '54.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3362, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['216.128', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 54, 1, 2], [3, 1, 2, 1], [3, 2, 1, 5], [3, 2, 2, 5], [3, 4, 1, 4], [3, 4, 2, 4], [4, 18, 1, 2], [6, 1, 2, 3], [6, 2, 1, 15], [6, 2, 2, 15], [6, 4, 1, 12], [6, 4, 2, 12], [6, 6, 2, 26], [6, 54, 2, 2], [12, 18, 2, 4], [12, 18, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2184, 'exponent': 12, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '648.747', 'hash': 3362, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 3, 3], 'inner_gens': [[1, 66, 72, 216], [13, 6, 144, 1080], [1, 150, 72, 216], [1, 438, 72, 216]], 'inner_hash': 39, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': False, 'inner_tex': 'C_3:S_3^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 126], [4, 48]], 'label': '1296.3362', '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': False, 'monomial': True, 'name': 'C6^2.S3^2', '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, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 198, 'number_divisions': 120, 'number_normal_subgroups': 184, 'number_subgroup_autclasses': 294, 'number_subgroup_classes': 1348, 'number_subgroups': 7616, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 123], [3, 80], [4, 36], [6, 768], [12, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [8, 4, 6, 4, 8, 2], 'outer_gen_pows': [24, 144, 0, 144, 24, 0], 'outer_gens': [[65, 1230, 576, 828], [1, 750, 72, 1116], [37, 978, 144, 1224], [709, 1074, 72, 1188], [25, 906, 504, 324], [65, 642, 72, 1152]], 'outer_group': '1536.408635824', 'outer_hash': 4361138917581321938, 'outer_nilpotent': False, 'outer_order': 1536, 'outer_permdeg': 128, 'outer_perms': [89583668295847324594740726774383443565021119123298594297581739851732209744140032040162867623715170544227672619492507320349106586591715619959626090772326131170075150927965106971600823891305465396463869270011843587216, 359942873521421702108601607803056912302502437336463585127357457568562776753751525177921695773186199927235785553748537992343272360120890080848680379640767633746091733739834106663741986156016596793477375712161849359815, 215388977647424827315947801980109063124684164364632886087727192328346660369383200828601618378663207759997769853949790484439098870815986485648694984297850677215882265824858315462753771591023654250494431259298500122536, 193853922665379314855922859445524697677861273489261850475447172785713299077239070575578377612787800512198380566400040889112081065929180677380102340750791717387838016394523420835808010251896484799456763880904423475982, 40627138867035402035663740486583804665768932294623384934680759784827267449544475676998480809619140650855427766587688514292276318911152864311438622501492849968011286128519763949426400453697790504366126566657947991431, 141133357667704680746172123539472334913919810106489580904592881020865065726778198223891935547349045554914928985487620640751723572891094094582735121593327229305597809588816938862293014795446072892209812680990442693561], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\SL(2,3).C_2^5.C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 30], [4, 64], [8, 18]], 'representations': {'PC': {'code': 90866975094182530829604590520083503598925, 'gens': [1, 3, 6, 7], 'pres': [8, -2, -3, -2, -2, -3, -3, -2, -3, 16, 1586, 66, 1923, 91, 1924, 1173, 10102, 166, 9239]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1197949, 1622293, 1166425, 930581, 370901, 91403, 793169, 47089]}, 'Perm': {'d': 18, 'gens': [20929016908809, 5045, 136, 43545600, 16, 376703623296000, 376610217984000, 45360]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_3^2', 'transitive_degree': 144, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': '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': 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, 3]], 'center_label': '4.2', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], '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': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
