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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '512.46623', 'ambient_counter': 46623, 'ambient_order': 512, 'ambient_tex': 'C_8^2:(C_2\\times C_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 128, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '512.46623.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.187', 'subgroup_hash': 187, 'subgroup_order': 128, 'subgroup_tex': 'C_8^2:C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '512.46623', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '512.519989', 'aut_weyl_index': 16, 'centralizer': '32.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.e1.a1', '2.e1.b1'], 'contains': ['8.c1.a1', '8.l1.a1', '8.m1.a1', '8.z1.a1', '8.bp1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5836, 7441, 4317, 5063, 5845, 7755, 4308, 5154], 'generators': [8, 2, 352], 'label': '512.46623.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.e1.a1', '2.e1.b1'], 'normal_contains': ['8.c1.a1', '8.l1.a1', '8.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '256.2416', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.22'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.21', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 4, 2, 2, 2, 2, 4, 2, 2, 12, 2, 8], 'aut_gens': [[1, 2, 16], [65, 74, 80], [1, 106, 80], [1, 66, 16], [1, 110, 24], [73, 66, 24], [1, 78, 48], [1, 46, 60], [1, 74, 88], [1, 34, 120], [1, 84, 86], [1, 10, 80], [1, 22, 56]], 'aut_group': '6144.bkd', 'aut_hash': 6249717923573788879, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 28, 'aut_perms': [35676083988847523720594808840, 37134125292893638598293880183, 2839214250471478266861279240, 52637620128741640750715966287, 167120353844821258904293649400, 3242506682674902575037329423, 157347192219302492607431363783, 167120339891884237633225651320, 52637620128741640750715966296, 208185988646704800375827261416, 35272793484459277113115487520, 49643996757765186543357070930], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 4, 1, 1], [4, 1, 12, 1], [4, 4, 3, 1], [8, 2, 24, 1], [8, 4, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.\\GL(2,\\mathbb{Z}/4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 904815073585671268, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6.C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [4, 1, 12], [4, 4, 3], [8, 2, 24], [8, 4, 12]], 'center_label': '16.2', 'center_order': 16, 'central_product': False, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 187, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [4, 1, 2, 6], [4, 4, 1, 3], [8, 2, 2, 12], [8, 4, 2, 6]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 112, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '8.5', 'hash': 187, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 10, 80], [9, 2, 16], [65, 2, 16]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 24]], 'label': '128.187', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 48, 'linQ_dim': 8, 'linQ_dim_count': 48, 'linR_count': 48, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C8^2:C2', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 56, 'number_divisions': 32, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 107, 'number_subgroups': 140, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 7], [4, 24], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 2, 3, 4, 4, 2, 2], 'outer_gen_pows': [0, 0, 1, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 82, 112], [1, 70, 120], [1, 34, 52], [1, 6, 48], [1, 82, 98], [1, 34, 84], [1, 102, 48], [1, 66, 24], [1, 66, 16]], 'outer_group': '768.1087525', 'outer_hash': 1087525, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 14, 'outer_perms': [20198171214, 21317952985, 17268277831, 21317952984, 41916442680, 15426861870, 23752774128, 21316380510, 2440935744], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^3.\\GL(2,\\mathbb{Z}/4)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 4, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 12]], 'representations': {'PC': {'code': 4900202407188759158, 'gens': [1, 2, 5], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 141, 36, 58, 2804, 102, 124]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 91714451877, 27831734212, 40946670943, 61054693752, 40879872504, 149861448128]}, 'Perm': {'d': 16, 'gens': [6580, 1414575560417, 268248520744, 19634, 2978079977295, 29514, 4209473347914]}}, 'schur_multiplier': [8], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 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', 'transitive_degree': 64, '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}
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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}
