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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 7260, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.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': '7260.f', 'subgroup_hash': 7584372576544646636, 'subgroup_order': 7260, 'subgroup_tex': 'C_{11}^2:C_{60}', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1', '484.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2701, 5939, 1554, 6360, 7406, 6178, 7413, 5078], 'generators': [30, 2640, 24, 60, 80, 2760], 'label': '29040.c.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '60.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [10, 20, 4, 22], 'aut_gens': [[1, 60, 660], [7091, 1260, 840], [5171, 6000, 6780], [7111, 4800, 5760], [4331, 600, 1200]], 'aut_group': None, 'aut_hash': 1191727547474175236, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 58080, 'aut_permdeg': 244, 'aut_perms': [9858298667526998819407837162436918828750945451470175545431059520005260294201356656628314278694765650887116960052539351508517689098121085934528078914198539402423201677975340919333038457015708781056481666175511442027690245977924071091467631629359810491413948019065583563238951602301084210664650534174854271566046934881623917583112164333803857768169024914385302098786181608694962098182462286043342545531726026803064390711604493974772340942006700927934888782679987690293743577116387, 4792313490302857112982170853225789870731900237011518533815679272141870075424838452393701060516957567326278552696405104779146479147648088708612138613400754690141531183693760960213615886623838348047522451964243144512443833957013971997510610997989694619814512851211364576508398999874347561344991314148499546371020812223385313191256996586548670540263653243753623540402472281875341487640470831439205659840033187360783720592461814205621970749883261139295524501659028941292578366443973, 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True, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [3, 1, 2, 1], [4, 121, 2, 1], [5, 121, 1, 4], [6, 121, 2, 1], [10, 121, 1, 4], [11, 20, 6, 1], [12, 121, 4, 1], [15, 121, 2, 4], [20, 121, 2, 4], [30, 121, 2, 4], [33, 20, 12, 1], [60, 121, 4, 4]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [2, 121, 1], [3, 1, 2], [4, 121, 2], [5, 121, 4], [6, 121, 2], [10, 121, 4], [11, 20, 6], [12, 121, 4], [15, 121, 8], [20, 121, 8], [30, 121, 8], [33, 20, 12], [60, 121, 16]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '2420.b', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2420.b', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [3, 1, 2, 1], [4, 121, 2, 1], [5, 121, 4, 1], [6, 121, 2, 1], [10, 121, 4, 1], [11, 20, 1, 6], [12, 121, 4, 1], [15, 121, 8, 1], [20, 121, 8, 1], [30, 121, 8, 1], [33, 20, 2, 6], [60, 121, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 660, 'exponents_of_order': [2, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[20, 0, 12]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '7260.f', 'hash': 7584372576544646636, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [20, 11, 11], 'inner_gens': [[1, 2460, 2400], [5521, 60, 660], [6181, 60, 660]], 'inner_hash': 4831136090400852969, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': False, 'inner_tex': 'C_{11}^2:C_{20}', 'inner_used': [1, 2], 'irrC_degree': 20, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 40, 'irrep_stats': [[1, 60], [20, 18]], 'label': '7260.f', 'linC_count': 12, 'linC_degree': 20, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 22, 'linQ_degree_count': 12, 'linQ_dim': 22, 'linQ_dim_count': 12, 'linR_count': 120, 'linR_degree': 22, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11^2:C60', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 78, 'number_divisions': 24, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 72, 'number_subgroups': 2040, 'old_label': None, 'order': 7260, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 121], [3, 2], [4, 242], [5, 484], [6, 242], [10, 484], [11, 120], [12, 484], [15, 968], [20, 968], [30, 968], [33, 240], [60, 1936]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 13], 'outer_gens': [[41, 600, 6600], [31, 4260, 4380], [1, 1800, 720]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 120, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 3], [8, 3], [16, 1], [20, 6], [40, 6]], 'representations': {'PC': {'code': '854385113673286876184905823656331269862044423001399', 'gens': [1, 5, 6], 'pres': [6, -2, -2, -3, -5, -11, 11, 12, 31, 68, 73804, 7210, 4066, 472, 86405, 95051, 53477, 5963]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [16280793, 207272754, 140740226, 1830210, 207916856, 58532609]}, 'Perm': {'d': 25, 'gens': [79102345851399529250184, 3, 732043497760373920319400, 1370644348715594434681923, 156754629610948768432443, 2051866659042956398467003]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [60], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:C_{60}', 'transitive_degree': 66, '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': '240.84', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [20, 10, 4, 10, 60], 'aut_gens': [[1, 120, 1320], [15811, 21360, 12240], [24811, 8040, 28680], [24811, 10920, 25920], [27251, 19200, 7080], [19921, 19200, 23280]], 'aut_group': None, 'aut_hash': 8062377920923750923, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 116160, 'aut_permdeg': 486, 'aut_perms': 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'aut_phi_ratio': 16.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 1, 4], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 1, 12], [11, 40, 3, 1], [12, 121, 4, 2], [15, 121, 2, 4], [20, 121, 2, 8], [22, 40, 3, 1], [24, 121, 8, 2], [30, 121, 2, 12], [33, 40, 6, 1], [40, 121, 4, 8], [60, 121, 4, 8], [66, 40, 6, 1], [120, 121, 8, 8]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_2^4', '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': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [3, 1, 2], [4, 121, 4], [5, 121, 4], [6, 1, 2], [6, 121, 4], [8, 121, 8], [10, 121, 12], [11, 40, 3], [12, 121, 8], [15, 121, 8], [20, 121, 16], [22, 40, 3], [24, 121, 16], [30, 121, 24], [33, 40, 6], [40, 121, 32], [60, 121, 32], [66, 40, 6], [120, 121, 64]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '4840.c', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4840.c', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 4, 1], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 4, 3], [11, 40, 1, 3], [12, 121, 4, 2], [15, 121, 8, 1], [20, 121, 8, 2], [22, 40, 1, 3], [24, 121, 8, 2], [30, 121, 8, 3], [33, 40, 2, 3], [40, 121, 16, 2], [60, 121, 16, 2], [66, 40, 2, 3], [120, 121, 32, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2304, 'exponent': 1320, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[40, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '29040.c', 'hash': 1832492014362143934, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 440, 'inner_gen_orders': [40, 11, 11], 'inner_gens': [[1, 22200, 12840], [8281, 120, 1320], [18841, 120, 1320]], 'inner_hash': 1340125317553616686, 'inner_nilpotent': False, 'inner_order': 4840, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_{40}', 'inner_used': [1, 2], 'irrC_degree': 40, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 80, 'irrep_stats': [[1, 240], [40, 18]], 'label': '29040.c', 'linC_count': 6, 'linC_degree': 40, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 18, 'linQ_dim': 42, 'linQ_dim_count': 18, 'linR_count': 360, 'linR_degree': 42, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C11^2:C120', '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, 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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 84, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 258, 'number_divisions': 44, 'number_normal_subgroups': 48, 'number_subgroup_autclasses': 100, 'number_subgroup_classes': 148, 'number_subgroups': 7048, 'old_label': None, 'order': 29040, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [3, 2], [4, 484], [5, 484], [6, 486], [8, 968], [10, 1452], [11, 120], [12, 968], [15, 968], [20, 1936], [22, 120], [24, 1936], [30, 2904], [33, 240], [40, 3872], [60, 3872], [66, 240], [120, 7744]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 102], 'outer_gens': [[41, 1200, 27720], [91, 27000, 22560], [14521, 21480, 4920]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 49, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 8], [8, 8], [16, 4], [32, 2], [40, 6], [80, 6]], 'representations': {'PC': {'code': '172219749243564175609130683064643333843943974933224474218801318983668488034901316703038770080775900013909', 'gens': [1, 6, 7], 'pres': [8, 2, 2, 2, 3, 5, 11, 2, 11, 16, 41, 66, 123, 1065605, 63373, 2901, 2909, 2197, 719046, 409934, 240262, 138630, 27758, 166, 1559047, 7695, 84503, 84511, 63399]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [16280793, 207272754, 140740226, 80979421, 1830210, 207916856, 58532609, 26573430]}, 'Perm': {'d': 49, 'gens': [14000005658767194322138849151509273456093287375561934835649870, 26667169170766690187178353532046274075554480316325393817632000, 30, 39334312563777554177172541404234401431449219459601552468275840, 52045486600559582527271472987696799888995126791267305791810481, 64672597377446824496185695107136948366849105137185555170832590, 77330186214435394099468424732940748724002691259426604052585550, 31]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 120], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{11}^2:C_{120}', 'transitive_degree': 264, 'wreath_data': None, 'wreath_product': False}
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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}