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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.3828', 'ambient_counter': 3828, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 112, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.3828.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.30', 'subgroup_hash': 30, 'subgroup_order': 112, 'subgroup_tex': 'D_{28}:C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.3828', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '672.1093', 'aut_weyl_index': 96, 'centralizer': '112.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.b1.a1', '24.c1.b1', '24.d1.b1', '24.e1.b1', '24.l1.b1', '84.d1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5317, 3060, 6965, 7887, 5376, 1590, 6725, 1040], 'generators': [25, 336, 672, 676, 192], 'label': '1344.3828.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.b1', '24.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '672.707', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '112.31'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 2, 6, 28], 'aut_gens': [[365837, 870, 682893], [341473, 24360, 682893], [365837, 870, 24417], [439023, 870, 682893], [365837, 12673, 682893]], 'aut_group': '672.1093', 'aut_hash': 1093, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 672, 'aut_permdeg': 13, 'aut_perms': [6, 127, 131045167, 559243734], 'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 14, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 14, 2, 1], [7, 2, 3, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 2, 6, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4\\times F_7', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 14, 2], [4, 1, 2], [4, 2, 1], [4, 14, 2], [7, 2, 3], [14, 2, 9], [28, 2, 12]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '28.3', 'commutator_count': 1, 'commutator_label': '14.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 30, '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, 14, 1, 2], [4, 1, 2, 1], [4, 2, 1, 1], [4, 14, 1, 2], [7, 2, 3, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 2, 6, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 672, 'exponent': 28, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[2, 0, 12]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '56.12', 'hash': 30, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [14, 2, 2], 'inner_gens': [[365837, 4002, 682893], [48793, 870, 24417], [365837, 24360, 682893]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 28, 'inner_split': True, 'inner_tex': 'D_{14}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 4, 'irrep_stats': [[1, 8], [2, 26]], 'label': '112.30', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D28:C2', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, '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': 12, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 34, 'number_divisions': 14, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 40, 'number_subgroups': 136, 'old_label': None, 'order': 112, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 31], [4, 32], [7, 6], [14, 18], [28, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [24390, 24390, 682893], 'outer_gens': [[658517, 870, 682893], [341473, 870, 682893], [195123, 10585, 682893]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 1], [6, 4], [24, 1]], 'representations': {'PC': {'code': 926931736852421, 'gens': [1, 2, 4], 'pres': [5, -2, -2, -2, 2, -7, 26, 2163, 58, 2404]}, 'GLFp': {'d': 2, 'p': 29, 'gens': [365837, 870, 682893]}, 'Perm': {'d': 15, 'gens': [88216168447, 194123381760, 25437928320, 288369849600, 973]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{28}:C_2', 'transitive_degree': 56, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 168, 'aut_gen_orders': [8, 6, 12, 12, 12, 12, 84], 'aut_gens': [[1, 2, 8, 48], [337, 690, 809, 628], [673, 694, 1192, 144], [677, 674, 1245, 1204], [337, 1030, 760, 240], [5, 678, 1309, 916], [1013, 370, 1064, 144], [5, 706, 536, 48]], 'aut_group': None, 'aut_hash': 729292253715603644, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 80, 'aut_perms': [43219293475409452921049075341831195472497527334433374567752889390879537033254556281694158945756471700920857819317903103, 17122616899945428675455841865808297374940379088443895592493756694523000744118064311136334605148084323625276607347017844, 41621345852788679283361538485056641203319746262707912125841406298470687948339176616628058535219977254061978929909474754, 48240148087835120748454477604974032421364528841896156982499386883343129213034434407584355787853948312634665519954020127, 48001485545445553149941110923823474600653601894945264116709274520302122799256680555946694780450337247287854074216984470, 64792252586952200964950031089396563666980086779841959670010826630750597960811950596889726542201468478762503058807340872, 65112561290618168069147084857164685201485520830512747085774925142457366235751363696617906262516457281163104854709322224], 'aut_phi_ratio': 168.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 2, 1], [2, 28, 2, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 12, 2, 1], [4, 24, 1, 1], [4, 28, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 4, 1], [6, 28, 4, 1], [7, 2, 3, 1], [8, 168, 2, 1], [12, 4, 2, 1], [12, 28, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 8, 6, 1], [21, 4, 3, 1], [28, 4, 6, 1], [28, 12, 12, 1], [28, 24, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 8, 12, 1], [84, 8, 6, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_{42}\\times D_4).C_6.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': 84, 'autcentquo_group': None, 'autcentquo_hash': 4773224379489722456, 'autcentquo_nilpotent': False, 'autcentquo_order': 8064, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '(C_2\\times C_6\\times F_7).C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 2], [2, 28, 2], [3, 2, 1], [4, 2, 2], [4, 12, 2], [4, 24, 1], [4, 28, 2], [6, 2, 1], [6, 4, 5], [6, 28, 4], [7, 2, 3], [8, 168, 2], [12, 4, 2], [12, 28, 4], [14, 2, 9], [14, 8, 6], [21, 4, 3], [28, 4, 6], [28, 12, 12], [28, 24, 6], [42, 4, 9], [42, 8, 12], [84, 8, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.707', 'commutator_count': 1, 'commutator_label': '168.39', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3828, '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, 2], [2, 28, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 12, 2, 1], [4, 24, 1, 1], [4, 28, 1, 2], [6, 2, 1, 1], [6, 4, 1, 1], [6, 4, 2, 2], [6, 28, 2, 2], [7, 2, 3, 1], [8, 168, 1, 2], [12, 4, 1, 2], [12, 28, 2, 2], [14, 2, 3, 1], [14, 2, 6, 1], [14, 8, 3, 2], [21, 4, 3, 1], [28, 4, 3, 2], [28, 12, 12, 1], [28, 24, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [42, 8, 6, 2], [84, 8, 3, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10752, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 3828, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 6, 14], 'inner_gens': [[1, 678, 8, 720], [677, 2, 376, 48], [1, 1026, 8, 1296], [673, 2, 104, 48]], 'inner_hash': 707, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': '(C_2\\times C_{42}):D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 46], [4, 44], [8, 7]], 'label': '1344.3828', 'linC_count': 192, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 16, 'linQ_dim_count': 16, 'linR_count': 24, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84.(C2*D4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 29, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 105, 'number_divisions': 42, 'number_normal_subgroups': 64, 'number_subgroup_autclasses': 180, 'number_subgroup_classes': 304, 'number_subgroups': 2164, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 67], [3, 2], [4, 108], [6, 134], [7, 6], [8, 336], [12, 120], [14, 66], [21, 12], [28, 312], [42, 132], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 4], 'outer_gens': [[1, 674, 40, 48], [1, 338, 8, 720], [1, 2, 9, 52], [1009, 2, 9, 1204]], 'outer_group': '96.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 11, 'outer_perms': [1680, 744, 41064, 11613843], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}:C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 6], [6, 4], [8, 2], [12, 8], [24, 2], [48, 2]], 'representations': {'PC': {'code': 7464659915662911726264200858335217079299275394198237, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -3, -2, -2, -7, 10849, 41, 6027, 5459, 91, 652, 34565, 7805, 141, 8766, 166, 9247]}, 'Perm': {'d': 26, 'gens': [621574835364374270965819, 358674775619804, 4863578940, 442670293840, 4491498768991, 5721228051186, 6758061133824000, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{84}.(C_2\\times D_4)', 'transitive_degree': 336, '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': '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, 6], 'aut_gens': [[1, 2], [1, 10], [3, 2]], 'aut_group': '12.4', 'aut_hash': 4, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12, 'aut_permdeg': 5, 'aut_perms': [6, 49], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [6, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6', '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': 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, 1], [2, 3, 2], [3, 2, 1], [6, 2, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [['2.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [6, 2, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '12.4', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 10], [5, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 2]], 'label': '12.4', 'linC_count': 1, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D6', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 6, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 10, 'number_subgroups': 16, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 7], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[7, 2]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2]], 'representations': {'PC': {'code': 43377, 'gens': [1, 2], 'pres': [3, -2, -2, -3, 61, 16, 74]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [17, 35]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 55, 56]}, 'Perm': {'d': 5, 'gens': [6, 1, 30]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_6', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
