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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34940', 'ambient_counter': 34940, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 864, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34940.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3144', 'subgroup_hash': 3144, 'subgroup_order': 864, 'subgroup_tex': 'C_6.(C_6\\times D_{12})', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.34940', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.c1', 'complements': ['864.f1', '864.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '4.e1', '4.s1', '4.t1', '4.w1', '4.ba1', '6.b1', '6.i1', '6.u1'], 'core': '2.f1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 72, 864, 36, 48, 576, 76, 432], 'label': '1728.34940.2.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '4.e1', '4.s1', '4.t1', '4.w1', '4.ba1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': None}
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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': 2, 'aut_exponent': 6, 'aut_gen_orders': [6, 6, 2, 2, 2, 6, 2, 6, 6, 6], 'aut_gens': [[1, 6, 72], [49, 726, 72], [29, 294, 792], [1, 474, 792], [1, 6, 396], [41, 750, 792], [49, 174, 540], [493, 498, 396], [49, 582, 360], [65, 750, 108], [61, 762, 396]], 'aut_group': None, 'aut_hash': 4181872362757125326, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 30, 'aut_perms': [106417719991011308923153718676420, 71359964199302144843827666727705, 4864376361753636494637484274, 2847917930646600284045586674, 239353587339140680287909534073669, 106424546826687828307856223892158, 97578672292900290129076213973038, 106417713767397011133581027106991, 257035134019204566673176221304405, 256730107334977175646166287482012], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 1], [2, 36, 1, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 2, 2, 1], [4, 6, 2, 2], [4, 12, 1, 1], [4, 36, 1, 1], [6, 1, 2, 3], [6, 2, 1, 6], [6, 2, 2, 6], [6, 4, 1, 3], [6, 4, 2, 3], [6, 12, 2, 2], [6, 12, 4, 1], [6, 36, 2, 1], [12, 2, 4, 2], [12, 2, 8, 1], [12, 4, 2, 1], [12, 4, 4, 2], [12, 4, 8, 1], [12, 6, 4, 4], [12, 6, 8, 2], [12, 12, 2, 2], [12, 12, 4, 1], [12, 36, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6^2.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '36.10', 'autcentquo_hash': 10, 'autcentquo_nilpotent': False, 'autcentquo_order': 36, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 12, 1], [2, 36, 1], [3, 1, 2], [3, 2, 6], [3, 4, 3], [4, 2, 2], [4, 6, 4], [4, 12, 1], [4, 36, 1], [6, 1, 6], [6, 2, 18], [6, 4, 9], [6, 12, 8], [6, 36, 2], [12, 2, 16], [12, 4, 18], [12, 6, 32], [12, 12, 8], [12, 36, 2]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '72.46', 'commutator_count': 1, 'commutator_label': '36.14', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3144, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['288.500', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 1], [2, 36, 1, 1], [3, 1, 2, 1], [3, 2, 1, 2], [3, 2, 2, 2], [3, 4, 1, 1], [3, 4, 2, 1], [4, 2, 2, 1], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 1, 1], [4, 36, 1, 1], [6, 1, 2, 3], [6, 2, 1, 6], [6, 2, 2, 6], [6, 4, 1, 3], [6, 4, 2, 3], [6, 12, 2, 4], [6, 36, 2, 1], [12, 2, 4, 4], [12, 4, 2, 1], [12, 4, 4, 4], [12, 6, 2, 4], [12, 6, 4, 6], [12, 12, 2, 2], [12, 12, 4, 1], [12, 36, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 34944, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '216.170', 'hash': 3144, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 6], 'inner_gens': [[1, 462, 108], [481, 6, 360], [37, 582, 72]], 'inner_hash': 46, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'S_3\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 90], [4, 30]], 'label': '864.3144', 'linC_count': 256, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 100, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.(C6*D12)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 60, 'number_characteristic_subgroups': 88, 'number_conjugacy_classes': 144, 'number_divisions': 68, 'number_normal_subgroups': 96, 'number_subgroup_autclasses': 378, 'number_subgroup_classes': 418, 'number_subgroups': 1828, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 51], [3, 26], [4, 76], [6, 246], [12, 464]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[37, 30, 360], [433, 30, 360], [1, 66, 72], [1, 438, 360], [1, 30, 504], [5, 6, 360]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [39916800, 362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 18], [8, 22], [16, 2]], 'representations': {'PC': {'code': 1765817201150957213088937507006150667062439241, 'gens': [1, 3, 6], 'pres': [8, 2, 3, 2, 2, 3, 2, 2, 3, 16, 11090, 66, 1923, 91, 1924, 5189, 2901, 141, 6742, 166, 6167]}, 'GLZN': {'d': 2, 'p': 78, 'gens': [18938907, 474613, 11863825, 29188012, 25151309, 302874, 28947733, 10124811]}, 'Perm': {'d': 21, 'gens': [2446418218105251600, 99641059201, 174847368984, 5243564987781120000, 274484468400, 274467916800, 3, 7664017935974400000]}}, 'schur_multiplier': [2, 4], '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.(C_6\\times D_{12})', 'transitive_degree': 96, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 12, 144], [73, 10, 12, 144], [865, 2, 60, 720], [1, 82, 12, 720], [1, 866, 60, 144], [1, 10, 84, 144], [1, 2, 876, 144], [1, 2, 60, 792], [1, 10, 60, 1008], [1, 10, 12, 144], [1, 2, 60, 144], [1, 2, 12, 720], [77, 2, 12, 144], [1, 50, 12, 144], [1, 2, 588, 144]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 55296, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 96.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 2], [2, 36, 1, 2], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 2, 3], [4, 12, 1, 1], [4, 18, 2, 2], [4, 36, 1, 2], [4, 54, 2, 1], [4, 108, 1, 1], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 12, 2, 2], [6, 24, 1, 2], [6, 24, 2, 2], [6, 36, 2, 1], [6, 72, 1, 1], [12, 4, 2, 2], [12, 4, 4, 1], [12, 6, 4, 1], [12, 8, 1, 1], [12, 8, 2, 2], [12, 8, 4, 1], [12, 12, 2, 5], [12, 12, 4, 2], [12, 24, 1, 2], [12, 24, 2, 2], [12, 36, 2, 2], [12, 72, 1, 2]], '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, 1, 3], [2, 12, 2], [2, 36, 2], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 4, 1], [4, 6, 6], [4, 12, 1], [4, 18, 4], [4, 36, 2], [4, 54, 2], [4, 108, 1], [6, 2, 9], [6, 4, 9], [6, 8, 3], [6, 12, 4], [6, 24, 6], [6, 36, 2], [6, 72, 1], [12, 4, 8], [12, 6, 4], [12, 8, 9], [12, 12, 18], [12, 24, 6], [12, 36, 4], [12, 72, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '108.45', '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', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 34940, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 2], [2, 36, 1, 2], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 1, 2], [4, 6, 2, 2], [4, 12, 1, 1], [4, 18, 2, 2], [4, 36, 1, 2], [4, 54, 1, 2], [4, 108, 1, 1], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 12, 2, 2], [6, 24, 1, 2], [6, 24, 2, 2], [6, 36, 2, 1], [6, 72, 1, 1], [12, 4, 2, 4], [12, 6, 4, 1], [12, 8, 1, 1], [12, 8, 2, 4], [12, 12, 1, 4], [12, 12, 2, 5], [12, 12, 4, 1], [12, 24, 1, 2], [12, 24, 2, 2], [12, 36, 2, 2], [12, 72, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 44291520, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '432.759', 'hash': 34940, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 10, 876, 216], [77, 2, 60, 1080], [865, 98, 12, 720], [73, 938, 1164, 144]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 432, 'inner_split': None, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 40], [4, 49], [8, 12]], 'label': '1728.34940', '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': '(C2*C4).S3^3', 'ngens': 9, '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': 78, 'number_characteristic_subgroups': 164, 'number_conjugacy_classes': 117, 'number_divisions': 85, 'number_normal_subgroups': 174, 'number_subgroup_autclasses': 1102, 'number_subgroup_classes': 1204, 'number_subgroups': 9572, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 99], [3, 26], [4, 412], [6, 414], [12, 776]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '128.2328', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 128, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^7', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 19], [8, 21], [16, 5]], 'representations': {'PC': {'code': 56989138930542028470234148948267225423606238581355052859202926001225, 'gens': [1, 2, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 181, 46, 2162, 506, 31539, 1092, 102, 2713, 130, 2606, 13614, 34035, 3813, 186, 8674, 214, 7811]}, 'Perm': {'d': 25, 'gens': [4819681, 623925025173558646167600, 622798599363497460617904, 20632580075844864, 27453328152022104, 16188504, 1320703288040697200640000, 3, 1938954779260553134080000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_2\\times C_4).S_3^3', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
