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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.810', 'ambient_counter': 810, 'ambient_order': 672, 'ambient_tex': 'C_{24}.D_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 117, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.810.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.178', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 178, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '672.810', 'aut_centralizer_order': 5376, 'aut_label': '336.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5376, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.c1.a1', '168.c1.b1', '168.d1.a1', '168.e1.a1', '168.e1.b1'], 'contains': ['672.a1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3428, 7520, 7150, 2247, 3115, 3449, 2505, 3014], 'generators': [336], 'label': '672.810.336.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.178', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.178', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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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}
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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': 168, 'aut_gen_orders': [24, 12, 24, 56, 8, 6, 12], 'aut_gens': [[1, 2, 4], [253, 482, 212], [85, 338, 268], [421, 50, 68], [421, 98, 340], [253, 338, 116], [421, 434, 124], [169, 98, 148]], 'aut_group': None, 'aut_hash': 6110678076673136339, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5376, 'aut_permdeg': 24, 'aut_perms': [107484780777141916292769, 226032853855540805187658, 324936026131314800665766, 331475474012303538615745, 128295850164558620560859, 324730899731119341410122, 433758221173078932771258], 'aut_phi_ratio': 28.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 7, 2, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 4, 2, 1], [4, 14, 1, 1], [4, 28, 2, 1], [6, 1, 2, 1], [6, 7, 4, 1], [7, 2, 3, 1], [8, 2, 2, 1], [8, 14, 2, 1], [12, 2, 2, 1], [12, 4, 4, 1], [12, 14, 2, 1], [12, 28, 4, 1], [14, 2, 3, 1], [21, 2, 6, 1], [24, 2, 4, 1], [24, 14, 4, 1], [28, 4, 3, 1], [28, 8, 6, 1], [42, 2, 6, 1], [56, 4, 6, 1], [84, 4, 6, 1], [84, 8, 12, 1], [168, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{28}.(C_2^5\\times C_6)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '336.125', 'autcentquo_hash': 125, 'autcentquo_nilpotent': False, 'autcentquo_order': 336, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 7, 2], [3, 1, 2], [4, 2, 1], [4, 4, 2], [4, 14, 1], [4, 28, 2], [6, 1, 2], [6, 7, 4], [7, 2, 3], [8, 2, 2], [8, 14, 2], [12, 2, 2], [12, 4, 4], [12, 14, 2], [12, 28, 4], [14, 2, 3], [21, 2, 6], [24, 2, 4], [24, 14, 4], [28, 4, 3], [28, 8, 6], [42, 2, 6], [56, 4, 6], [84, 4, 6], [84, 8, 12], [168, 4, 12]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '112.31', 'commutator_count': 1, 'commutator_label': '28.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 810, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['14.1', 1], ['16.9', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 7, 1, 2], [3, 1, 2, 1], [4, 2, 1, 1], [4, 4, 1, 2], [4, 14, 1, 1], [4, 28, 1, 2], [6, 1, 2, 1], [6, 7, 2, 2], [7, 2, 3, 1], [8, 2, 2, 1], [8, 14, 2, 1], [12, 2, 2, 1], [12, 4, 2, 2], [12, 14, 2, 1], [12, 28, 2, 2], [14, 2, 3, 1], [21, 2, 6, 1], [24, 2, 4, 1], [24, 14, 4, 1], [28, 4, 3, 1], [28, 8, 3, 2], [42, 2, 6, 1], [56, 4, 6, 1], [84, 4, 6, 1], [84, 8, 6, 2], [168, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 17472, 'exponent': 168, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '168.54', 'hash': 810, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 2, 28], 'inner_gens': [[1, 2, 508], [1, 2, 388], [169, 290, 4]], 'inner_hash': 31, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': False, 'inner_tex': 'D_4\\times D_7', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 54], [4, 27]], 'label': '672.810', 'linC_count': 396, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 64, 'linQ_dim': 14, 'linQ_dim_count': 8, 'linR_count': 48, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24.D14', 'ngens': 7, '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': 28, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 105, 'number_divisions': 36, 'number_normal_subgroups': 58, 'number_subgroup_autclasses': 84, 'number_subgroup_classes': 120, 'number_subgroups': 476, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 80], [6, 30], [7, 6], [8, 32], [12, 160], [14, 6], [21, 12], [24, 64], [28, 60], [42, 12], [56, 24], [84, 120], [168, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 28], 'outer_gens': [[1, 338, 4], [1, 2, 340], [1, 2, 452], [85, 2, 292]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [24, 3628800, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [6, 4], [8, 2], [12, 5], [24, 2], [48, 1]], 'representations': {'PC': {'code': 2373655772404062697072760523154491262023028619, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 2352, 10670, 4083, 58, 9635, 1466, 80, 3651, 102, 8748, 166, 14125]}, 'GLZN': {'d': 2, 'p': 91, 'gens': [40371124, 16927702, 12057152, 754909, 19491198, 20346444, 60183982]}, 'Perm': {'d': 26, 'gens': [621574835363025223680000, 1610629112133, 2987351515484, 6758061133824000, 4404319792351, 5808408640626, 16754357281155028254720000]}}, 'schur_multiplier': [2, 2], '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_{24}.D_{14}', 'transitive_degree': 336, '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': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 2, 2, 6, 28], 'aut_gens': [[1, 2, 4], [1, 2, 116], [1, 170, 4], [1, 2, 172], [1, 2, 124], [85, 242, 4]], 'aut_group': '1344.11434', 'aut_hash': 11434, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1344, 'aut_permdeg': 20, 'aut_perms': [33068312, 77418490355115925, 1800761010048000, 1856630217444663, 909361666614772153], 'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 7, 2, 1], [2, 14, 2, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 14, 1, 1], [6, 1, 2, 1], [6, 2, 4, 1], [6, 7, 4, 1], [6, 14, 4, 1], [7, 2, 3, 1], [12, 2, 2, 1], [12, 14, 2, 1], [14, 2, 3, 1], [14, 4, 6, 1], [21, 2, 6, 1], [28, 4, 3, 1], [42, 2, 6, 1], [42, 4, 12, 1], [84, 4, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times D_4\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', '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, 2], [2, 7, 2], [2, 14, 2], [3, 1, 2], [4, 2, 1], [4, 14, 1], [6, 1, 2], [6, 2, 4], [6, 7, 4], [6, 14, 4], [7, 2, 3], [12, 2, 2], [12, 14, 2], [14, 2, 3], [14, 4, 6], [21, 2, 6], [28, 4, 3], [42, 2, 6], [42, 4, 12], [84, 4, 6]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '56.12', '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', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 178, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['14.1', 1], ['3.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 7, 1, 2], [2, 14, 1, 2], [3, 1, 2, 1], [4, 2, 1, 1], [4, 14, 1, 1], [6, 1, 2, 1], [6, 2, 2, 2], [6, 7, 2, 2], [6, 14, 2, 2], [7, 2, 3, 1], [12, 2, 2, 1], [12, 14, 2, 1], [14, 2, 3, 1], [14, 4, 3, 2], [21, 2, 6, 1], [28, 4, 3, 1], [42, 2, 6, 1], [42, 4, 6, 2], [84, 4, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8736, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 0, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '168.54', 'hash': 178, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 14], 'inner_gens': [[1, 2, 172], [1, 2, 52], [169, 290, 4]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 56, 'inner_split': True, 'inner_tex': 'C_2\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 42], [4, 9]], 'label': '336.178', 'linC_count': 198, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 72, 'linQ_dim': 10, 'linQ_dim_count': 72, 'linR_count': 264, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12:D14', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 75, 'number_divisions': 30, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 68, 'number_subgroup_classes': 108, 'number_subgroups': 440, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 16], [6, 94], [7, 6], [12, 32], [14, 30], [21, 12], [28, 12], [42, 60], [84, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 28], 'outer_gens': [[1, 170, 4], [1, 2, 116], [85, 2, 244]], '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': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2], [6, 4], [12, 5], [24, 1]], 'representations': {'PC': {'code': 118545945446551872627193446155, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -7, 3098, 476, 50, 1257, 69, 3130, 118, 5195]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [142311, 9325, 9269, 74096, 59004, 37048]}, 'Perm': {'d': 14, 'gens': [127, 6266937600, 997920000, 403200, 13412044800, 973]}}, 'schur_multiplier': [2, 2, 2], '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_{12}:D_{14}', 'transitive_degree': 84, 'wreath_data': None, 'wreath_product': False}
