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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1440.5010', 'ambient_counter': 5010, 'ambient_order': 1440, 'ambient_tex': 'C_{30}.(C_4\\times D_6)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 10, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5010.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.140', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 140, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1440.5010', 'aut_centralizer_order': 576, 'aut_label': '144.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '20.3', 'aut_weyl_index': 576, 'centralizer': '20.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.h1.a1', '72.a1.a1', '72.f1.a1', '72.f1.b1'], 'contains': ['288.a1.a1', '720.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2564, 1913, 9712, 7968, 1138, 3096, 9041, 3163], 'generators': [732, 288], 'label': '1440.5010.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['48.d1.a1', '48.c1.a1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '1440.5010', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 5], 'aut_gens': [[1, 2], [3, 6], [5, 2]], 'aut_group': '20.3', 'aut_hash': 3, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20, 'aut_permdeg': 5, 'aut_perms': [17, 89], 'aut_phi_ratio': 5.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [5, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_5', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '20.3', 'autcentquo_hash': 3, 'autcentquo_nilpotent': False, 'autcentquo_order': 20, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5', 'cc_stats': [[1, 1, 1], [2, 5, 1], [5, 2, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '10.1', 'commutator_count': 1, 'commutator_label': '5.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 5, 1, 1], [5, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[2, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 5], 'inner_gens': [[1, 8], [5, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 10, 'inner_split': False, 'inner_tex': 'D_5', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 2]], 'label': '10.1', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D5', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 8, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 5], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [1], 'outer_gens': [[1, 6]], '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], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 1]], 'representations': {'PC': {'code': 227, 'gens': [1, 2], 'pres': [2, -2, -5, 33]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [23707240, 26329372]}, 'Lie': [{'d': 2, 'q': 4, 'gens': [81, 94], 'family': 'CSOMinus'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 129]}, 'Perm': {'d': 5, 'gens': [23, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_5', 'transitive_degree': 5, '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': 2, 'aut_exponent': 60, 'aut_gen_orders': [6, 20, 60, 60, 12, 30, 2], 'aut_gens': [[1, 2, 24], [737, 770, 1416], [1081, 218, 24], [1089, 986, 984], [1089, 1130, 984], [361, 34, 168], [1097, 1130, 744], [1, 442, 696]], 'aut_group': None, 'aut_hash': 3555297260956627131, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11520, 'aut_permdeg': 72, 'aut_perms': [17934984785178264638378021674029392721292336189041559975144454882645738827723301681501127934961776587347, 49619403316558637895447253219175843564119549460439016115525801443547264333067592681295854018058317006358, 55513156026908319172435874163365180205628754534825569768007839164365081785545410669990897104247631449412, 55441284375207262871139882109632679118006847574943848515672247766228295892768661871888937606494012813612, 21678845095738879225948798728750813175025317004090499478341374500389015736085087728116709107483606969312, 3084158880278779900543543377706409636344369733744445813072779278364824452506477289449094807185582582211, 191982484347994560268850956851654597459912062108535923872402462698752415162616115120930922437145403242], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 2, 1], [4, 10, 1, 1], [4, 30, 2, 3], [4, 45, 2, 2], [4, 90, 1, 2], [5, 4, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 10, 1, 4], [6, 20, 1, 2], [10, 4, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 12, 2, 1], [12, 20, 1, 2], [12, 20, 2, 1], [12, 60, 2, 3], [15, 4, 2, 1], [15, 8, 1, 1], [15, 8, 2, 1], [20, 8, 1, 1], [20, 24, 2, 1], [30, 4, 2, 1], [30, 8, 1, 1], [30, 8, 2, 1], [60, 8, 2, 2], [60, 8, 4, 1], [60, 24, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times S_3\\times D_5).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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '1440.5889', 'autcentquo_hash': 5889, 'autcentquo_nilpotent': False, 'autcentquo_order': 1440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_5.D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [3, 2, 2], [3, 4, 1], [4, 2, 1], [4, 6, 2], [4, 10, 1], [4, 30, 6], [4, 45, 4], [4, 90, 2], [5, 4, 1], [6, 2, 2], [6, 4, 1], [6, 10, 4], [6, 20, 2], [10, 4, 1], [12, 4, 4], [12, 12, 2], [12, 20, 4], [12, 60, 6], [15, 4, 2], [15, 8, 3], [20, 8, 1], [20, 24, 2], [30, 4, 2], [30, 8, 3], [60, 8, 8], [60, 24, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '720.804', 'commutator_count': 1, 'commutator_label': '90.10', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5010, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 10, 1, 1], [4, 30, 1, 2], [4, 30, 2, 2], [4, 45, 2, 2], [4, 90, 2, 1], [5, 4, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 10, 1, 4], [6, 20, 1, 2], [10, 4, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 12, 1, 2], [12, 20, 1, 2], [12, 20, 2, 1], [12, 60, 1, 2], [12, 60, 2, 2], [15, 4, 2, 1], [15, 8, 1, 1], [15, 8, 2, 1], [20, 8, 1, 1], [20, 24, 1, 2], [30, 4, 2, 1], [30, 8, 1, 1], [30, 8, 2, 1], [60, 8, 2, 2], [60, 8, 4, 1], [60, 24, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 64512, 'exponent': 60, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '720.804', 'hash': 5010, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 12, 30], 'inner_gens': [[1, 10, 744], [17, 2, 1128], [721, 338, 24]], 'inner_hash': 804, 'inner_nilpotent': False, 'inner_order': 720, 'inner_split': True, 'inner_tex': 'D_{10}.S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 20], [4, 24], [8, 15]], 'label': '1440.5010', 'linC_count': 324, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 384, 'linQ_dim': 12, 'linQ_dim_count': 224, 'linR_count': 16, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C30.(C4*D6)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 50, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 75, 'number_divisions': 55, 'number_normal_subgroups': 88, 'number_subgroup_autclasses': 234, 'number_subgroup_classes': 310, 'number_subgroups': 2388, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 11], [3, 8], [4, 564], [5, 4], [6, 88], [10, 4], [12, 480], [15, 32], [20, 56], [30, 32], [60, 160]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 360], 'outer_gens': [[1, 10, 24], [1, 2, 984], [721, 10, 24], [361, 362, 24]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 15], [8, 9], [16, 4], [32, 1]], 'representations': {'PC': {'code': 3325937840427595664100828815536067748258052365523813900062952001044743, 'gens': [1, 2, 5], 'pres': [8, -2, -2, -2, -3, -2, -2, -3, -5, 5760, 161, 41, 482, 66, 515, 29764, 22572, 11780, 116, 19597, 10965, 141, 5390, 5398, 222, 18447, 18455]}, 'Perm': {'d': 19, 'gens': [377918376086184, 7348561, 12516744, 753220451269704, 15301704, 3, 6706022400, 6799906713600000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{30}.(C_4\\times D_6)', 'transitive_degree': 120, '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': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 3, 3], 'aut_gens': [[1, 2, 12], [114, 61, 40], [1, 2, 84], [73, 10, 12], [109, 38, 84], [73, 2, 12], [73, 74, 12], [73, 82, 60], [9, 98, 12], [9, 2, 12]], 'aut_group': '1152.138373', 'aut_hash': 2700593171953895555, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152, 'aut_permdeg': 14, 'aut_perms': [6267324096, 11543, 7620487, 121, 7, 5167, 87096367, 26824089600, 1956286080], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 2, 1], [3, 2, 2, 1], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 4, 1], [4, 18, 1, 1], [6, 2, 2, 1], [6, 4, 1, 1], [12, 4, 2, 2], [12, 12, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_6^2:C_2^3', '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': 12, 'autcentquo_group': '144.186', 'autcentquo_hash': 186, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [3, 2, 2], [3, 4, 1], [4, 2, 1], [4, 6, 4], [4, 18, 1], [6, 2, 2], [6, 4, 1], [12, 4, 4], [12, 12, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '72.46', 'commutator_count': 1, 'commutator_label': '18.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 140, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 1, 4], [4, 18, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 12, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 12, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '72.46', 'hash': 140, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 6], 'inner_gens': [[1, 10, 84], [77, 2, 132], [73, 26, 12]], 'inner_hash': 46, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': False, 'inner_tex': 'S_3\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 6]], 'label': '144.140', 'linC_count': 2, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 44, 'linQ_dim': 8, 'linQ_dim_count': 37, 'linR_count': 37, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12.D6', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 13, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 24, 'number_divisions': 23, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 45, 'number_subgroup_classes': 84, 'number_subgroups': 256, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 19], [3, 8], [4, 44], [6, 8], [12, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 36, 36], 'outer_gens': [[73, 10, 60], [1, 74, 60], [37, 38, 12], [42, 61, 40]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, '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, 4], [8, 1]], 'representations': {'PC': {'code': 260914992432058291422730534857, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -3, -2, -2, -3, 432, 121, 31, 1442, 338, 2019, 1593, 69, 1810, 88, 1739]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [17959695, 36972346, 14659948, 42523844, 28816400, 42015870]}, 'Perm': {'d': 14, 'gens': [6314119039, 6354398719, 12593, 18619, 13971242880, 20122058880]}}, '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': 'C_{12}.D_6', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
