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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46787', 'ambient_counter': 46787, 'ambient_order': 1728, 'ambient_tex': 'C_2\\times C_6^2:D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46787.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.46787', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 32, 'centralizer': '144.a1.a1', 'complements': ['144.m1.a1', '144.bs1.a1', '144.o1.a1', '144.bu1.a1', '144.o1.b1', '144.bu1.b1', '144.m1.b1', '144.bs1.b1', '144.o1.c1', '144.bu1.c1', '144.o1.d1', '144.bu1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.c1.a1', '6.f1.a1', '6.f1.c1'], 'contains': ['24.g1.a1', '24.cj1.a1', '36.ck1.a1', '36.cl1.a1', '36.cm1.a1', '48.be1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2599, 4227, 2960, 4266, 1560, 3873, 2231, 3930], 'generators': [13468, 33321, 329687, 285389, 345948, 548809], 'label': '1728.46787.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.c1.a1', '6.c1.a1', '6.f1.c1', '6.f1.a1'], 'normal_contains': ['24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '864.4690', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', '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, 6, 6, 6], 'aut_gens': [[5047, 1, 5790, 30, 41040, 90720], [5046, 1, 5790, 30, 41040, 90720], [5047, 1, 10128, 48, 90720, 41040], [775, 1, 5790, 48, 90720, 131760], [126745, 1, 51150, 30, 41040, 90720], [5047, 1, 80688, 30, 41040, 90720]], 'aut_group': '864.4000', 'aut_hash': 4000, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 864, 'aut_permdeg': 15, 'aut_perms': [316, 13898309095, 467233805178, 100602351629, 1009612882], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 2, 1], [3, 2, 1, 1], [3, 8, 3, 1], [4, 18, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6^2: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': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 18, 2], [3, 2, 1], [3, 8, 3], [4, 18, 2], [6, 2, 1], [6, 6, 2], [6, 8, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '72.43', 'commutator_count': 1, 'commutator_label': '36.11', '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': 189, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['72.43', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 1, 2], [3, 2, 1, 1], [3, 8, 1, 3], [4, 18, 1, 2], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1260, 'exponent': 12, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '144.189', 'hash': 189, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 3, 3, 2, 2], 'inner_gens': [[5047, 1, 10128, 48, 90720, 41040], [5047, 1, 5790, 30, 41040, 90720], [775, 1, 5790, 30, 90720, 131760], [5095, 1, 5790, 30, 41040, 90720], [126727, 1, 126030, 30, 41040, 90720], [126727, 1, 51150, 30, 41040, 90720]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_3:S_4', 'inner_used': [1, 3, 4, 5], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 8], [3, 4], [6, 2]], 'label': '144.189', 'linC_count': 18, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 18, 'linQ_dim': 5, 'linQ_dim_count': 18, 'linR_count': 18, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6:S4', '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': 12, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 18, 'number_divisions': 18, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 86, 'number_subgroups': 450, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 43], [3, 26], [4, 36], [6, 38]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[5047, 1, 5790, 48, 41040, 90720], [5046, 1, 10110, 48, 90720, 41040]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [7, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [6, 2]], 'representations': {'PC': {'code': 10844907660983108922775100553, 'gens': [1, 2, 4, 5], 'pres': [6, -2, -2, -3, -2, 2, -3, 121, 31, 146, 1017, 447, 3964, 1630, 286, 88, 3461]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [48234383051, 140826816560, 142764393341]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 18685, 9565, 2665, 1777, 1801]}, 'Perm': {'d': 9, 'gens': [5047, 1, 5790, 30, 41040, 90720]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6:S_4', 'transitive_degree': 18, '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': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 12, 6, 12, 6, 12], 'aut_gens': [[329295, 192688, 173796, 252459, 208961], [592731, 329489, 317555, 252459, 241887], [329295, 137418, 158298, 252459, 560177], [592731, 609169, 469756, 505311, 515883], [329295, 598193, 166194, 241875, 252471], [329295, 593293, 12145, 252459, 505299], [329295, 285587, 481124, 560193, 505299], [329295, 137418, 328923, 241875, 208961]], 'aut_group': None, 'aut_hash': 8765063099206293740, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9216, 'aut_permdeg': 38, 'aut_perms': [356687815650180491291197543550721770602250486, 98631104855017234839743416254758466751149614, 281779835186876897114942576196803940700595496, 326461513717763429449058281300523838397215444, 508854386204979089342462496212427298863973154, 495060207007763464354985760608081422961362644, 98631104854862216466400769978518956406822322], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 12, 2, 1], [2, 36, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [4, 6, 2, 1], [4, 12, 2, 1], [4, 18, 2, 1], [4, 36, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [6, 3, 2, 2], [6, 3, 4, 1], [6, 6, 1, 2], [6, 6, 2, 3], [6, 6, 4, 1], [6, 8, 1, 1], [6, 8, 2, 2], [6, 8, 4, 1], [6, 12, 4, 2], [6, 12, 8, 1], [6, 16, 1, 1], [6, 16, 2, 2], [6, 16, 4, 1], [6, 36, 4, 1], [12, 6, 4, 1], [12, 12, 4, 2], [12, 12, 8, 1], [12, 18, 4, 1], [12, 24, 4, 1], [12, 24, 8, 1], [12, 36, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_6\\times A_4).C_2^6.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.202', 'autcent_hash': 202, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 12, 2], [2, 36, 2], [3, 1, 2], [3, 2, 3], [3, 8, 3], [3, 16, 3], [4, 6, 2], [4, 12, 2], [4, 18, 2], [4, 36, 2], [6, 1, 6], [6, 2, 9], [6, 3, 8], [6, 6, 12], [6, 8, 9], [6, 12, 16], [6, 16, 9], [6, 36, 4], [12, 6, 4], [12, 12, 16], [12, 18, 4], [12, 24, 12], [12, 36, 4]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '144.183', 'commutator_count': 1, 'commutator_label': '72.47', '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': 46787, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['288.855', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 12, 1, 2], [2, 36, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [3, 16, 1, 1], [3, 16, 2, 1], [4, 6, 1, 2], [4, 12, 1, 2], [4, 18, 1, 2], [4, 36, 1, 2], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 3, 2, 4], [6, 6, 1, 4], [6, 6, 2, 4], [6, 8, 1, 3], [6, 8, 2, 3], [6, 12, 2, 8], [6, 16, 1, 3], [6, 16, 2, 3], [6, 36, 2, 2], [12, 6, 2, 2], [12, 12, 2, 8], [12, 18, 2, 2], [12, 24, 2, 2], [12, 24, 4, 2], [12, 36, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 131040, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4690', 'hash': 46787, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [1, 2, 6, 2, 6], 'inner_gens': [[329295, 192688, 173796, 252459, 208961], [329295, 192688, 2611, 241875, 208961], [329295, 290879, 173796, 241875, 252471], [329295, 500002, 470162, 252459, 208961], [329295, 192688, 165788, 252459, 208961]], 'inner_hash': 183, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3\\times S_4', 'inner_used': [2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 54], [3, 24], [4, 12], [6, 30]], 'label': '1728.46787', 'linC_count': 128, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 16, 'linQ_dim': 7, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*C6^2:D12', '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': 54, 'number_characteristic_subgroups': 50, 'number_conjugacy_classes': 144, 'number_divisions': 88, 'number_normal_subgroups': 106, 'number_subgroup_autclasses': 653, 'number_subgroup_classes': 1179, 'number_subgroups': 8324, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 111], [3, 80], [4, 144], [6, 672], [12, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [21953, 21953, 21953, 21953, 21953], 'outer_gens': [[329295, 181320, 8771, 241875, 208961], [329295, 181320, 20153, 241875, 560177], [329295, 192688, 173796, 515895, 560177], [329295, 192688, 173796, 252459, 560177], [592731, 181320, 20153, 505311, 208961]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [806401, 1, 127, 367927, 5057], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, '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], [3, 8], [4, 22], [6, 14], [8, 6], [12, 12]], 'representations': {'PC': {'code': 533821624729984981153743822106665450463292452506774205227948053, 'gens': [1, 2, 3, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 605, 74, 732, 102, 733, 24638, 12335, 7160, 3119, 158, 12985, 3922, 5875, 214, 23354]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [214622, 19852, 548825, 340271, 158599, 22345, 21977, 33321, 285389]}, 'Perm': {'d': 16, 'gens': [1321086821167, 85696, 806527, 2889377568000, 806400, 304, 4185076896000, 126, 7]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_6^2:D_{12}', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '12.5', '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], [6, 9], [6, 11]], 'aut_group': '12.4', 'aut_hash': 4, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12, 'aut_permdeg': 5, 'aut_perms': [6, 31], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [3, 1, 2, 1], [6, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.4', 'autcent_hash': 4, 'autcent_nilpotent': False, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_6', '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], [3, 1, 2], [6, 1, 6]], 'center_label': '12.5', 'center_order': 12, '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', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [6, 1, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 4, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12.5', 'hash': 5, '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, 12]], 'label': '12.5', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 6, 'linQ_dim': 3, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C6', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 12, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [3, 2], [6, 6]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[6, 9], [6, 11]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4]], 'representations': {'PC': {'code': 273, 'gens': [1, 2], 'pres': [3, -2, -2, -3, 16]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [3362, 16507]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [1030, 2064]}, 'Perm': {'d': 7, 'gens': [720, 24, 4]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_6', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
