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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113568.h', 'ambient_counter': 8, 'ambient_order': 113568, 'ambient_tex': 'C_{13}^2:(C_4\\times C_{168})', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 273, 'counter': 809, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '113568.h.416._.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '416.D', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '416.66', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 416, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{104}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '273.5', 'subgroup_hash': None, 'subgroup_order': 273, 'subgroup_tex': 'C_{273}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '113568.h', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [28, 26292, 12], 'label': '113568.h.416._.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '416.D', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '416._.D', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '273.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 12, 'aut_gen_orders': [2, 6, 12], 'aut_gens': [[1], [92], [40], [106]], 'aut_group': '144.178', 'aut_hash': 178, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 144, 'aut_permdeg': 20, 'aut_perms': [121645100408832000, 1778437140480000, 43954713], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [7, 1, 6, 1], [13, 1, 12, 1], [21, 1, 12, 1], [39, 1, 24, 1], [91, 1, 72, 1], [273, 1, 144, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6\\times C_{12}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '144.178', 'autcent_hash': 178, 'autcent_nilpotent': True, 'autcent_order': 144, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6\\times C_{12}', '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], [3, 1, 2], [7, 1, 6], [13, 1, 12], [21, 1, 12], [39, 1, 24], [91, 1, 72], [273, 1, 144]], 'center_label': '273.5', 'center_order': 273, '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': ['3.1', '7.1', '13.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['13.1', 1], ['3.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [7, 1, 6, 1], [13, 1, 12, 1], [21, 1, 12, 1], [39, 1, 24, 1], [91, 1, 72, 1], [273, 1, 144, 1]], 'element_repr_type': 'PC', 'elementary': 273, 'eulerian_function': 1, 'exponent': 273, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3, 7, 13], 'faithful_reps': [[1, 0, 144]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '273.5', 'hash': 5, 'hyperelementary': 273, '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': 144, 'irrQ_dim': 144, 'irrR_degree': 2, 'irrep_stats': [[1, 273]], 'label': '273.5', 'linC_count': 144, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 72, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C273', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 273, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 273, 'order_factorization_type': 11, 'order_stats': [[1, 1], [3, 2], [7, 6], [13, 12], [21, 12], [39, 24], [91, 72], [273, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 6, 12], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[92], [40], [106]], 'outer_group': '144.178', 'outer_hash': 178, 'outer_nilpotent': True, 'outer_order': 144, 'outer_permdeg': 20, 'outer_perms': [121645100408832000, 1778437140480000, 43954713], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6\\times C_{12}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [3, 7, 13], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [6, 1], [12, 2], [24, 1], [72, 1], [144, 1]], 'representations': {'PC': {'code': 15820055, 'gens': [1], 'pres': [3, -3, -7, -13, 9, 46]}, 'GLFp': {'d': 2, 'p': 181, 'gens': [126445716]}, 'Perm': {'d': 23, 'gens': [2248001455555215360000, 729870602452992000, 5748019200]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [273], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{273}', 'transitive_degree': 273, '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': '672.260', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 84, 1092], [20497, 96600, 102564], [4973, 35112, 43596], [100889, 69972, 82320], [2449, 70728, 71820], [46513, 61488, 47040], [44201, 8904, 55776], [75265, 79464, 97188]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 850397184, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 28392.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 169, 2, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 169, 2, 1], [4, 169, 4, 2], [6, 1, 2, 1], [6, 169, 4, 1], [7, 1, 6, 1], [8, 1, 4, 1], [8, 169, 4, 3], [12, 1, 4, 1], [12, 169, 4, 1], [12, 169, 8, 2], [13, 4, 42, 1], [14, 1, 6, 1], [14, 169, 12, 1], [21, 1, 12, 1], [24, 1, 8, 1], [24, 169, 8, 3], [26, 4, 42, 1], [28, 1, 12, 1], [28, 169, 12, 1], [28, 169, 24, 2], [39, 4, 84, 1], [42, 1, 12, 1], [42, 169, 24, 1], [52, 4, 84, 1], [56, 1, 24, 1], [56, 169, 24, 3], [78, 4, 84, 1], [84, 1, 24, 1], [84, 169, 24, 1], [84, 169, 48, 2], [91, 4, 252, 1], [104, 4, 168, 1], [156, 4, 168, 1], [168, 1, 48, 1], [168, 169, 48, 3], [182, 4, 252, 1], [273, 4, 504, 1], [312, 4, 336, 1], [364, 4, 504, 1], [546, 4, 504, 1], [728, 4, 1008, 1], [1092, 4, 1008, 1], [2184, 4, 2016, 1]], '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, 1], [2, 169, 2], [3, 1, 2], [4, 1, 2], [4, 169, 10], [6, 1, 2], [6, 169, 4], [7, 1, 6], [8, 1, 4], [8, 169, 12], [12, 1, 4], [12, 169, 20], [13, 4, 42], [14, 1, 6], [14, 169, 12], [21, 1, 12], [24, 1, 8], [24, 169, 24], [26, 4, 42], [28, 1, 12], [28, 169, 60], [39, 4, 84], [42, 1, 12], [42, 169, 24], [52, 4, 84], [56, 1, 24], [56, 169, 72], [78, 4, 84], [84, 1, 24], [84, 169, 120], [91, 4, 252], [104, 4, 168], [156, 4, 168], [168, 1, 48], [168, 169, 144], [182, 4, 252], [273, 4, 504], [312, 4, 336], [364, 4, 504], [546, 4, 504], [728, 4, 1008], [1092, 4, 1008], [2184, 4, 2016]], 'center_label': '168.6', 'center_order': 168, 'central_product': None, 'central_quotient': '676.10', 'commutator_count': None, 'commutator_label': '169.2', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1', '13.1', '13.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 169, 1, 2], [3, 1, 2, 1], [4, 1, 2, 1], [4, 169, 2, 5], [6, 1, 2, 1], [6, 169, 2, 2], [7, 1, 6, 1], [8, 1, 4, 1], [8, 169, 4, 3], [12, 1, 4, 1], [12, 169, 4, 5], [13, 4, 3, 14], [14, 1, 6, 1], [14, 169, 6, 2], [21, 1, 12, 1], [24, 1, 8, 1], [24, 169, 8, 3], [26, 4, 3, 14], [28, 1, 12, 1], [28, 169, 12, 5], [39, 4, 6, 14], [42, 1, 12, 1], [42, 169, 12, 2], [52, 4, 6, 14], [56, 1, 24, 1], [56, 169, 24, 3], [78, 4, 6, 14], [84, 1, 24, 1], [84, 169, 24, 5], [91, 4, 18, 14], [104, 4, 12, 14], [156, 4, 12, 14], [168, 1, 48, 1], [168, 169, 48, 3], [182, 4, 18, 14], [273, 4, 36, 14], [312, 4, 24, 14], [364, 4, 36, 14], [546, 4, 36, 14], [728, 4, 72, 14], [1092, 4, 72, 14], [2184, 4, 144, 14]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 2184, 'exponents_of_order': [5, 2, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': None, 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '28392.q', 'hash': 562341391272748438, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [4, 13, 13], 'inner_gens': [[1, 420, 62244], [757, 84, 1092], [52417, 84, 1092]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 676, 'inner_split': None, 'inner_tex': 'C_{13}^2:C_4', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '113568.h', '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': 'C13^2:(C4*C168)', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 1, 1, 1, 1, 1, 14, 1, 0, 1, 1, 14, 1, 0, 14, 1, 0, 14, 1, 14, 1, 14, 0, 14, 0, 14, 1, 1, 14, 0, 0, 14, 14, 0, 3, 14, 0, 1, 14, 0, 0, 7, 14, 3, 14, 1, 0, 7, 0, 7, 14, 3, 3, 0, 1, 7, 0, 7, 1, 3, 3, 0, 7, 7, 1, 3, 7, 1, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 60, 'number_characteristic_subgroups': 64, 'number_conjugacy_classes': 7728, 'number_divisions': 280, 'number_normal_subgroups': 328, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 113568, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 339], [3, 2], [4, 1692], [6, 678], [7, 6], [8, 2032], [12, 3384], [13, 168], [14, 2034], [21, 12], [24, 4064], [26, 168], [28, 10152], [39, 336], [42, 4068], [52, 336], [56, 12192], [78, 336], [84, 20304], [91, 1008], [104, 672], [156, 672], [168, 24384], [182, 1008], [273, 2016], [312, 1344], [364, 2016], [546, 2016], [728, 4032], [1092, 4032], [2184, 8064]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 1257984, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': 3, 'perfect': False, 'permutation_degree': 44, 'pgroup': 0, 'primary_abelian_invariants': [4, 8, 3, 7], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '6732673370046379042574606518928035315226679136139304545585073212161879680136474075666017569379714827', 'gens': [1, 5, 6], 'pres': [9, -2, -2, -3, -7, -13, -2, -2, -2, -13, 18, 46, 101, 18904, 22693, 3361181, 737114, 158, 687966, 1719915, 186, 1572487, 3931216, 214, 3538088, 4245713]}, 'GLFq': {'d': 2, 'q': 169, 'gens': [702115112, 390971610, 633621821, 101363010, 41556260, 801250460, 463785558, 772289600, 448893330]}, 'Perm': {'d': 44, 'gens': [2979826173675174842572074905909114879579158105045453, 756110252631068, 64768273131732349893611459479363508401253188856302748, 1135323372556800, 5824125694368593309229993189555776986447270379536984, 378017524708537, 127924972843476976086337887557051277774398241758005427, 1778437619481600, 1532594838314584]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 168], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 1014, 'supersolvable': True, 'sylow_subgroups_known': False, 'tex_name': 'C_{13}^2:(C_4\\times C_{168})', 'transitive_degree': None, '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': '32.3', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 156, 'aut_gen_orders': [2, 12, 2, 52], 'aut_gens': [[1, 4], [1, 204], [1, 388], [1, 212], [73, 4]], 'aut_group': '2496.m', 'aut_hash': 203795305191032416, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2496, 'aut_permdeg': 56, 'aut_perms': [375255912943571649608758266282692034355446318039910280167027600124860110699, 677589312679247996073606266072674447529905821634091604993951237490298668339, 413332299908359263057503103589173484823083967513180090512085688479081373004, 657870009361306646304447708362532377142151620858788439755690031911498039302], 'aut_phi_ratio': 13.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 13, 2, 1], [4, 1, 2, 1], [4, 13, 2, 1], [4, 13, 4, 2], [8, 1, 4, 1], [8, 13, 4, 3], [13, 4, 3, 1], [26, 4, 3, 1], [52, 4, 6, 1], [104, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4\\times F_{13}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 156, 'autcentquo_group': '156.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 156, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{13}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 13, 2], [4, 1, 2], [4, 13, 10], [8, 1, 4], [8, 13, 12], [13, 4, 3], [26, 4, 3], [52, 4, 6], [104, 4, 12]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '52.3', 'commutator_count': 1, 'commutator_label': '13.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '13.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 66, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['52.3', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 13, 1, 2], [4, 1, 2, 1], [4, 13, 2, 5], [8, 1, 4, 1], [8, 13, 4, 3], [13, 4, 3, 1], [26, 4, 3, 1], [52, 4, 6, 1], [104, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 104, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 13], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '104.12', 'hash': 66, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 52, 'inner_gen_orders': [4, 13], 'inner_gens': [[1, 228], [193, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 52, 'inner_split': True, 'inner_tex': 'C_{13}:C_4', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [4, 24]], 'label': '416.66', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 8, 'linQ_dim': 16, 'linQ_dim_count': 8, 'linR_count': 48, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C104:C4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 15, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 56, 'number_divisions': 18, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 44, 'number_subgroups': 260, 'old_label': None, 'order': 416, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 27], [4, 132], [8, 160], [13, 12], [26, 12], [52, 24], [104, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 12], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 308], [1, 204], [105, 356]], 'outer_group': '48.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [24, 10800, 46107], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [4, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [12, 2], [24, 1], [48, 1]], 'representations': {'PC': {'code': 2229695061671779145326799672747753719812107, 'gens': [1, 3], 'pres': [6, -2, -2, -2, -2, -2, -13, 12, 4106, 908, 50, 963, 2409, 69, 2404, 6010, 88, 5765, 6923]}, 'GLFq': {'d': 2, 'q': 169, 'gens': [58921344, 57921720, 395130710, 91709390, 61491841, 38614480]}, 'Perm': {'d': 21, 'gens': [128821980471172861, 12443, 262581480247986498, 6781, 18498, 2823515358096787200]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 8], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{104}:C_4', 'transitive_degree': 104, 'wreath_data': None, 'wreath_product': False}
