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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '559872.bi', 'ambient_counter': 35, 'ambient_order': 559872, 'ambient_tex': 'C_6\\wr D_6', 'central': False, 'central_factor': False, 'centralizer_order': 46656, 'characteristic': True, 'core_order': 432, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '559872.bi.1296.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.j1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1296.1067', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1067, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\wr S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.775', 'subgroup_hash': 775, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times C_6^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '559872.bi', 'aut_centralizer_order': None, 'aut_label': '1296.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.J', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6784, -1, 6892], 'generators': [47952, 197856, 186624, 7776, 191808, 326592, 279936], 'label': '559872.bi.1296.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1296.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1296.j1.N', 'projective_image': '559872.bi', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.J', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '432.775', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 10920, 'aut_gen_orders': [12, 12], 'aut_gens': [[1, 2, 12, 72], [253, 44, 337, 159], [252, 405, 287, 371]], 'aut_group': None, 'aut_hash': 7758337322324614110, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 226437120, 'aut_permdeg': 41, 'aut_perms': [6593897624139959330038015176671645460036385430207, 4897710361607405388981572558962103163759402013847], 'aut_phi_ratio': 1572480.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 15, 1], [3, 1, 26, 1], [6, 1, 390, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times A_8\\times \\SL(3,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 10920, 'autcent_group': None, 'autcent_hash': 7758337322324614110, 'autcent_nilpotent': False, 'autcent_order': 226437120, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times A_8\\times \\SL(3,3)', '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, 15], [3, 1, 26], [6, 1, 390]], 'center_label': '432.775', 'center_order': 432, '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', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 775, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 4], ['3.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [3, 1, 2, 13], [6, 1, 2, 195]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 40, 'exponent': 6, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3, 5, 7, 13], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '432.775', 'hash': 775, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 12, 72], [1, 2, 12, 72], [1, 2, 12, 72], [1, 2, 12, 72]], '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, 432]], 'label': '432.775', 'linC_count': None, 'linC_degree': 4, '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*C6^3', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 432, 'number_divisions': 224, 'number_normal_subgroups': 1876, 'number_subgroup_autclasses': 20, 'number_subgroup_classes': 1876, 'number_subgroups': 1876, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 15], [3, 26], [6, 390]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 10920, 'outer_gen_orders': [28, 60], 'outer_gen_pows': [0, 0], 'outer_gens': [[6, 78, 357, 57], [222, 236, 27, 382]], 'outer_group': None, 'outer_hash': 7758337322324614110, 'outer_nilpotent': False, 'outer_order': 226437120, 'outer_permdeg': 41, 'outer_perms': [5752206094899217703858378077196390859017124903751, 11611680569218413968561069664618752936859540660177], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times A_8\\times \\SL(3,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 3, 3, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 208]], 'representations': {'PC': {'code': 3251324602815765, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -3, -2, -3, -2, -3, 36, 80, 124]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [548825, 214622, 340649, 21977, 285389, 21965, 33335]}, 'Perm': {'d': 17, 'gens': [20922789888000, 87178291200, 479001600, 3628800, 80640, 240, 4]}}, 'schur_multiplier': [2, 2, 2, 6, 6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6, 6, 6], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_6^3', 'transitive_degree': 432, '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': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [12, 6, 12, 18, 6, 18, 12, 12], 'aut_gens': [[1, 6, 36, 432, 2592, 15552, 93312], [263593, 46686, 357876, 339120, 106272, 399168, 285120], [417197, 46878, 303660, 332208, 469152, 269568, 290304], [442877, 327894, 289212, 373680, 382320, 134784, 425088], [194717, 545646, 347796, 102384, 13392, 408672, 435024], [476809, 46902, 58728, 332208, 469152, 393984, 290304], [367361, 444558, 506568, 331344, 472608, 35856, 481248], [55081, 390126, 449460, 154224, 54864, 533088, 201744], [511849, 227046, 61524, 479952, 95040, 402192, 3456]], 'aut_group': None, 'aut_hash': 8207797665160455094, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 13436928, 'aut_permdeg': 452, 'aut_perms': 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'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 5], [2, 6, 2, 1], [2, 12, 1, 1], [2, 108, 2, 1], [2, 216, 1, 2], [2, 648, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 6, 1], [3, 6, 1, 2], [3, 6, 2, 1], [3, 6, 3, 1], [3, 6, 6, 3], [3, 6, 18, 1], [3, 12, 1, 2], [3, 12, 2, 1], [3, 12, 3, 1], [3, 12, 6, 2], [3, 12, 18, 1], [3, 2592, 1, 1], [4, 108, 2, 1], [4, 216, 1, 2], [4, 216, 2, 2], [4, 648, 1, 5], [4, 1296, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 3, 2, 2], [6, 3, 6, 3], [6, 6, 1, 8], [6, 6, 2, 17], [6, 6, 3, 3], [6, 6, 4, 7], [6, 6, 6, 21], [6, 6, 8, 1], [6, 6, 12, 12], [6, 6, 18, 3], [6, 6, 24, 2], [6, 6, 36, 4], [6, 6, 72, 1], [6, 12, 1, 20], [6, 12, 2, 47], [6, 12, 3, 7], [6, 12, 4, 42], [6, 12, 6, 48], [6, 12, 8, 12], [6, 12, 12, 62], [6, 12, 18, 11], [6, 12, 24, 20], [6, 12, 36, 22], [6, 12, 72, 8], [6, 108, 4, 1], [6, 108, 12, 1], [6, 216, 2, 4], [6, 216, 4, 2], [6, 216, 6, 3], [6, 216, 12, 4], [6, 216, 36, 2], [6, 648, 2, 1], [6, 648, 6, 2], [6, 1296, 1, 2], [6, 1296, 2, 1], [6, 1296, 6, 1], [6, 2592, 1, 1], [6, 5184, 1, 1], [6, 15552, 1, 1], [9, 2592, 2, 1], [9, 5184, 1, 1], [9, 5184, 2, 1], [12, 108, 4, 1], [12, 108, 12, 1], [12, 216, 2, 4], [12, 216, 4, 6], [12, 216, 6, 3], [12, 216, 8, 2], [12, 216, 12, 8], [12, 216, 24, 4], [12, 216, 36, 2], [12, 216, 72, 2], [12, 648, 2, 5], [12, 648, 6, 6], [12, 1296, 1, 6], [12, 1296, 2, 9], [12, 1296, 4, 2], [12, 1296, 6, 7], [12, 1296, 12, 2], [12, 15552, 1, 1], [18, 2592, 2, 1], [18, 5184, 1, 1], [18, 5184, 2, 3], [18, 5184, 4, 1], [18, 15552, 2, 1], [36, 15552, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2\\times C_6^3).C_3^5.C_2^6.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '24.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 5946030899765991394, 'autcentquo_nilpotent': False, 'autcentquo_order': 559872, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_2\\times C_6^3).C_3^4.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 7], [2, 12, 1], [2, 108, 2], [2, 216, 2], [2, 648, 1], [3, 1, 2], [3, 2, 3], [3, 3, 6], [3, 6, 43], [3, 12, 37], [3, 2592, 1], [4, 108, 2], [4, 216, 6], [4, 648, 5], [4, 1296, 2], [6, 1, 2], [6, 2, 11], [6, 3, 22], [6, 6, 675], [6, 12, 3477], [6, 108, 16], [6, 216, 154], [6, 648, 14], [6, 1296, 10], [6, 2592, 1], [6, 5184, 1], [6, 15552, 1], [9, 2592, 2], [9, 5184, 3], [12, 108, 16], [12, 216, 474], [12, 648, 46], [12, 1296, 98], [12, 15552, 1], [18, 2592, 2], [18, 5184, 11], [18, 15552, 2], [36, 15552, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': False, 'central_quotient': '93312.dd', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 15, 'conjugacy_classes_known': False, 'counter': 35, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 7], [2, 12, 1, 1], [2, 108, 1, 2], [2, 216, 1, 2], [2, 648, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 3, 2, 3], [3, 6, 1, 5], [3, 6, 2, 19], [3, 12, 1, 5], [3, 12, 2, 16], [3, 2592, 1, 1], [4, 108, 1, 2], [4, 216, 1, 6], [4, 648, 1, 5], [4, 1296, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 3, 2, 11], [6, 6, 1, 17], [6, 6, 2, 329], [6, 12, 1, 73], [6, 12, 2, 1702], [6, 108, 2, 8], [6, 216, 1, 8], [6, 216, 2, 73], [6, 648, 2, 7], [6, 1296, 1, 2], [6, 1296, 2, 4], [6, 2592, 1, 1], [6, 5184, 1, 1], [6, 15552, 1, 1], [9, 2592, 2, 1], [9, 5184, 1, 1], [9, 5184, 2, 1], [12, 108, 2, 8], [12, 216, 1, 8], [12, 216, 2, 233], [12, 648, 2, 23], [12, 1296, 1, 6], [12, 1296, 2, 46], [12, 15552, 1, 1], [18, 2592, 2, 1], [18, 5184, 1, 1], [18, 5184, 2, 5], [18, 15552, 2, 1], [36, 15552, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [8, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 144], [12, 0, 612]], 'familial': False, 'frattini_label': '648.757', 'frattini_quotient': '864.4690', 'hash': 4241488071790213181, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 6, 6, 6, 6, 6, 6], 'inner_gens': [[1, 435486, 397632, 427680, 376704, 445392, 289440], [217741, 6, 545868, 432, 2592, 15552, 93312], [544201, 110382, 36, 475632, 4752, 262656, 236304], [241489, 6, 102852, 432, 2592, 15552, 93312], [188353, 6, 468, 432, 2592, 15552, 93312], [241489, 6, 424260, 432, 2592, 15552, 93312], [381889, 6, 528372, 432, 2592, 15552, 93312]], 'inner_hash': 3323133199427353792, 'inner_nilpotent': False, 'inner_order': 93312, 'inner_split': True, 'inner_tex': 'C_2\\times C_6^4.S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 42], [3, 120], [4, 15], [6, 1450], [12, 3515]], 'label': '559872.bi', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C6wrD6', 'ngens': 15, '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, 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': 546, 'number_characteristic_subgroups': 214, 'number_conjugacy_classes': 5166, 'number_divisions': 2666, 'number_normal_subgroups': 222, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 559872, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1359], [3, 3320], [4, 7344], [6, 126216], [9, 20736], [12, 276480], [18, 93312], [36, 31104]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6, 6], 'outer_gen_pows': [326592, 130320, 326592, 326592], 'outer_gens': [[346969, 46686, 125028, 147312, 282528, 15552, 93312], [194717, 545646, 347796, 102384, 13392, 408672, 435024], [101621, 46878, 509748, 339120, 106272, 274752, 285120], [215569, 47958, 303960, 518832, 434160, 165888, 51840]], 'outer_group': '144.197', 'outer_hash': 197, 'outer_nilpotent': True, 'outer_order': 144, 'outer_permdeg': 144, 'outer_perms': [813070977858625807072173948992575236454327914753103444101698985150136703873590569872666239502868044789575739366730562964234046649868410030957336649820915876942557831594604587312429981054568228441875312455200900354769023684838890670427447786565270306, 158263861150980573914807541864249465426724059406861475147328991830668803889362694100854768199660757882477453359423580854395720745693765731829202523561308592353516895296472205702560741965680396813247321632916369919081976123987972829618486097253685106, 4390849613066553776715841051853876977820465367249298168817823350855017510945164564257071384845324618884735973202398856391227466602863052730391321610293754114487114184809031556240194803849106945195396502696612863491026938314755992023192700856227788810, 1719307910704413235196752871927772188232005624074130600021698240453264750361737322979189663493380365469006250892628643160882024607207326963132321332169448302891973676016760393259767201236347842869322064099037226377261903329997716358930683620281776624], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '488825928176712750775774816461662600258426314310097112530527890561048203287574733555487603005105645965254913493597383812830699803134292081077724750079915743934387486630312093356326804046502026232759639245877246954451513335038213935899507396117625132220556886563697004802262847791921116607983268700094844132903624912789362433311623632683477902207317', 'gens': [1, 3, 5, 8, 10, 12, 14], 'pres': [15, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 30, 19596872, 122, 13065123, 29822404, 9333019, 6823384, 2721874, 214, 48245765, 548660, 6669035, 1633550, 260, 17812626, 3863811, 4629276, 3811551, 51321607, 1585507, 258562, 123217, 352, 25194248, 1399748, 372683, 175058, 56505609, 19869, 217884, 306999, 444, 31933450, 31750, 443605, 12970, 80170571, 1313351, 1113566, 23321, 536, 42793932, 2255832, 594447, 50412, 60782413, 1378513, 844288, 564583, 628, 194414, 2370674, 2789, 310604]}, 'Perm': {'d': 30, 'gens': [9495141366552477447845123234767, 18654712517018113153307153423417, 33100923358908400710844458846]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 18, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\wr D_6', 'transitive_degree': 36, 'wreath_data': ['C_6', 'D_6', '6T3'], 'wreath_product': True}
-
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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': [2, 12, 12, 6, 6, 6], 'aut_gens': [[1, 6, 36, 216], [161, 390, 36, 1080], [245, 336, 1026, 1080], [293, 636, 738, 1080], [581, 294, 180, 1080], [145, 912, 954, 216], [1025, 336, 810, 1080]], 'aut_group': None, 'aut_hash': 2799146922247543772, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 40, 'aut_perms': [152030522768379967373104577999489699653687581199, 557382259095836618923315867785923678735990995380, 344298867087126865615646817294812049435188749745, 570725018021525247696910985468092068565123160520, 436309363478781070716095960395067359579637045698, 224214781908969226749757616596692491199107670259], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 9, 2, 1], [2, 18, 2, 1], [3, 1, 2, 1], [3, 3, 6, 1], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 4, 1], [6, 3, 6, 1], [6, 6, 1, 1], [6, 6, 12, 1], [6, 9, 4, 1], [6, 9, 12, 1], [6, 12, 2, 1], [6, 18, 1, 1], [6, 18, 4, 1], [6, 18, 12, 1], [6, 36, 2, 1], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 6, 1], [12, 12, 1, 1], [12, 18, 2, 1], [12, 18, 6, 1], [12, 36, 1, 1], [18, 18, 2, 1], [18, 36, 4, 1], [36, 36, 2, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times \\He_3).C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '24.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '216.102', 'autcentquo_hash': 102, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_6.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 9, 2], [2, 18, 2], [3, 1, 2], [3, 3, 6], [3, 6, 1], [3, 18, 1], [4, 2, 1], [4, 18, 1], [6, 1, 2], [6, 2, 4], [6, 3, 6], [6, 6, 13], [6, 9, 16], [6, 12, 2], [6, 18, 17], [6, 36, 2], [9, 18, 2], [12, 2, 2], [12, 6, 6], [12, 12, 1], [12, 18, 8], [12, 36, 1], [18, 18, 2], [18, 36, 4], [36, 36, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '216.110', 'commutator_count': 1, 'commutator_label': '54.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1067, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['162.10', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [3, 1, 2, 1], [3, 3, 2, 3], [3, 6, 1, 1], [3, 18, 1, 1], [4, 2, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 2, 2], [6, 3, 2, 3], [6, 6, 1, 1], [6, 6, 2, 6], [6, 9, 2, 8], [6, 12, 1, 2], [6, 18, 1, 1], [6, 18, 2, 8], [6, 36, 1, 2], [9, 18, 2, 1], [12, 2, 2, 1], [12, 6, 2, 3], [12, 12, 1, 1], [12, 18, 2, 4], [12, 36, 1, 1], [18, 18, 2, 1], [18, 36, 2, 2], [36, 36, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 117936, 'exponent': 36, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 12]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '72.48', 'hash': 1067, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 6, 6, 1], 'inner_gens': [[1, 966, 1044, 216], [1021, 6, 252, 216], [505, 1086, 36, 216], [1, 6, 36, 216]], 'inner_hash': 110, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_6^2:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 18], [3, 48], [4, 3], [6, 16], [12, 1]], 'label': '1296.1067', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C3wrS3*D4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 33, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 110, 'number_divisions': 65, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': 216, 'number_subgroup_classes': 448, 'number_subgroups': 2800, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 59], [3, 44], [4, 20], [6, 652], [9, 36], [12, 232], [18, 180], [36, 72]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [4, 0, 0], 'outer_gens': [[649, 78, 36, 216], [5, 78, 180, 1080], [13, 60, 1026, 216]], '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': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 7], [6, 28], [8, 1], [12, 7]], 'representations': {'PC': {'code': 512097290824814612035178249279607355395188684464543061, 'gens': [1, 3, 5, 7], 'pres': [8, -2, -3, -2, -3, -2, -3, -2, -3, 16, 23186, 946, 66, 5379, 9419, 41764, 1700, 1588, 116, 27653, 4053, 3773, 166]}, 'Perm': {'d': 13, 'gens': [123753607, 16, 1, 163790040, 7, 614367480, 1124973360, 1597166040]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\wr S_3\\times D_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
