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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '62208.s', 'ambient_counter': 19, 'ambient_order': 62208, 'ambient_tex': 'C_6^3.(D_6\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2592, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '62208.s.12.DL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.dl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.hx', 'subgroup_hash': 4408017417877629614, 'subgroup_order': 5184, 'subgroup_tex': '(S_3\\times C_6^2):S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '62208.s', 'aut_centralizer_order': None, 'aut_label': '12.DL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.E', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [3, 46656, 59328, 11232, 31104, 18, 14988, 38880, 1296, 31106], 'label': '62208.s.12.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.Y', 'old_label': '12.dl1', 'projective_image': '62208.s', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DL', 'subgroup_fusion': None, 'weyl_group': '5184.hx'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 6, 12, 3], 'aut_gens': [[1, 6, 36, 216, 432, 2592], [2141, 5178, 180, 1620, 576, 2700], [4673, 42, 2628, 1404, 5040, 108], [3269, 1050, 4248, 1404, 3636, 1296], [3013, 3594, 2952, 1404, 3528, 1296], [4201, 3282, 2628, 1404, 3240, 108]], 'aut_group': None, 'aut_hash': 1185205024585165281, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 54, 'aut_perms': [129528446411614780634831361657221839780872001049214038342228940463069347, 66409650204620372834425544930652626732423089059682098102547573348350812, 66439110745916828337851338858557801017995344011298063886710885164387759, 31646372079112777676076082170458812537394896088051020749659892731157113, 94643875333776734855483584639139077592228611994110719499416437288296227], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 12, 1, 1], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 2, 1], [3, 96, 1, 1], [3, 96, 2, 1], [3, 192, 1, 1], [3, 192, 2, 1], [4, 36, 1, 2], [4, 72, 1, 1], [4, 108, 1, 1], [4, 216, 1, 1], [6, 3, 2, 1], [6, 6, 1, 2], [6, 6, 2, 5], [6, 6, 4, 1], [6, 12, 1, 4], [6, 12, 2, 6], [6, 12, 4, 2], [6, 24, 1, 1], [6, 36, 2, 2], [6, 72, 1, 1], [6, 72, 2, 1], [6, 108, 2, 1], [6, 288, 1, 1], [6, 288, 2, 1], [12, 36, 2, 2], [12, 72, 1, 2], [12, 72, 2, 4], [12, 72, 4, 1], [12, 108, 2, 1], [12, 216, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^2\\times C_6^2).D_6^2', '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': 12, 'autcentquo_group': None, 'autcentquo_hash': 1185205024585165281, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_2^2\\times C_6^2).D_6^2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 6, 2], [2, 12, 1], [2, 36, 1], [2, 108, 1], [3, 2, 2], [3, 3, 2], [3, 4, 1], [3, 6, 2], [3, 96, 3], [3, 192, 3], [4, 36, 2], [4, 72, 1], [4, 108, 1], [4, 216, 1], [6, 3, 2], [6, 6, 16], [6, 12, 24], [6, 24, 1], [6, 36, 4], [6, 72, 3], [6, 108, 2], [6, 288, 3], [12, 36, 4], [12, 72, 14], [12, 108, 2], [12, 216, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5184.hx', 'commutator_count': 1, 'commutator_label': '432.771', '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', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 206, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 6, 1, 2], [2, 12, 1, 1], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 2, 1], [3, 96, 1, 1], [3, 96, 2, 1], [3, 192, 1, 1], [3, 192, 2, 1], [4, 36, 1, 2], [4, 72, 1, 1], [4, 108, 1, 1], [4, 216, 1, 1], [6, 3, 2, 1], [6, 6, 1, 2], [6, 6, 2, 7], [6, 12, 1, 6], [6, 12, 2, 9], [6, 24, 1, 1], [6, 36, 2, 2], [6, 72, 1, 1], [6, 72, 2, 1], [6, 108, 2, 1], [6, 288, 1, 1], [6, 288, 2, 1], [12, 36, 2, 2], [12, 72, 1, 2], [12, 72, 2, 6], [12, 108, 2, 1], [12, 216, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 12, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 10], [12, 1, 2]], 'familial': False, 'frattini_label': '12.5', 'frattini_quotient': '432.745', 'hash': 4408017417877629614, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 6, 2, 6, 2], 'inner_gens': [[1, 4674, 2772, 216, 4968, 2592], [4873, 6, 2880, 1620, 4464, 4104], [2665, 2994, 36, 216, 432, 2592], [1, 1410, 36, 216, 432, 2592], [3673, 3966, 36, 216, 432, 2592], [1, 1518, 36, 216, 432, 2592]], 'inner_hash': 4408017417877629614, 'inner_nilpotent': False, 'inner_order': 5184, 'inner_split': True, 'inner_tex': '(S_3\\times C_6^2):S_4', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 12], [3, 12], [4, 3], [6, 38], [12, 25]], 'label': '5184.hx', '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': '(S3*C6^2):S4', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 61, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 102, 'number_divisions': 66, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 1045, 'number_subgroup_classes': 1127, 'number_subgroups': 23940, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 171], [3, 890], [4, 468], [6, 1854], [12, 1800]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 1800], 'outer_gens': [[5, 3522, 4248, 216, 4428, 2808], [1801, 222, 1440, 216, 1836, 2808]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [4, 5], [6, 14], [8, 1], [12, 21], [24, 9]], 'representations': {'PC': {'code': '1822500070366994349336280086817547654753011473226644226070093462451985042492164055599569767568135506', 'gens': [1, 3, 5, 7, 8, 10], 'pres': [10, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 20, 140222, 27102, 82, 93123, 20413, 138604, 24024, 10984, 144, 8645, 1465, 18926, 8226, 397447, 59547, 21637, 237, 155528, 14068, 68429, 939]}, 'Perm': {'d': 20, 'gens': [262560177969063422, 134847567642417967]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(S_3\\times C_6^2):S_4', 'transitive_degree': 36, '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': 12, 'aut_gen_orders': [6, 12, 12, 12, 12, 12, 12, 4], 'aut_gens': [[1, 6, 36, 432, 2592, 15552, 31104], [15581, 26142, 18564, 38448, 23760, 40176, 1296], [44861, 12474, 3156, 11664, 8208, 55728, 32400], [59357, 55242, 10716, 54864, 13824, 31104, 15552], [22625, 36666, 60180, 27648, 29808, 1296, 40176], [233, 35670, 30504, 45360, 17712, 32400, 55728], [36877, 16710, 38148, 43200, 53136, 40176, 1296], [15065, 32994, 8340, 37152, 58320, 40176, 1296], [1469, 50850, 13296, 41040, 59616, 31104, 15552]], 'aut_group': '5000.ct', 'aut_hash': 1279279635359283046, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 497664, 'aut_permdeg': 296, 'aut_perms': 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8437693201232057581234096050832898053416185375035880343718286424353089463663839697918439188802639513494446796495622035664980903907974640318033276444123470684599710480844504707418390893006701579175036703023924766603749935854341958770699167396643194018548695247966482760469007121264699846620667645300943170928203625602276131133743569763709062361210520319591884560215740185183259855586069817648874167247614080117645170943863216270142274895535784580742163567897962942253622681714057029752897506623093406132634862202463423765611863947959006646893107220565659320543689761927475107187544877077409602615123889244], 'aut_phi_ratio': 24.0, '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, 72, 1, 1], [2, 108, 2, 1], [2, 216, 1, 2], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 1, 1], [3, 6, 2, 2], [3, 12, 1, 1], [3, 12, 2, 1], [3, 288, 1, 1], [3, 288, 2, 1], [3, 576, 1, 1], [3, 576, 2, 1], [4, 72, 1, 1], [4, 108, 2, 1], [4, 216, 1, 6], [4, 216, 2, 2], [4, 432, 1, 2], [6, 2, 1, 2], [6, 3, 2, 3], [6, 4, 1, 3], [6, 4, 2, 1], [6, 6, 1, 7], [6, 6, 2, 20], [6, 6, 4, 8], [6, 6, 8, 1], [6, 12, 1, 17], [6, 12, 2, 46], [6, 12, 4, 42], [6, 12, 8, 12], [6, 108, 4, 1], [6, 144, 1, 1], [6, 216, 2, 5], [6, 216, 4, 2], [6, 288, 1, 1], [6, 288, 2, 1], [6, 432, 1, 1], [6, 432, 2, 1], [6, 576, 1, 2], [6, 576, 2, 3], [6, 576, 4, 1], [6, 1728, 1, 1], [6, 1728, 2, 1], [12, 108, 4, 1], [12, 144, 1, 1], [12, 216, 2, 9], [12, 216, 4, 6], [12, 216, 8, 2], [12, 432, 1, 5], [12, 432, 2, 9], [12, 432, 4, 2], [12, 1728, 1, 1], [12, 1728, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_5\\wr C_4', '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': None, 'autcentquo_hash': 8360958546735120612, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^4.C_6.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 7], [2, 12, 1], [2, 72, 1], [2, 108, 2], [2, 216, 2], [3, 2, 2], [3, 3, 2], [3, 4, 1], [3, 6, 5], [3, 12, 3], [3, 288, 3], [3, 576, 3], [4, 72, 1], [4, 108, 2], [4, 216, 10], [4, 432, 2], [6, 2, 2], [6, 3, 6], [6, 4, 5], [6, 6, 87], [6, 12, 373], [6, 108, 4], [6, 144, 1], [6, 216, 18], [6, 288, 3], [6, 432, 3], [6, 576, 12], [6, 1728, 3], [12, 108, 4], [12, 144, 1], [12, 216, 58], [12, 432, 31], [12, 1728, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '31104.cu', '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'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 19, '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, 72, 1, 1], [2, 108, 1, 2], [2, 216, 1, 2], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 1, 1], [3, 6, 2, 2], [3, 12, 1, 1], [3, 12, 2, 1], [3, 288, 1, 1], [3, 288, 2, 1], [3, 576, 1, 1], [3, 576, 2, 1], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 10], [4, 432, 1, 2], [6, 2, 1, 2], [6, 3, 2, 3], [6, 4, 1, 5], [6, 6, 1, 7], [6, 6, 2, 40], [6, 12, 1, 35], [6, 12, 2, 169], [6, 108, 2, 2], [6, 144, 1, 1], [6, 216, 1, 2], [6, 216, 2, 8], [6, 288, 1, 1], [6, 288, 2, 1], [6, 432, 1, 1], [6, 432, 2, 1], [6, 576, 1, 2], [6, 576, 2, 5], [6, 1728, 1, 1], [6, 1728, 2, 1], [12, 108, 2, 2], [12, 144, 1, 1], [12, 216, 1, 2], [12, 216, 2, 28], [12, 432, 1, 5], [12, 432, 2, 13], [12, 1728, 1, 1], [12, 1728, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 12, 'exponents_of_order': [8, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 68], [12, 1, 4]], 'familial': False, 'frattini_label': '72.50', 'frattini_quotient': '864.4690', 'hash': 9035446963654338750, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [12, 6, 6, 6, 6, 2, 2], 'inner_gens': [[1, 32694, 5964, 31536, 60480, 15552, 31104], [31249, 6, 15372, 20736, 3024, 32400, 55728], [61501, 3246, 36, 49680, 48816, 1296, 40176], [31105, 26358, 59652, 432, 2592, 15552, 31104], [53569, 2166, 49716, 432, 2592, 15552, 31104], [1, 47958, 16884, 432, 2592, 15552, 31104], [1, 24630, 9108, 432, 2592, 15552, 31104]], 'inner_hash': 5946889041822224518, 'inner_nilpotent': False, 'inner_order': 31104, 'inner_split': True, 'inner_tex': 'C_2\\times C_6^4:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 42], [3, 24], [4, 15], [6, 178], [12, 383]], 'label': '62208.s', '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': 'C6^3.(D6*S4)', 'ngens': 13, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 261, 'number_characteristic_subgroups': 145, 'number_conjugacy_classes': 666, 'number_divisions': 386, 'number_normal_subgroups': 153, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 62208, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 783], [3, 2672], [4, 3312], [6, 23760], [12, 31680]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [11232, 0, 31106, 0], 'outer_gens': [[19009, 11238, 34596, 39312, 49248, 31104, 15552], [23329, 5190, 38916, 41040, 59616, 31104, 15552], [7993, 27942, 21516, 56592, 4320, 31104, 15552], [23333, 5190, 36924, 41040, 59616, 31104, 15552]], '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': None, 'perfect': False, 'permutation_degree': 30, '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, 19], [6, 42], [8, 6], [12, 115], [24, 170]], 'representations': {'PC': {'code': '451245313523526526016284614640763688927420526040009017447402946190824104037434474441760913413878394706578328314800451215132402039545763996811763260158559998183654265602203915284995258905710027989298944897956351266778551491865402371115946218111185631096363619136829262927226083819759881881457715796', 'gens': [1, 3, 5, 8, 10, 12, 13], 'pres': [13, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 26, 404366, 1275068, 418758, 106, 1468275, 1306672, 387664, 231287, 166560, 121918, 186, 2881949, 890622, 163831, 110024, 226, 1142238, 2648119, 559136, 60105, 3279751, 359457, 333262, 143579, 59976, 27853, 306, 202210, 117983, 19716, 8497, 9914, 7862409, 65555, 257448, 176341, 41414, 21537, 386, 1729738, 144180, 10345, 6926, 24099, 946, 842437, 522338, 5679, 120820, 43613, 1569710, 18303, 188668, 76127, 1611]}, 'Perm': {'d': 30, 'gens': [338845644383267868597295838116, 18643854231788292200731289749723, 9474995539835772767946882959907]}}, 'schur_multiplier': [2, 2, 2, 2, 6], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 36, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^3.(D_6\\times S_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
