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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1088.248', 'ambient_counter': 248, 'ambient_order': 1088, 'ambient_tex': 'C_{136}.C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 1088, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1088.248.544.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '544.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '544.193', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 193, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 544, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_{34}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1088.248', 'aut_centralizer_order': 12288, 'aut_label': '544.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24576, 'centralizer': '1.a1', 'complements': ['2.d1'], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '272.a1', '272.f1'], 'contains': ['1088.a1'], 'core': '544.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9642, 7995, 8251, 6116], 'generators': [1], 'label': '1088.248.544.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '544.a1', 'normal_contained_in': ['32.a1', '272.a1'], 'normal_contains': ['1088.a1'], 'normalizer': '1.a1', 'old_label': '544.a1', 'projective_image': '544.193', 'quotient_action_image': '1.1', 'quotient_action_kernel': '544.193', 'quotient_action_kernel_order': 544, 'quotient_fusion': None, 'short_label': '544.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': '544.236', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 48, 'aut_gen_orders': [16, 16, 24, 8, 8, 2], 'aut_gens': [[1, 2, 4, 8], [545, 5, 2, 233], [545, 547, 822, 329], [545, 822, 547, 424], [545, 3, 5, 473], [545, 278, 4, 424], [1, 547, 4, 536]], 'aut_group': None, 'aut_hash': 5699998382362180818, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 36, 'aut_perms': [162575475360392609348435857141010623272361, 109449795768948362783515289407457140760558, 42141116626566619890437489773065710201297, 295550547084870389289455986942285675258750, 42522642528535697324931906604284653079377, 202126736621668282824662072961617120367937], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 6, 1], [4, 1, 2, 2], [4, 2, 6, 1], [8, 1, 8, 1], [8, 2, 12, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 1, 32, 1], [34, 2, 96, 1], [68, 1, 32, 2], [68, 2, 96, 1], [136, 1, 128, 1], [136, 2, 192, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.(C_2\\times C_{48}).C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': None, 'autcent_hash': 7395273026431593086, 'autcent_nilpotent': True, 'autcent_order': 4096, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{16}\\times C_2^4.C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [4, 1, 4], [4, 2, 6], [8, 1, 8], [8, 2, 12], [17, 1, 16], [34, 1, 48], [34, 2, 96], [68, 1, 64], [68, 2, 96], [136, 1, 128], [136, 2, 192]], 'center_label': '272.23', 'center_order': 272, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '17.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 248, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['2.1', 1], ['32.38', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [4, 1, 2, 2], [4, 2, 1, 6], [8, 1, 4, 2], [8, 2, 2, 6], [17, 1, 16, 1], [34, 1, 16, 3], [34, 2, 16, 6], [68, 1, 32, 2], [68, 2, 16, 6], [136, 1, 64, 2], [136, 2, 32, 6]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 17539200, 'exponent': 136, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 17], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '272.54', 'hash': 248, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 548, 8], [1, 546, 4, 8], [1, 2, 4, 8]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 544], [2, 136]], 'label': '1088.248', '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': 'C136.C2^3', 'ngens': 7, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 680, 'number_divisions': 52, 'number_normal_subgroups': 242, 'number_subgroup_autclasses': 66, 'number_subgroup_classes': 266, 'number_subgroups': 290, 'old_label': None, 'order': 1088, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [4, 16], [8, 32], [17, 16], [34, 240], [68, 256], [136, 512]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 48, 'outer_gen_orders': [12, 48, 48, 16, 16, 24], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 823, 547, 377], [545, 278, 3, 360], [1, 549, 279, 520], [545, 3, 822, 505], [1, 548, 546, 728], [1, 548, 279, 424]], 'outer_group': None, 'outer_hash': 5945176071614498864, 'outer_nilpotent': False, 'outer_order': 6144, 'outer_permdeg': 26, 'outer_perms': [129269504915737337437136101, 225869121460582314392119863, 47854489502615251978368612, 161586879985752780716922576, 225869121460582314391354050, 209440675610440527053607017], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '(C_2\\times C_8\\times A_4).C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 17], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [8, 2], [16, 16], [32, 8], [128, 2]], 'representations': {'PC': {'code': 1160092643002836639174098959, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, -2, -2, -2, -17, 5763, 80, 102, 124]}, 'Perm': {'d': 35, 'gens': [313414327073320586469482319931465728000, 1587326795321342278566413989306368000, 625249533734860170300823019820146688000, 6402373705728000, 930983224284231568360703654967705600000, 1234667501948337223146738581029847040000, 334764638208000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 68], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{136}.C_2^3', 'transitive_degree': 544, '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': '272.46', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 48, 'aut_gen_orders': [16, 12, 48, 12, 4], 'aut_gens': [[18906, 95140161, 7714062], [18906, 37401, 290563002], [708153, 1890600, 205708320], [2571489, 2552721, 249421338], [349704009, 37401, 205708320], [2571489, 1890600, 321419250]], 'aut_group': '1536.408624996', 'aut_hash': 737399360701677454, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 26, 'aut_perms': [75905091810364813774283196, 209222309660816803931434716, 327878235575797253536381603, 203622538035030082598810676, 233544056780311854686787440], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [4, 1, 2, 1], [4, 2, 3, 1], [8, 1, 4, 1], [8, 2, 6, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 48, 1], [68, 1, 32, 1], [68, 2, 48, 1], [136, 1, 64, 1], [136, 2, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_{16}\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '256.55608', 'autcent_hash': 55608, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{16}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [4, 1, 2], [4, 2, 3], [8, 1, 4], [8, 2, 6], [17, 1, 16], [34, 1, 16], [34, 2, 48], [68, 1, 32], [68, 2, 48], [136, 1, 64], [136, 2, 96]], 'center_label': '136.2', 'center_order': 136, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '17.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 193, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['32.38', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [4, 1, 2, 1], [4, 2, 1, 3], [8, 1, 4, 1], [8, 2, 2, 3], [17, 1, 16, 1], [34, 1, 16, 1], [34, 2, 16, 3], [68, 1, 32, 1], [68, 2, 16, 3], [136, 1, 64, 1], [136, 2, 32, 3]], 'element_repr_type': 'GLFp', 'elementary': 2, 'eulerian_function': 34384, 'exponent': 136, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 17], 'faithful_reps': [[2, 0, 64]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '136.15', 'hash': 193, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1], 'inner_gens': [[18906, 257135337, 7714062], [2571216, 95140161, 7714062], [18906, 95140161, 7714062]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 128, 'irrQ_dim': 128, 'irrR_degree': 4, 'irrep_stats': [[1, 272], [2, 68]], 'label': '544.193', 'linC_count': 64, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 8, 'linQ_dim': 24, 'linQ_dim_count': 8, 'linR_count': 32, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'OD16:C34', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, '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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 340, 'number_divisions': 26, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 30, 'number_subgroup_classes': 62, 'number_subgroups': 68, 'old_label': None, 'order': 544, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [4, 8], [8, 16], [17, 16], [34, 112], [68, 128], [136, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 48, 'outer_gen_orders': [2, 2, 2, 48], 'outer_gen_pows': [2571354, 18906, 2571354, 2571354], 'outer_gens': [[18906, 257135337, 233993214], [18906, 37401, 7714062], [18906, 95140161, 344561436], [349704009, 37401, 210851028]], 'outer_group': '384.14574', 'outer_hash': 14574, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 192, 'outer_perms': [5595583159870777171214009893842698048600257745175452484407649725872711984453196564574776563124882393507372551987995960665667704360311368365758732898861093646989103991232035076823858401801213924423424939137815477103623423147338777486537521476562085064063638839490323793573369549153409602142848382880614362230511696665958671511284082298294968173109623606178, 11478850970224075363249399217047056215505552606381871510622231916906567392983943323458853144925052141072681935599971295523181274430572586259794024110698545102348418732313351889087327683533640783733243738039206081701843255478559430947820430404889330858043490753982456080005395759663810350221842705289824149854024217946790760014876096300709223796040, 1849095291190910202026690308931268032397199826603479882553246239609040457656946999269211814162635650898686870673303244132021579681207428838124886451122471435496786720716550300142673265586292908645836845827983769996629277450165916460250061700678876144119901263298957347209983141177648133879346847201932368001677596413891871771152961624143346365692200337641, 107900871624413825386521991183812980497021937679906691453128154508395622636638941500014548712589317938675114915483795411145112546934103068007744609681815047348402985001097467132442122428342262924388356194363538707086705860133345346551822662536256534739020076351307994377050150595125474880760714552424130376410130088233479919257326913315483318728584963815604], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{48}:C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 17], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [8, 1], [16, 8], [32, 4], [128, 1]], 'representations': {'PC': {'code': 2837377259010847080448, 'gens': [1, 3, 4], 'pres': [6, -2, -17, -2, -2, -2, -2, 12, 5510, 69, 88]}, 'GLFp': {'d': 2, 'p': 137, 'gens': [18906, 95140161, 7714062]}, 'Perm': {'d': 33, 'gens': [2978863815797762108496860676096000000, 1629484621320921002409183539871744000, 1086511080841299437022706003476480000, 334764638208000, 805839124554122228896064701906944000, 263396395085763368908085856657408000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 68], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\OD_{16}:C_{34}', 'transitive_degree': 272, 'wreath_data': None, 'wreath_product': False}
