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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.8372', 'ambient_counter': 8372, 'ambient_order': 1728, 'ambient_tex': 'C_{48}.D_{18}', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 54, 'counter': 123, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.8372.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.36', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.8372', 'aut_centralizer_order': 576, 'aut_label': '32.a1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 576, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [683, 765, 782, 8621, 1065, 2550, 9131, 7996], 'generators': [864, 28, 576, 12], 'label': '1728.8372.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1', '16.e1.b1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '288.110', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '54.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 6, 'aut_gen_orders': [3, 3, 2, 2, 6], 'aut_gens': [[1, 3], [1, 22], [1, 39], [2, 51], [2, 5], [20, 15]], 'aut_group': '108.28', 'aut_hash': 28, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 108, 'aut_permdeg': 11, 'aut_perms': [4556304, 11088384, 1, 169567, 26386807], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 1, 6, 1], [6, 1, 2, 1], [6, 1, 6, 1], [9, 1, 18, 1], [18, 1, 18, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^2:D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '108.28', 'autcent_hash': 28, 'autcent_nilpotent': False, 'autcent_order': 108, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^2: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, 1], [3, 1, 8], [6, 1, 8], [9, 1, 18], [18, 1, 18]], 'center_label': '54.9', 'center_order': 54, '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', '3.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [6, 1, 2, 4], [9, 1, 6, 3], [18, 1, 6, 3]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 12, 'exponent': 18, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '18.5', 'hash': 9, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 54]], 'label': '54.9', 'linC_count': 648, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 27, 'linQ_dim': 8, 'linQ_dim_count': 27, 'linR_count': 162, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C18', 'ngens': 4, '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': 54, 'number_divisions': 16, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 20, 'number_subgroups': 20, 'old_label': None, 'order': 54, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 8], [6, 8], [9, 18], [18, 18]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [3, 3, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 22], [1, 39], [2, 51], [2, 5], [20, 15]], 'outer_group': '108.28', 'outer_hash': 28, 'outer_nilpotent': False, 'outer_order': 108, 'outer_permdeg': 11, 'outer_perms': [4556304, 11088384, 1, 169567, 26386807], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2:D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [6, 6]], 'representations': {'PC': {'code': 467051, 'gens': [1, 2], 'pres': [4, -3, -2, -3, -3, 21, 46]}, 'GLFp': {'d': 2, 'p': 19, 'gens': [13719, 75456]}, 'Perm': {'d': 14, 'gens': [6227020800, 357120, 79833600, 80884]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 18], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{18}', 'transitive_degree': 54, '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': '96.176', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 36, 'aut_gen_orders': [18, 6, 6, 12, 36, 36, 12], 'aut_gens': [[1, 2, 36], [881, 890, 828], [21, 874, 828], [13, 2, 1476], [1331, 22, 270], [435, 14, 54], [443, 866, 1278], [447, 886, 270]], 'aut_group': None, 'aut_hash': 615940292106638721, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 54, 'aut_perms': [195984168659305446005715886751977836172229512910482872731098756401280437, 195987272722494149671436817098703726093843577169253889172526367868824891, 38365646307389935481726415206356491716776688250233017293405093159269672, 52406211347826355637357831720351522320678469499337633939158251662243258, 130458499574860196635224165571681398291461696812557923412282171323711428, 117572024614499079523566575609824324339273857409594278443490450608368947, 22254005389346660065755350868209838527296596046677792449498086663812388], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 18, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 18, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 4, 1, 1], [6, 4, 2, 1], [6, 18, 4, 1], [8, 1, 4, 1], [8, 2, 2, 1], [8, 18, 4, 1], [9, 2, 3, 1], [9, 2, 6, 1], [12, 1, 4, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 4, 1, 1], [12, 4, 2, 1], [12, 18, 4, 1], [16, 2, 8, 1], [16, 9, 8, 1], [16, 18, 4, 1], [18, 2, 3, 1], [18, 2, 6, 1], [18, 4, 3, 1], [18, 4, 6, 1], [24, 1, 8, 1], [24, 2, 4, 2], [24, 2, 8, 1], [24, 4, 2, 1], [24, 4, 4, 1], [24, 18, 8, 1], [36, 2, 6, 1], [36, 2, 12, 1], [36, 4, 3, 1], [36, 4, 6, 1], [48, 2, 16, 1], [48, 4, 8, 1], [48, 4, 16, 1], [48, 9, 16, 1], [48, 18, 8, 1], [72, 2, 12, 1], [72, 2, 24, 1], [72, 4, 6, 1], [72, 4, 12, 1], [144, 4, 24, 1], [144, 4, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{18}.(C_2^4\\times C_{12}).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.260', 'autcent_hash': 260, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '108.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 108, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{18}:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 18, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 1], [4, 18, 2], [6, 1, 2], [6, 2, 5], [6, 4, 3], [6, 18, 4], [8, 1, 4], [8, 2, 2], [8, 18, 4], [9, 2, 9], [12, 1, 4], [12, 2, 8], [12, 4, 3], [12, 18, 4], [16, 2, 8], [16, 9, 8], [16, 18, 4], [18, 2, 9], [18, 4, 9], [24, 1, 8], [24, 2, 16], [24, 4, 6], [24, 18, 8], [36, 2, 18], [36, 4, 9], [48, 2, 16], [48, 4, 24], [48, 9, 16], [48, 18, 8], [72, 2, 36], [72, 4, 18], [144, 4, 72]], 'center_label': '24.2', 'center_order': 24, 'central_product': True, 'central_quotient': '72.17', 'commutator_count': 1, 'commutator_label': '18.2', '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': 8372, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['576.469', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 18, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 18, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 4, 1, 1], [6, 4, 2, 1], [6, 18, 2, 2], [8, 1, 4, 1], [8, 2, 2, 1], [8, 18, 2, 2], [9, 2, 3, 1], [9, 2, 6, 1], [12, 1, 4, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 4, 1, 1], [12, 4, 2, 1], [12, 18, 2, 2], [16, 2, 4, 2], [16, 9, 8, 1], [16, 18, 4, 1], [18, 2, 3, 1], [18, 2, 6, 1], [18, 4, 3, 1], [18, 4, 6, 1], [24, 1, 8, 1], [24, 2, 4, 2], [24, 2, 8, 1], [24, 4, 2, 1], [24, 4, 4, 1], [24, 18, 4, 2], [36, 2, 6, 1], [36, 2, 12, 1], [36, 4, 3, 1], [36, 4, 6, 1], [48, 2, 8, 2], [48, 4, 4, 2], [48, 4, 8, 2], [48, 9, 16, 1], [48, 18, 8, 1], [72, 2, 12, 1], [72, 2, 24, 1], [72, 4, 6, 1], [72, 4, 12, 1], [144, 4, 12, 2], [144, 4, 24, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 209664, 'exponent': 144, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 24]], 'familial': False, 'frattini_label': '24.2', 'frattini_quotient': '72.48', 'hash': 8372, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 18, 2], 'inner_gens': [[1, 898, 36], [869, 2, 900], [1, 866, 36]], 'inner_hash': 17, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_2\\times D_{18}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 96, 'irrQ_dim': 96, 'irrR_degree': 8, 'irrep_stats': [[1, 96], [2, 216], [4, 48]], 'label': '1728.8372', 'linC_count': 3096, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 64, 'linQ_dim': 24, 'linQ_dim_count': 32, 'linR_count': 96, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C48.D18', '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': 58, 'number_characteristic_subgroups': 78, 'number_conjugacy_classes': 360, 'number_divisions': 70, 'number_normal_subgroups': 126, 'number_subgroup_autclasses': 210, 'number_subgroup_classes': 278, 'number_subgroups': 946, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 39], [3, 8], [4, 40], [6, 96], [8, 80], [9, 18], [12, 104], [16, 160], [18, 54], [24, 208], [36, 72], [48, 416], [72, 144], [144, 288]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1315, 866, 1350], [1, 2, 612], [1, 2, 1116], [1, 22, 1332]], 'outer_group': '96.220', 'outer_hash': 220, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 13, 'outer_perms': [3628800, 479001600, 40320, 42027], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{12}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 44, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 8, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 14], [6, 4], [8, 8], [12, 6], [16, 4], [24, 4], [32, 2], [48, 3], [96, 1]], 'representations': {'PC': {'code': 4983765386067907000798466069125418517047274593, 'gens': [1, 2, 5], 'pres': [9, -2, -2, -3, -3, -2, -2, -2, -2, -3, 16165, 46, 866, 101, 867, 20263, 130, 158, 186, 214]}, 'Perm': {'d': 44, 'gens': [60519802266326946225259354809269451613849905695356800, 129269725253673982508418103211444292208037580248140800, 191384582786014718463648402793473272448910306853683200, 3, 253245506020153423038557514401310380595138827621990400, 305164842381510278683471681063692894284211892295270400, 375516343154743529094463148776633529034252763167052800, 51894240, 95943600]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 24], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{48}.D_{18}', 'transitive_degree': 288, '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': '32.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [3, 2, 4], [1, 2, 28], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 18, 4], [17, 2, 4], [1, 2, 20]], 'aut_group': '384.20089', 'aut_hash': 20089, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 10, 'aut_perms': [374407, 1, 823080, 2810574, 2003886, 367920, 5160, 368046], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [4, 1, 2, 1], [4, 1, 6, 1], [8, 1, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '384.20089', 'autcent_hash': 20089, 'autcent_nilpotent': False, 'autcent_order': 384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4:S_4', '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, 7], [4, 1, 8], [8, 1, 16]], 'center_label': '32.36', 'center_order': 32, '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', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 36, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 1, 2, 4], [8, 1, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 28, 'exponent': 8, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '8.5', 'hash': 36, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 32]], 'label': '32.36', 'linC_count': 1792, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 48, 'linQ_dim': 6, 'linQ_dim_count': 48, 'linR_count': 96, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C8', '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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 32, 'number_divisions': 16, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 38, 'number_subgroups': 38, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 8], [8, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 4], [1, 2, 28], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 18, 4], [17, 2, 4], [1, 2, 20]], 'outer_group': '384.20089', 'outer_hash': 20089, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 10, 'outer_perms': [374407, 1, 823080, 2810574, 2003886, 367920, 5160, 368046], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 4]], 'representations': {'PC': {'code': 557068, 'gens': [1, 2, 3], 'pres': [5, -2, 2, 2, -2, -2, 42, 58]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [25038659807093174, 125101739941717066, 24992906222183252]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [34876415, 3397304, 28816400, 3054512, 28233362]}, 'Perm': {'d': 12, 'gens': [40176, 362880, 39916800, 16582, 5167]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 8], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_8', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
