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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9136', 'ambient_counter': 9136, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 400, 'characteristic': False, 'core_order': 100, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9136.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.8', 'subgroup_hash': 8, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1600.9136', 'aut_centralizer_order': 640, 'aut_label': '16.f1', 'aut_quo_index': 8, 'aut_stab_index': 2, 'aut_weyl_group': '32.21', 'aut_weyl_index': 1280, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.m1.b1', '8.m1.d1', '8.o1.b1', '8.s1.b1', '8.u1.b1', '8.v1.b1'], 'contains': ['32.b1.a1', '80.h1.b1', '80.i1.b1', '80.v1.c1', '80.v1.d1'], 'core': '16.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5302, 3721, 8078, 2457, 1050, 5582, 9025, 7404], 'generators': [1222, 320, 40, 16], 'label': '1600.9136.16.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.b1', 'normal_contained_in': ['8.d1.a1', '8.m1.d1', '8.m1.b1'], 'normal_contains': ['32.b1.a1', '80.h1.b1', '80.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.b1', 'projective_image': '160.217', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '100.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [4, 8, 24, 2, 2], 'aut_gens': [[1, 5], [3, 65], [40, 26], [43, 7], [4, 95], [1, 55]], 'aut_group': '960.5693', 'aut_hash': 5693, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 26, 'aut_perms': [132452688999246611361025110, 112751431305824517956146086, 269501317265718416039387070, 83933120542028405485259647, 1], 'aut_phi_ratio': 24.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 24, 1], [10, 1, 24, 1], [20, 1, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\GL(2,5)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 120, 'autcent_group': '960.5693', 'autcent_hash': 5693, 'autcent_nilpotent': False, 'autcent_order': 960, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times \\GL(2,5)', '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], [4, 1, 2], [5, 1, 24], [10, 1, 24], [20, 1, 48]], 'center_label': '100.8', 'center_order': 100, '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', '5.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['5.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 4, 6], [10, 1, 4, 6], [20, 1, 8, 6]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 6, 'exponent': 20, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '50.5', 'hash': 8, 'hyperelementary': 5, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 5], [1, 5]], '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, 100]], 'label': '100.8', 'linC_count': 2880, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 60, 'linQ_dim': 10, 'linQ_dim_count': 60, 'linR_count': 720, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5*C20', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 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': 100, 'number_divisions': 21, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 24, 'number_subgroups': 24, 'old_label': None, 'order': 100, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [4, 2], [5, 24], [10, 24], [20, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 120, 'outer_gen_orders': [4, 8, 24, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[3, 65], [40, 26], [43, 7], [4, 95], [1, 55]], 'outer_group': '960.5693', 'outer_hash': 5693, 'outer_nilpotent': False, 'outer_order': 960, 'outer_permdeg': 26, 'outer_perms': [132452688999246611361025110, 112751431305824517956146086, 269501317265718416039387070, 83933120542028405485259647, 1], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(2,5)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [4, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 12], [8, 6]], 'representations': {'PC': {'code': 13764291, 'gens': [1, 2], 'pres': [4, -5, -2, -2, -5, 21, 34]}, 'GLFp': {'d': 2, 'p': 41, 'gens': [2481157, 2550087]}, 'Perm': {'d': 14, 'gens': [19639065600, 1451520, 96, 6266937600]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5, 20], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_{20}', 'transitive_degree': 100, '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': '80.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 4, 4, 4, 4, 10, 4, 4, 10, 4], 'aut_gens': [[1, 2, 4, 80], [641, 2, 1210, 182], [361, 2, 852, 1360], [321, 842, 852, 720], [161, 42, 450, 342], [1441, 842, 812, 1400], [481, 42, 844, 120], [1161, 842, 52, 280], [201, 42, 1258, 1502], [681, 2, 458, 1342], [1481, 842, 76, 600]], 'aut_group': None, 'aut_hash': 6027430083213153847, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 40960, 'aut_permdeg': 36, 'aut_perms': [269196473858871968094790546142160460153083, 354637802189312074709705167294721868074036, 145017408213925023491838643258710684659629, 95601469497538327023120625067930642951912, 333379656038836095052311344209380876680839, 236501460144259049945619953748470224680342, 294117054678579340650004641947659733657385, 177099531120626088355153398186072443226741, 120418322310483278357233074933845635472446, 46310603937663149989357076322129727740019], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 5, 4, 1], [2, 10, 2, 1], [4, 2, 2, 2], [4, 4, 2, 2], [4, 10, 2, 2], [4, 20, 2, 2], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [10, 1, 4, 3], [10, 2, 2, 3], [10, 2, 8, 4], [10, 4, 4, 1], [10, 4, 16, 1], [10, 5, 16, 1], [10, 10, 8, 1], [20, 2, 8, 2], [20, 4, 4, 2], [20, 4, 8, 2], [20, 4, 16, 2], [20, 8, 4, 2], [20, 8, 16, 2], [20, 10, 8, 2], [20, 20, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_4\\times C_2^6.C_2\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 1718285292446712972, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '40.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 40, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 5, 4], [2, 10, 2], [4, 2, 4], [4, 4, 4], [4, 10, 4], [4, 20, 4], [5, 1, 4], [5, 2, 10], [10, 1, 12], [10, 2, 38], [10, 4, 20], [10, 5, 16], [10, 10, 8], [20, 2, 16], [20, 4, 56], [20, 8, 40], [20, 10, 16], [20, 20, 16]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '80.51', 'commutator_count': 1, 'commutator_label': '20.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9136, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['10.1', 1], ['32.29', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 5, 1, 4], [2, 10, 1, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 4], [4, 10, 1, 2], [4, 10, 2, 1], [4, 20, 1, 4], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [10, 1, 4, 3], [10, 2, 2, 3], [10, 2, 4, 8], [10, 4, 2, 2], [10, 4, 4, 4], [10, 5, 4, 4], [10, 10, 4, 2], [20, 2, 4, 2], [20, 2, 8, 1], [20, 4, 2, 2], [20, 4, 4, 9], [20, 4, 8, 2], [20, 8, 2, 4], [20, 8, 4, 8], [20, 10, 4, 2], [20, 10, 8, 1], [20, 20, 4, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48746880, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '400.219', 'hash': 9136, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 2, 2, 10], 'inner_gens': [[1, 2, 4, 720], [1, 2, 844, 920], [1, 842, 4, 880], [961, 842, 804, 80]], 'inner_hash': 51, 'inner_nilpotent': False, 'inner_order': 80, 'inner_split': False, 'inner_tex': 'C_2^2\\times D_{10}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 80], [2, 140], [4, 60]], 'label': '1600.9136', 'linC_count': 97536, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2304, 'linQ_dim': 14, 'linQ_dim_count': 3584, 'linR_count': 1088, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C10^2.C2^4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 86, 'number_conjugacy_classes': 280, 'number_divisions': 91, 'number_normal_subgroups': 242, 'number_subgroup_autclasses': 378, 'number_subgroup_classes': 718, 'number_subgroups': 2500, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 47], [4, 144], [5, 24], [10, 328], [20, 1056]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 2, 2, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 961, 641, 1220, 0, 0], 'outer_gens': [[641, 2, 450, 1142], [1001, 802, 836, 720], [841, 42, 1234, 1182], [641, 802, 76, 560], [161, 42, 76, 560], [1121, 42, 426, 1142], [321, 802, 68, 1040], [681, 2, 852, 560]], 'outer_group': '512.10494201', 'outer_hash': 8909733522074432791, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 512, 'outer_perms': 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^7\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 26], [8, 28], [16, 11], [32, 2]], 'representations': {'PC': {'code': 1097423387731581219598284079479104757367046339, 'gens': [1, 2, 3, 6], 'pres': [8, 2, 2, 2, 2, 5, 2, 2, 5, 10138, 66, 91, 34565, 22093, 10581, 141, 80646, 166, 81927]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [681481, 30666285, 1198429, 31010893, 52054276, 6133257, 8119947, 685345]}, 'Perm': {'d': 22, 'gens': [51353502436370539729, 12460, 7620480, 40298203, 109847011193484364800, 87091200, 5329, 160598585713210444800]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}^2.C_2^4', 'transitive_degree': 160, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2], 'aut_gens': [[126, 55, 289, 288], [127, 55, 289, 288], [126, 265, 1, 288], [54, 127, 289, 288], [414, 55, 289, 288], [127, 54, 289, 288], [414, 265, 289, 288]], 'aut_group': '64.138', 'aut_hash': 138, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 64, 'aut_permdeg': 8, 'aut_perms': [2309, 526, 5329, 3043, 12316, 18498], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 4, 1], [4, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\wr C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [4, 2, 2]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 11, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [4, 2, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 21, 'exponent': 4, 'exponents_of_order': [4], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '8.5', 'hash': 11, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1, 1], 'inner_gens': [[126, 265, 289, 288], [414, 55, 289, 288], [126, 55, 289, 288], [126, 55, 289, 288]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 2]], 'label': '16.11', 'linC_count': 8, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 8, 'linQ_dim': 3, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*D4', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 10, 'number_divisions': 10, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 27, 'number_subgroups': 35, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 11], [4, 4]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 151, 0], 'outer_gens': [[54, 127, 289, 288], [127, 55, 289, 288], [415, 54, 1, 288], [127, 54, 289, 288]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [126, 55, 289, 288], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2]], 'representations': {'PC': {'code': 8772, 'gens': [1, 2, 3], 'pres': [4, -2, 2, 2, -2, 78, 34]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16322, 16432, 3198]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [8912, 8156, 13286, 14044]}, 'Perm': {'d': 6, 'gens': [126, 55, 289, 288]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times D_4', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
