-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3840.bf', 'ambient_counter': 32, 'ambient_order': 3840, 'ambient_tex': 'C_2\\times F_5\\times \\GL(2,\\mathbb{Z}/4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 120, 'counter': 457, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3840.bf.32.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.39', 'subgroup_hash': 39, 'subgroup_order': 120, 'subgroup_tex': 'D_5\\times A_4', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '3840.bf', 'aut_centralizer_order': 64, 'aut_label': '32.E', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '480.1189', 'aut_weyl_index': 128, 'centralizer': '480.B', 'complements': ['120.EW', '120.HG', '120.HA', '120.EX', '120.HB'], 'conjugacy_class_count': 2, 'contained_in': ['16.A', '16.B', '16.F', '16.BN', '16.BT'], 'contains': ['64.A', '96.M', '128.F', '160.BJ'], 'core': '32.E', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72001, 92011, 12201, 94116, 8161], 'label': '3840.bf.32.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.E', 'normal_contained_in': ['16.A', '16.B', '16.F'], 'normal_contains': ['64.A', '96.M'], 'normalizer': '1.a1', 'old_label': '32.e1', 'projective_image': '3840.bf', 'quotient_action_image': '8.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '32.E', 'subgroup_fusion': None, 'weyl_group': '480.1189'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [4, 2, 2, 3, 5, 2, 2], 'aut_gens': [[1, 6, 12], [1, 6, 84], [5, 60, 78], [1, 6, 108], [1, 66, 78], [25, 6, 12], [7, 6, 12], [67, 6, 12]], 'aut_group': '480.1189', 'aut_hash': 1189, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 480, 'aut_permdeg': 9, 'aut_perms': [9, 5040, 16, 5760, 34, 41040, 90720], 'aut_phi_ratio': 15.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 15, 1, 1], [3, 4, 2, 1], [5, 2, 2, 1], [6, 20, 2, 1], [10, 6, 2, 1], [15, 8, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5\\times S_4', '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': 60, 'autcentquo_group': '480.1189', 'autcentquo_hash': 1189, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 5, 1], [2, 15, 1], [3, 4, 2], [5, 2, 2], [6, 20, 2], [10, 6, 2], [15, 8, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '120.39', 'commutator_count': 1, 'commutator_label': '20.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 39, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['10.1', 1], ['12.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 15, 1, 1], [3, 4, 2, 1], [5, 2, 2, 1], [6, 20, 2, 1], [10, 6, 2, 1], [15, 8, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 30, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '120.39', 'hash': 39, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [6, 2, 10], 'inner_gens': [[1, 60, 114], [67, 6, 12], [31, 6, 12]], 'inner_hash': 39, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': False, 'inner_tex': 'D_5\\times A_4', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 6, 'irrep_stats': [[1, 6], [2, 6], [3, 2], [6, 2]], 'label': '120.39', 'linC_count': 12, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 2, 'linQ_dim': 7, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D5*A4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 16, 'number_divisions': 9, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 24, 'number_subgroups': 116, 'old_label': None, 'order': 120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 23], [3, 8], [5, 4], [6, 40], [10, 12], [15, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [3, 0], 'outer_gens': [[1, 6, 84], [5, 60, 78]], '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': 3, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [3, 2], [4, 1], [8, 1], [12, 1]], 'representations': {'PC': {'code': 854573617691797464131, 'gens': [1, 3, 4], 'pres': [5, -2, -3, -2, 2, -5, 10, 902, 502, 2283, 788, 58, 2404]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1081249281, 1131437057, 1074906625, 2183565504, 1074939649]}, 'Perm': {'d': 9, 'gens': [7, 10080, 41040, 90720, 37]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_5\\times A_4', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [4, 12, 12, 2, 10, 12, 12], 'aut_gens': [[12211, 72009, 88111, 90312, 88211, 12281], [12211, 72009, 72309, 34143, 88211, 92251], [156209, 72009, 94011, 14062, 92011, 88051], [92201, 72009, 50316, 14062, 12201, 92251], [76219, 72009, 152319, 14142, 88211, 12121], [12211, 72009, 90011, 130237, 92011, 12281], [92201, 152019, 14001, 10262, 92011, 88051], [92201, 72009, 114304, 14142, 12201, 92251]], 'aut_group': None, 'aut_hash': 1483974879331033022, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 61440, 'aut_permdeg': 48, 'aut_perms': [7270097062406548665379863880022850115030821524940660411832391, 174894643565875825335786362160824267687670753713596420668292, 147381237708647174285383740880237405794003485426611046730414, 40079281769968161433988783371233597627783243094825022242073, 1711710200357906132947618862651571380897195208005912864115299, 232975830393164902411894669673216302036052213885257993453012, 5718962853188742813148899057515018623512941228647728101580527], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 5, 1, 2], [2, 5, 2, 1], [2, 6, 2, 1], [2, 10, 2, 1], [2, 12, 2, 1], [2, 15, 1, 2], [2, 15, 2, 1], [2, 30, 2, 1], [2, 60, 2, 1], [3, 8, 1, 1], [4, 5, 4, 2], [4, 10, 2, 2], [4, 12, 2, 3], [4, 15, 4, 2], [4, 30, 2, 2], [4, 60, 2, 11], [5, 4, 1, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 8, 4, 1], [6, 40, 1, 2], [6, 40, 2, 1], [6, 40, 4, 1], [10, 4, 1, 1], [10, 4, 2, 1], [10, 8, 2, 1], [10, 12, 1, 2], [10, 12, 2, 1], [10, 24, 2, 1], [10, 48, 2, 1], [12, 40, 4, 4], [15, 32, 1, 1], [20, 48, 2, 3], [30, 32, 1, 1], [30, 32, 2, 1], [30, 32, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_5\\times A_4).C_2^4.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '480.1189', 'autcentquo_hash': 1189, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 3, 4], [2, 5, 4], [2, 6, 2], [2, 10, 2], [2, 12, 2], [2, 15, 4], [2, 30, 2], [2, 60, 2], [3, 8, 1], [4, 5, 8], [4, 10, 4], [4, 12, 6], [4, 15, 8], [4, 30, 4], [4, 60, 22], [5, 4, 1], [6, 8, 7], [6, 40, 8], [10, 4, 3], [10, 8, 2], [10, 12, 4], [10, 24, 2], [10, 48, 2], [12, 40, 16], [15, 32, 1], [20, 48, 6], [30, 32, 7]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '960.11361', 'commutator_count': 1, 'commutator_label': '120.43', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 32, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['20.3', 1], ['96.195', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 3, 1, 4], [2, 5, 1, 4], [2, 6, 1, 2], [2, 10, 1, 2], [2, 12, 1, 2], [2, 15, 1, 4], [2, 30, 1, 2], [2, 60, 1, 2], [3, 8, 1, 1], [4, 5, 2, 4], [4, 10, 2, 2], [4, 12, 1, 6], [4, 15, 2, 4], [4, 30, 2, 2], [4, 60, 1, 6], [4, 60, 2, 8], [5, 4, 1, 1], [6, 8, 1, 3], [6, 8, 2, 2], [6, 40, 1, 4], [6, 40, 2, 2], [10, 4, 1, 3], [10, 8, 1, 2], [10, 12, 1, 4], [10, 24, 1, 2], [10, 48, 1, 2], [12, 40, 2, 4], [12, 40, 4, 2], [15, 32, 1, 1], [20, 48, 1, 6], [30, 32, 1, 3], [30, 32, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 1023684480, 'exponent': 60, 'exponents_of_order': [8, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1920.240396', 'hash': 5245989847885864621, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 1, 4, 12, 2, 10], 'inner_gens': [[12211, 72009, 8301, 90312, 88211, 12281], [12211, 72009, 88111, 90312, 88211, 12281], [92201, 72009, 88111, 50117, 88211, 92091], [12211, 72009, 134106, 90312, 12201, 92251], [12211, 72009, 88111, 10102, 88211, 12281], [12211, 72009, 8101, 94192, 88211, 12281]], 'inner_hash': 11361, 'inner_nilpotent': False, 'inner_order': 960, 'inner_split': False, 'inner_tex': 'C_2\\times F_5\\times S_4', 'inner_used': [1, 3, 4, 6], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 40], [3, 32], [4, 8], [6, 8], [8, 10], [12, 8], [24, 2]], 'label': '3840.bf', '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': 'C2*F5*GL(2,Z/4)', '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, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 68, 'number_characteristic_subgroups': 76, 'number_conjugacy_classes': 140, 'number_divisions': 104, 'number_normal_subgroups': 264, 'number_subgroup_autclasses': 2228, 'number_subgroup_classes': 6074, 'number_subgroups': 80772, 'old_label': None, 'order': 3840, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 335], [3, 8], [4, 1712], [5, 4], [6, 376], [10, 220], [12, 640], [15, 32], [20, 288], [30, 224]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [8001, 8001, 8001, 8001, 8001], 'outer_gens': [[12211, 72009, 8101, 118313, 88211, 92091], [76219, 72009, 72109, 118313, 88211, 92091], [12211, 72009, 72109, 54317, 88211, 92091], [12211, 72009, 88111, 14112, 88211, 12281], [76219, 152019, 88111, 154308, 88211, 12281]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [362880, 16, 368047, 367920, 1174342], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 20], [3, 16], [4, 18], [6, 12], [8, 8], [12, 10], [16, 2], [24, 2]], 'representations': {'PC': {'code': '23916915778682086780133533227577233948904804313086516374677291868213750050162200939212046403', 'gens': [1, 2, 3, 5, 8, 9], 'pres': [10, -2, -2, -2, -2, -2, -2, -3, -2, 2, -5, 6122, 82, 3424, 13334, 144, 31225, 14675, 175, 5626, 19076, 9647, 5337, 2467, 12988, 7608, 4918, 878, 268, 14449, 9659]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [8009, 76219, 8101, 12201, 8081, 72009, 130311, 156209, 8003, 8201]}, 'Perm': {'d': 15, 'gens': [362886, 268719897600, 354940548607, 5167, 5047, 5040, 362125600566, 1, 175314585726, 3260759]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times F_5\\times \\GL(2,\\mathbb{Z}/4)', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', '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, 4], 'aut_gens': [[1, 2, 8], [17, 18, 8], [5, 22, 8], [5, 2, 12], [5, 22, 24], [5, 2, 8], [9, 6, 8]], 'aut_group': '128.2163', 'aut_hash': 2163, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 128, 'aut_permdeg': 12, 'aut_perms': [98155447, 23, 302376360, 132452776, 136095240, 222848663], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 4, 1], [4, 1, 4, 1], [4, 2, 2, 2], [4, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', '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, 1, 4], [4, 2, 8]], 'center_label': '8.2', 'center_order': 8, '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'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 84, 'exponent': 4, 'exponents_of_order': [5], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '8.5', 'hash': 25, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 1, 2], 'inner_gens': [[1, 2, 24], [1, 2, 8], [17, 2, 8]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4]], 'label': '32.25', 'linC_count': 32, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 8, 'linQ_dim': 4, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4*D4', 'ngens': 3, 'nilpotency_class': 2, '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': 9, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 20, 'number_divisions': 15, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 47, 'number_subgroups': 62, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 11], [4, 20]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[5, 18, 8], [5, 22, 8], [5, 22, 12], [13, 18, 12]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [7, 23, 1576, 5880], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1]], 'representations': {'PC': {'code': 17367114, 'gens': [1, 2, 4], 'pres': [5, 2, 2, 2, 2, 2, 26, 483, 58]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931074, 16917782, 35931238]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1173753, 1816751, 611879, 438254, 1565004]}, 'Perm': {'d': 8, 'gens': [1569, 5176, 9, 11520, 16]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times D_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
