Formats: - HTML - YAML - JSON - 2025-11-17T18:23:34.889994
Query: /api/gps_groups/?_offset=0
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [2, 4, 20], 'aut_gens': [[1, 2], [11, 22], [1, 26], [3, 2]], 'aut_group': '160.207', 'aut_hash': 207, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 160, 'aut_permdeg': 9, 'aut_perms': [16, 6480, 162737], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 10, 2, 1], [5, 2, 2, 1], [10, 2, 2, 1], [20, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', '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, 1], [4, 2, 1], [4, 10, 2], [5, 2, 2], [10, 2, 2], [20, 2, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '20.4', 'commutator_count': 1, 'commutator_label': '10.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 10, 1, 2], [5, 2, 2, 1], [10, 2, 2, 1], [20, 2, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 20, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[2, -1, 4]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '20.4', 'hash': 4, 'hyperelementary': 2, 'id': 151879, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 10], 'inner_gens': [[1, 38], [5, 2]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 20, 'inner_split': True, 'inner_tex': 'D_{10}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 9]], 'label': '40.4', 'linC_count': 4, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5:Q8', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, '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': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 13, 'number_divisions': 8, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 12, 'number_subgroups': 24, 'old_label': None, 'order': 40, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [4, 22], [5, 4], [10, 4], [20, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [10, 0], 'outer_gens': [[11, 2], [1, 26]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 2], [8, 1]], 'representations': {'PC': {'code': 41683230015235, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -5, 80, 305, 21, 434, 34, 515]}, 'Lie': [{'d': 2, 'q': 19, 'gens': [123480, 124003, 85659, 10772], 'family': 'CSOMinus'}], 'GLFp': {'d': 2, 'p': 19, 'gens': [129999, 27002]}, 'Perm': {'d': 13, 'gens': [40286719, 12593, 18619, 559198080]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5:Q_8', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}