Formats: - HTML - YAML - JSON - 2026-03-15T15:46:39.901100
Query: /api/gps_groups_test/?_offset=0
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_gens': [[1, 2], [11, 18], [1, 6], [5, 2]], 'aut_group': '40.12', 'aut_order': 40, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 2, 1], [5, 2, 2, 1], [10, 2, 2, 1]], 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [5, 2, 2], [10, 2, 2]], 'center_label': '2.1', 'central_product': True, 'central_quotient': '10.1', 'commutator_count': 1, 'commutator_label': '5.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1'], 'composition_length': 3, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'direct_factorization': [['10.1', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [5, 2, 2, 1], [10, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[2, 1, 2]], 'frattini_label': '1.1', 'frattini_quotient': '20.4', 'hash': 4, 'hyperelementary': 2, 'id': 52, 'irrC_degree': 2, 'irrQ_degree': 4, 'irrep_stats': [[1, 4], [2, 4]], 'label': '20.4', 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D10', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': None, 'normal_index_bound': None, 'normal_order_bound': None, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 8, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 10, 'number_subgroups': 22, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 11], [5, 4], [10, 4]], 'outer_equivalence': False, 'outer_group': '4.2', 'outer_order': 4, 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 2]], 'representations': {'PC': {'code': 2624387, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 109, 16, 146]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7430093, 16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504, 501]}, 'Perm': {'d': 7, 'gens': [126, 1, 966]}}, 'schur_multiplier': [2], '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': 'D_{10}', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}