Formats: - HTML - YAML - JSON - 2025-12-30T04:51:43.001104
Query: /api/gps_groups/?_offset=0
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 42, 'aut_gen_orders': [6, 7], 'aut_gens': [[1, 6], [1, 30], [37, 6]], 'aut_group': '42.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 42, 'aut_permdeg': 7, 'aut_perms': [604, 3498], 'aut_phi_ratio': 3.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 7, 1, 2], [6, 7, 1, 2], [7, 6, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_7', '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': 42, 'autcentquo_group': '42.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 42, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_7', 'cc_stats': [[1, 1, 1], [2, 7, 1], [3, 7, 2], [6, 7, 2], [7, 6, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '42.1', 'commutator_count': 1, 'commutator_label': '7.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [3, 7, 2, 1], [6, 7, 2, 1], [7, 6, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 42, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[6, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '42.1', 'hash': 1, 'hyperelementary': 1, 'id': 152471, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [6, 7], 'inner_gens': [[1, 30], [19, 6]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 42, 'inner_split': True, 'inner_tex': 'F_7', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 6], [6, 1]], 'label': '42.1', 'linC_count': 1, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1, 'linQ_dim': 6, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'F7', 'ngens': 3, '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': 5, 'number_conjugacy_classes': 7, 'number_divisions': 5, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 26, 'old_label': None, 'order': 42, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 7], [3, 14], [6, 14], [7, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 1]], 'representations': {'PC': {'code': 37793315, 'gens': [1, 3], 'pres': [3, -2, -3, -7, 6, 272, 113]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [73201889465453740, 74634653676981556]}, 'Lie': [{'d': 1, 'q': 7, 'gens': [346, 873], 'family': 'AGL'}, {'d': 1, 'q': 7, 'gens': [346, 873], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 7, 'gens': [351, 1030]}, 'Perm': {'d': 7, 'gens': [719, 186, 4320]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'F_7', 'transitive_degree': 7, 'wreath_data': None, 'wreath_product': False}