Formats: - HTML - YAML - JSON - 2026-07-21T21:19:31.141979
Query: /api/gps_groups/?_offset=0
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [8, 2, 4, 2, 3, 3], 'aut_gens': [[474, 25, 244, 3], [474, 25, 3, 243], [451, 25, 148, 3], [474, 25, 243, 144], [474, 25, 147, 4], [477, 125, 244, 3], [573, 265, 244, 3]], 'aut_group': '144.182', 'aut_hash': 182, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 144, 'aut_permdeg': 9, 'aut_perms': [150716, 86194, 47170, 96371, 173037, 109253], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 4, 2, 1], [4, 9, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_9:C_2', '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': 24, 'autcentquo_group': '144.182', 'autcentquo_hash': 182, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:C_2', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 4, 2], [4, 9, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '36.9', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 4, 1, 2], [4, 9, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '36.9', 'hash': 9, 'hyperelementary': 1, 'id': 149504, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 2, 3, 3], 'inner_gens': [[474, 25, 243, 144], [474, 25, 147, 4], [570, 122, 244, 3], [574, 29, 244, 3]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': False, 'inner_tex': 'C_3^2:C_4', 'inner_used': [1, 3], 'irrC_degree': 4, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [4, 2]], 'label': '36.9', 'linC_count': 2, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 2, 'linQ_dim': 4, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:C4', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 5, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 10, 'number_subgroups': 38, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 9], [3, 8], [4, 18]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 474], 'outer_gens': [[451, 25, 148, 3], [474, 25, 3, 243]], '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': 6, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 2]], 'representations': {'PC': {'code': 14948871955, 'gens': [1, 3, 4], 'pres': [4, -2, -2, -3, 3, 8, 194, 54, 451, 199]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16858733, 20971525]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [11017, 11777, 8101, 8183]}, 'Perm': {'d': 6, 'gens': [474, 25, 244, 3]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:C_4', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}