Formats: - HTML - YAML - JSON - 2025-11-10T01:50:43.136035
Query: /api/gps_groups/?_offset=0
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [2, 6, 6, 18], 'aut_gens': [[1, 2, 4], [37, 38, 4], [36, 39, 69], [1, 38, 28], [1, 47, 4]], 'aut_group': '1296.2920', 'aut_hash': 2920, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1296, 'aut_permdeg': 13, 'aut_perms': [1, 255998163, 284509447, 2138981056], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 9, 4, 1], [3, 2, 1, 1], [6, 2, 3, 1], [9, 2, 3, 1], [18, 2, 9, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.S_3^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 18, 'autcentquo_group': '54.6', 'autcentquo_hash': 6, 'autcentquo_nilpotent': False, 'autcentquo_order': 54, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_9:C_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 9, 4], [3, 2, 1], [6, 2, 3], [9, 2, 3], [18, 2, 9]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '18.1', 'commutator_count': 1, 'commutator_label': '9.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.1', 1], ['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 9, 1, 4], [3, 2, 1, 1], [6, 2, 1, 3], [9, 2, 3, 1], [18, 2, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 84, 'exponent': 18, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '24.14', 'hash': 17, 'hyperelementary': 2, 'id': 132232, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [1, 2, 9], 'inner_gens': [[1, 2, 4], [1, 2, 68], [1, 10, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': True, 'inner_tex': 'D_9', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 16]], 'label': '72.17', 'linC_count': 36, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 12, 'linQ_dim': 7, 'linQ_dim_count': 12, 'linR_count': 36, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*D18', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 24, 'number_divisions': 16, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 48, 'number_subgroups': 158, 'old_label': None, 'order': 72, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 39], [3, 2], [6, 6], [9, 6], [18, 18]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [6, 6, 2, 3, 3], 'outer_gen_pows': [0, 0, 0, 2, 2], 'outer_gens': [[1, 38, 44], [37, 38, 20], [1, 39, 4], [36, 2, 21], [1, 2, 20]], 'outer_group': '72.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 7, 'outer_perms': [747, 28, 1680, 1444, 4], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3\\times S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [6, 4]], 'representations': {'PC': {'code': 15089870102915, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -3, -3, 517, 42, 648, 78, 609]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [99161, 5869, 5849, 5941, 5995]}, 'Perm': {'d': 13, 'gens': [94434607, 7, 16, 609725520, 1133733000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times D_{18}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}