Formats: - HTML - YAML - JSON - 2026-07-25T13:31:44.961722
Query: /api/gps_groups/?_offset=0
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8], [1, 2, 40], [25, 6, 8], [24, 3, 9], [1, 34, 8], [1, 3, 8], [1, 26, 8], [1, 3, 12], [5, 30, 8], [1, 6, 8]], 'aut_group': '1152.157664', 'aut_hash': 6171274809820688557, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152, 'aut_permdeg': 11, 'aut_perms': [1, 11653224, 8166480, 4, 24133200, 7985040, 24174240, 7985784, 3669864], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [3, 2, 1, 1], [4, 3, 8, 1], [6, 2, 1, 1], [6, 2, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times C_2^3:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '192.1493', 'autcent_hash': 1493, 'autcent_nilpotent': False, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^3:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 2, 1], [4, 3, 8], [6, 2, 7]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 42, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 2, 1, 1], [4, 3, 2, 4], [6, 2, 1, 7]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 28, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.14', 'hash': 42, 'hyperelementary': 2, 'id': 128990, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 3], 'inner_gens': [[1, 2, 8], [1, 2, 40], [1, 18, 8]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 8]], 'label': '48.42', 'linC_count': 336, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 48, 'linQ_dim': 5, 'linQ_dim_count': 48, 'linR_count': 48, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.C2^3', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 20, 'number_normal_subgroups': 43, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 54, 'number_subgroups': 76, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [6, 14]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[29, 30, 8], [24, 27, 13], [5, 27, 12], [1, 3, 12], [1, 2, 12], [5, 6, 12], [1, 6, 8]], 'outer_group': '192.1493', 'outer_hash': 1493, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 8, 'outer_perms': [5381, 24609, 30235, 19342, 18619, 35278, 12341], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^3:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12]], 'representations': {'PC': {'code': 60426338625, 'gens': [1, 2, 4], 'pres': [5, -2, -2, -2, -2, -3, 26, 408, 58, 409]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705946294637, 705946295608, 141602720900]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 147006733710, 25631507539, 75365757720, 82446106855]}, 'Perm': {'d': 11, 'gens': [368070, 5328, 5329, 288, 3991680]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.C_2^3', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}