Formats: - HTML - YAML - JSON - 2025-11-15T12:58:16.917529
Query: /api/gps_groups/?_offset=0
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 12, 2, 2], 'aut_gens': [[3782, 1815856, 11349061], [43981, 12030046, 2496841], [226920, 12030046, 11349061], [227041, 6355496, 7381], [226920, 1815856, 2496841], [226920, 1815856, 11349061]], 'aut_group': '192.1469', 'aut_hash': 1469, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 10, 'aut_perms': [5040, 1, 80790, 1174320, 367920], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [4, 1, 2, 1], [4, 2, 3, 1], [5, 1, 4, 1], [10, 1, 4, 1], [10, 2, 12, 1], [20, 1, 8, 1], [20, 2, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.45', 'autcent_hash': 45, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_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, 1], [2, 2, 3], [4, 1, 2], [4, 2, 3], [5, 1, 4], [10, 1, 4], [10, 2, 12], [20, 1, 8], [20, 2, 12]], 'center_label': '20.2', 'center_order': 20, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 48, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.13', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [4, 1, 2, 1], [4, 2, 1, 3], [5, 1, 4, 1], [10, 1, 4, 1], [10, 2, 4, 3], [20, 1, 8, 1], [20, 2, 4, 3]], 'element_repr_type': 'GLFp', 'elementary': 2, 'eulerian_function': 868, 'exponent': 20, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [[2, 0, 8]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '40.14', 'hash': 48, 'hyperelementary': 2, 'id': 158856, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 1, 2], 'inner_gens': [[3782, 1815856, 2496841], [3782, 1815856, 11349061], [226920, 1815856, 11349061]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 40], [2, 10]], 'label': '80.48', 'linC_count': 8, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D4:C10', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, '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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 50, 'number_divisions': 18, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 20, 'number_subgroup_classes': 40, 'number_subgroups': 46, 'old_label': None, 'order': 80, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [4, 8], [5, 4], [10, 28], [20, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 12], 'outer_gen_pows': [226982, 226982, 226982], 'outer_gens': [[13618861, 1815856, 41602], [3782, 12030046, 2496841], [13618861, 6355496, 223321]], 'outer_group': '48.35', 'outer_hash': 35, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [1, 24, 46084], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 9], [16, 1]], 'representations': {'PC': {'code': 753045368835, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -2, -5, 421, 42, 58]}, 'GLFp': {'d': 2, 'p': 61, 'gens': [3782, 1815856, 11349061]}, 'Perm': {'d': 13, 'gens': [3133236960, 2091640320, 1516969440, 96, 482671440]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4:C_{10}', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}