Formats: - HTML - YAML - JSON - 2025-11-21T23:56:57.453816
Query: /api/gps_groups/?_offset=0
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '99.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 30, 'aut_gen_orders': [2, 30], 'aut_gens': [[1], [89], [79]], 'aut_group': '60.13', 'aut_hash': 13, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 60, 'aut_permdeg': 12, 'aut_perms': [362880, 40285473], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [9, 1, 6, 1], [11, 1, 10, 1], [33, 1, 20, 1], [99, 1, 60, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{30}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 30, 'autcent_group': '60.13', 'autcent_hash': 13, 'autcent_nilpotent': True, 'autcent_order': 60, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{30}', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [3, 1, 2], [9, 1, 6], [11, 1, 10], [33, 1, 20], [99, 1, 60]], 'center_label': '99.1', 'center_order': 99, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '11.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [9, 1, 6, 1], [11, 1, 10, 1], [33, 1, 20, 1], [99, 1, 60, 1]], 'element_repr_type': 'PC', 'elementary': 33, 'eulerian_function': 1, 'exponent': 99, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [3, 11], 'faithful_reps': [[1, 0, 60]], 'familial': True, 'frattini_label': '3.1', 'frattini_quotient': '33.1', 'hash': 1, 'hyperelementary': 33, 'id': 160253, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': 2, 'irrep_stats': [[1, 99]], 'label': '99.1', 'linC_count': 60, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 1, 'linQ_dim': 16, 'linQ_dim_count': 1, 'linR_count': 30, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C99', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 99, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 99, 'order_factorization_type': 22, 'order_stats': [[1, 1], [3, 2], [9, 6], [11, 10], [33, 20], [99, 60]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 30], 'outer_gen_pows': [0, 0], 'outer_gens': [[89], [79]], 'outer_group': '60.13', 'outer_hash': 13, 'outer_nilpotent': True, 'outer_order': 60, 'outer_permdeg': 12, 'outer_perms': [362880, 40285473], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{30}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [9, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [6, 1], [10, 1], [20, 1], [60, 1]], 'representations': {'PC': {'code': 3523119, 'gens': [1], 'pres': [3, -3, -3, -11, 9, 22]}, 'GLFp': {'d': 2, 'p': 89, 'gens': [48560782]}, 'Perm': {'d': 20, 'gens': [1013709170073600000, 36288000, 243332058851481600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [99], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{99}', 'transitive_degree': 99, 'wreath_data': None, 'wreath_product': False}