Formats: - HTML - YAML - JSON - 2026-09-22T11:48:30.886980
Query: /api/gps_groups/?_offset=0
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [20, 4, 2], 'aut_gens': [[873460098142623179389602209644892650585571564852335, 383691507931091386758258565563740844961908370748160], [960905282869288884797521732780353381585780200703865, 645876609121925686719473288805375188095186504782529], [718944595352215069368417524179443946560110255947729, 881263432564956763403730670563312947243865183635904], [1048300395436943164069917074731095608143610245152775, 164021882476314236389125244727733696756166212322848]], 'aut_group': '960.10871', 'aut_hash': 10871, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 40, 'aut_perms': [651484207202906980216756211559060320579762423006, 353775167343812031412650107009843352854852513094, 663658459281326222818834147010266121577253435560], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 20, 2, 1], [3, 20, 1, 1], [4, 30, 1, 2], [5, 24, 1, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 20, 4, 1], [8, 30, 4, 1], [10, 24, 1, 1], [10, 24, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.34', 'autcentquo_hash': 34, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 20, 2], [3, 20, 1], [4, 30, 2], [5, 24, 1], [6, 20, 7], [8, 30, 4], [10, 24, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '120.34', 'commutator_count': 1, 'commutator_label': '120.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '60.5'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 950, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['240.90', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 20, 1, 2], [3, 20, 1, 1], [4, 30, 1, 2], [5, 24, 1, 1], [6, 20, 1, 3], [6, 20, 2, 2], [8, 30, 2, 2], [10, 24, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 57, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.189', 'hash': 950, 'hyperelementary': 1, 'id': 129665, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [3, 4], 'inner_gens': [[873460098142623179389602209644892650585571564852335, 1029251913462739648170227714034217169338081266330054], [705495111338243025415396094301641703980223705895465, 383691507931091386758258565563740844961908370748160]], 'inner_hash': 34, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'S_5', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [4, 10], [5, 4], [6, 6]], 'label': '480.950', 'linC_count': 12, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 4, 'linQ_dim': 9, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,5):C2^2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 14, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 24, 'number_divisions': 20, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 78, 'number_subgroups': 826, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 43], [3, 20], [4, 60], [5, 24], [6, 140], [8, 120], [10, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1186397458801114847900684359069942869305648233204687, 383691507931091386758258565563740844961908370748160], [1186397458801114847900684359069942869305648233204687, 826377542339693536611577113022497314854335057280849]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 6], [5, 4], [6, 2], [8, 2], [12, 2]], 'representations': {'Perm': {'d': 42, 'gens': [873460098142623179389602209644892650585571564852335, 383691507931091386758258565563740844961908370748160]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,5):C_2^2', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}