Query:
/api/gps_groups/?_offset=0
{'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': 5, 'aut_exponent': 24, 'aut_gen_orders': [3, 4, 6, 2, 4, 4, 3, 3, 6, 6, 2, 2], 'aut_gens': [[64885519, 44719201, 1217311, 65103776, 53803441], [64888219, 44719201, 1217311, 65103776, 53803441], [65124019, 44716501, 730351, 65103776, 53803441], [21627979, 731701, 44717851, 65103776, 879733], [21627979, 44719201, 44717851, 65103776, 53803441], [65126719, 731701, 44712451, 65103776, 53803441], [64882819, 731701, 12271996, 45709163, 879733], [65129419, 44719201, 730351, 65103776, 53803441], [65126719, 44719201, 1217311, 65103776, 53803441], [65126719, 1215961, 33905296, 12904118, 53803441], [64882819, 734401, 45078301, 12904118, 53803441], [64888219, 1215961, 44717851, 65103776, 53803441], [64885519, 44716501, 64980011, 53807491, 1097596]], 'aut_group': '31104.mm', 'aut_hash': 8544079931638136565, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 31104, 'aut_permdeg': 15, 'aut_perms': [878602735010, 529797035768, 355818589634, 355540757880, 791434794440, 1045199094213, 442604903160, 791632897922, 839634823192, 1045602598412, 878660260328, 74696814475], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 2, 1], [2, 9, 1, 2], [2, 27, 2, 1], [2, 81, 1, 1], [3, 2, 2, 1], [3, 2, 4, 1], [3, 4, 1, 1], [3, 4, 8, 1], [3, 8, 4, 1], [6, 6, 2, 1], [6, 6, 8, 1], [6, 12, 8, 1], [6, 18, 2, 1], [6, 18, 4, 1], [6, 36, 1, 1], [6, 54, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(D_4\\times \\GL(2,3))', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '31104.mm', 'autcentquo_hash': 8544079931638136565, 'autcentquo_nilpotent': False, 'autcentquo_order': 31104, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(D_4\\times \\GL(2,3))', 'cc_stats': [[1, 1, 1], [2, 3, 2], [2, 9, 2], [2, 27, 2], [2, 81, 1], [3, 2, 6], [3, 4, 9], [3, 8, 4], [6, 6, 10], [6, 12, 8], [6, 18, 6], [6, 36, 1], [6, 54, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '648.732', 'commutator_count': 1, 'commutator_label': '81.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 732, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18.4', 1], ['6.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 2], [2, 27, 1, 2], [2, 81, 1, 1], [3, 2, 1, 6], [3, 4, 1, 9], [3, 8, 1, 4], [6, 6, 1, 10], [6, 12, 1, 8], [6, 18, 1, 6], [6, 36, 1, 1], [6, 54, 1, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 6, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '648.732', 'hash': 732, 'hyperelementary': 1, 'id': 542748, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 6, 6, 3], 'inner_gens': [[64885519, 1215961, 44717851, 65103776, 53803441], [65129419, 44719201, 1217311, 65103776, 53803441], [21627979, 44719201, 1217311, 32298821, 53803441], [64885519, 44719201, 33657766, 65103776, 879733], [64885519, 44719201, 1217311, 12904118, 53803441]], 'inner_hash': 732, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3:S_3^3', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 24], [4, 18], [8, 4]], 'label': '648.732', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:S3^3', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 54, 'number_divisions': 54, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 165, 'number_subgroup_classes': 630, 'number_subgroups': 6996, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 159], [3, 80], [6, 408]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [65468321, 65468321, 882539, 64885519, 64885519], 'outer_gens': [[64885519, 44719201, 64982711, 53807491, 33902551], [64885519, 44719201, 64980011, 53807491, 33902551], [64885519, 1215961, 735751, 32298821, 879733], [64885519, 44716501, 730351, 32298821, 879733], [64885519, 1221361, 1220011, 32298821, 879733]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [396, 341, 186, 339, 107], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 24], [4, 18], [8, 4]], 'representations': {'PC': {'code': 828050992474867285832432151083, 'gens': [1, 2, 3, 5, 7], 'pres': [7, -2, -3, -2, -3, -2, -3, -3, 57, 632, 58, 675, 1068, 102, 1027, 622]}, 'GLZN': {'d': 2, 'p': 90, 'gens': [733051, 65464271, 879733, 1097596, 64885519, 45079696, 731701]}, 'Perm': {'d': 12, 'gens': [40723200, 41091120, 25, 147, 240, 91450800, 130682160]}}, 'schur_multiplier': [2, 2, 6], '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_3:S_3^3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}