Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '243.61', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 72, 'aut_gen_orders': [18, 8, 24], 'aut_gens': [[1, 3, 9, 27, 243], [164, 414, 9, 631, 259], [91, 673, 18, 314, 489], [92, 431, 18, 613, 85]], 'aut_group': None, 'aut_hash': 5481057200711108027, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17006112, 'aut_permdeg': 486, 'aut_perms': 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'aut_phi_ratio': 34992.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 2], [3, 1, 4, 1], [3, 3, 6, 1], [3, 3, 72, 1], [9, 3, 162, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^7.C_3:S_3.C_6^2.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '6561.1396077', 'autcent_hash': 7374565384238773860, 'autcent_nilpotent': True, 'autcent_order': 6561, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '2592.ca', 'autcentquo_hash': 3538079198398614329, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SU(3,2):D_6', 'cc_stats': [[1, 1, 1], [3, 1, 8], [3, 3, 78], [9, 3, 162]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '81.15', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 422, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4], [3, 3, 2, 39], [9, 3, 6, 27]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 9360, 'exponent': 9, 'exponents_of_order': [6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '81.15', 'hash': 422, 'hyperelementary': 3, 'id': 295394, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [3, 3, 1, 3, 3], 'inner_gens': [[1, 3, 9, 45, 243], [1, 3, 9, 27, 261], [1, 3, 9, 27, 243], [10, 3, 9, 27, 243], [1, 12, 9, 27, 243]], 'inner_hash': 15, 'inner_nilpotent': True, 'inner_order': 81, 'inner_split': True, 'inner_tex': 'C_3^4', 'inner_used': [1, 2, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 243], [9, 6]], 'label': '729.422', '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': 'C3^2.C3^4', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 249, 'number_divisions': 71, 'number_normal_subgroups': 400, 'number_subgroup_autclasses': 33, 'number_subgroup_classes': 589, 'number_subgroups': 1471, 'old_label': None, 'order': 729, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 242], [9, 486]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 72, 'outer_gen_orders': [12, 6, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[164, 349, 9, 542, 248], [2, 512, 9, 242, 84], [2, 5, 18, 375, 669]], 'outer_group': None, 'outer_hash': 4381912502052973173, 'outer_nilpotent': False, 'outer_order': 209952, 'outer_permdeg': 83, 'outer_perms': [16167996779730258555473952285465453107341083530798466933682537250831538373857759633586426310979788866417116096965234478896689, 2709874070470138484694338712535165212115822739919895970324000209936945475300399589989289522239650231252367585711770482244711, 30311505535244929090652701516365288080396443975791698812213011146301428861595820438119178793219475212602374810543728359054447], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^4.C_3:S_3.A_4.D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 36, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 9], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 40], [6, 27], [18, 3]], 'representations': {'PC': {'code': 30133120409736, 'gens': [1, 2, 3, 4, 6], 'pres': [6, 3, 3, 3, 3, 3, 3, 1083, 93, 3143]}, 'Perm': {'d': 36, 'gens': [11584910813152087158942842652412741184823, 22197005032721123397287238566827864706356, 32850391621342916487785293966423530395956, 33154308002685149286115670155364150402356, 43792958104144393837218401267281941004800, 98356]}}, 'schur_multiplier': [3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 9], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2.C_3^4', 'transitive_degree': 81, 'wreath_data': None, 'wreath_product': False}