Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '81.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 72, 'aut_gen_orders': [12, 6, 6, 9], 'aut_gens': [[1, 3, 9, 27, 81, 243], [326, 24, 340, 63, 324, 567], [568, 512, 414, 147, 324, 486], [325, 104, 409, 235, 405, 162], [1, 99, 102, 279, 486, 567]], 'aut_group': None, 'aut_hash': 8737133825163724417, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 306110016, 'aut_permdeg': 486, 'aut_perms': 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'aut_phi_ratio': 629856.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 8, 1], [3, 1, 18, 1], [3, 3, 72, 1], [3, 9, 54, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^9.C_3^4.Q_8.D_6.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': None, 'autcent_hash': 720202149919232562, 'autcent_nilpotent': False, 'autcent_order': 354294, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^8.C_3^3.C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '864.4661', 'autcentquo_hash': 4661, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [3, 1, 26], [3, 3, 72], [3, 9, 54]], 'center_label': '27.5', 'center_order': 27, 'central_product': True, 'central_quotient': '27.5', 'commutator_count': 1, 'commutator_label': '9.2', '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': 425, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['243.37', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 13], [3, 3, 2, 36], [3, 9, 2, 27]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 520, 'exponent': 3, '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': 425, 'hyperelementary': 3, 'id': 295397, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [1, 3, 3, 3, 1, 1], 'inner_gens': [[1, 3, 9, 27, 81, 243], [1, 3, 9, 189, 81, 243], [1, 3, 9, 513, 81, 243], [1, 84, 252, 27, 81, 243], [1, 3, 9, 27, 81, 243], [1, 3, 9, 27, 81, 243]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 27, 'inner_split': False, 'inner_tex': 'C_3^3', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 81], [3, 72]], 'label': '729.425', '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': 'C3^5:C3', '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': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 153, 'number_divisions': 77, 'number_normal_subgroups': 310, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 1912, 'number_subgroups': 5764, 'old_label': None, 'order': 729, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 728]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 72, 'outer_gen_orders': [6, 8, 4, 6], 'outer_gen_pows': [0, 699, 0, 0], 'outer_gens': [[487, 590, 5, 300, 405, 162], [569, 173, 580, 200, 243, 324], [163, 586, 165, 709, 243, 162], [488, 509, 570, 391, 405, 162]], 'outer_group': None, 'outer_hash': 7594568951909758545, 'outer_nilpotent': False, 'outer_order': 11337408, 'outer_permdeg': 63, 'outer_perms': [1109838323573960626433065418132403302429585879271934057402046730512743640572237797708971, 988502103801468861668300662598567806655631381663214542626054080883892085703633947943246, 989517226955770088734506093232980923397434979954704289137504745567517686996180371142438, 829148139464831468794406981281624482244016567504492646464686398784126046382713028732577], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^8.C_3^2.Q_8.D_6.C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 21, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 40], [6, 36]], 'representations': {'PC': {'code': 1535133696, 'gens': [1, 2, 3, 4, 5, 6], 'pres': [6, -3, 3, 3, 3, -3, 3, 1521, 1383]}, 'Perm': {'d': 21, 'gens': [250845943359524868, 2812067596232294400, 79890976, 43545600, 5129431175169100800, 93313]}}, 'schur_multiplier': [3, 3, 3, 3, 3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 3], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5:C_3', 'transitive_degree': 81, 'wreath_data': None, 'wreath_product': False}