Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', '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, 4, 2, 3, 3, 6, 6, 2, 2], 'aut_gens': [[1, 2, 6, 36, 108], [3, 2, 330, 36, 108], [1, 338, 682, 36, 108], [1, 16, 658, 36, 108], [1, 348, 344, 36, 864], [1, 660, 32, 36, 108], [339, 326, 330, 36, 108], [29, 24, 658, 36, 756], [675, 16, 42, 36, 864], [1, 4, 354, 36, 108], [5, 4, 728, 72, 864]], 'aut_group': '7776.jy', 'aut_hash': 6858566785119505195, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 18, 'aut_perms': [1320926013395304, 232213416434904, 43502486238144, 4769988440453, 1016050297800, 3643680530672160, 4700328888396749, 591094110453627, 127025516233680, 1679316272318053], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 6, 4, 1], [3, 12, 4, 1], [6, 3, 2, 1], [6, 9, 2, 1], [6, 18, 1, 1], [6, 18, 2, 1], [6, 18, 4, 1], [6, 27, 2, 1], [9, 1, 6, 1], [9, 2, 6, 1], [9, 6, 8, 1], [9, 12, 8, 1], [18, 3, 6, 1], [18, 9, 6, 1], [18, 18, 6, 1], [18, 18, 8, 1], [18, 27, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times C_3^3:\\GL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 3, 'autcent_group': '3.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 3, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '2592.fv', 'autcentquo_hash': 9019849488891309561, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 9, 1], [2, 27, 1], [3, 1, 2], [3, 2, 3], [3, 6, 4], [3, 12, 4], [6, 3, 2], [6, 9, 2], [6, 18, 7], [6, 27, 2], [9, 1, 6], [9, 2, 6], [9, 6, 8], [9, 12, 8], [18, 3, 6], [18, 9, 6], [18, 18, 14], [18, 27, 6]], 'center_label': '9.1', 'center_order': 9, 'central_product': True, 'central_quotient': '108.39', 'commutator_count': 1, 'commutator_label': '81.12', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 795, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['162.44', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 27, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 6, 1, 4], [3, 12, 1, 4], [6, 3, 2, 1], [6, 9, 2, 1], [6, 18, 1, 5], [6, 18, 2, 1], [6, 27, 2, 1], [9, 1, 6, 1], [9, 2, 6, 1], [9, 6, 2, 4], [9, 12, 2, 4], [18, 3, 6, 1], [18, 9, 6, 1], [18, 18, 2, 4], [18, 18, 6, 1], [18, 27, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 39312, 'exponent': 18, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 12]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '324.166', 'hash': 795, 'hyperelementary': 1, 'id': 318084, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 6, 3, 1], 'inner_gens': [[1, 4, 354, 36, 108], [5, 2, 654, 36, 108], [661, 326, 6, 72, 108], [1, 2, 78, 36, 108], [1, 2, 6, 36, 108]], 'inner_hash': 39, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': False, 'inner_tex': 'C_3:S_3^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 30], [3, 24], [4, 12], [6, 12]], 'label': '972.795', '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': False, 'metacyclic': False, 'monomial': True, 'name': '(C3*C9):S3^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 90, 'number_divisions': 42, 'number_normal_subgroups': 47, 'number_subgroup_autclasses': 113, 'number_subgroup_classes': 292, 'number_subgroups': 1452, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 39], [3, 80], [6, 204], [9, 162], [18, 486]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 6, 2, 3, 3], 'outer_gen_pows': [1, 0, 1, 1, 0], 'outer_gens': [[1, 16, 658, 36, 756], [1, 16, 654, 72, 540], [1, 348, 670, 36, 108], [1, 4, 32, 36, 432], [1, 2, 6, 36, 432]], 'outer_group': '72.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 7, 'outer_perms': [747, 28, 2424, 2188, 4], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3\\times S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 14], [4, 14], [8, 4], [18, 4], [36, 2]], 'representations': {'PC': {'code': 126758170481158732105436718756399, 'gens': [1, 2, 3, 5, 6], 'pres': [7, -2, -3, -2, -3, -3, -3, -3, 57, 7436, 6876, 58, 18819, 4714, 438, 166]}, 'Perm': {'d': 30, 'gens': [1, 79480952248588299408682388400, 10106548111225803837422031124344, 19287931234418868667131293493120, 28390607782314919684827619119360, 3, 37591330973438220090252954328800]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_9):S_3^2', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}