Query:
/api/gps_groups/?_offset=0
{'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': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 2, 2, 6], 'aut_gens': [[19897, 12973, 13432, 12175, 12967], [9535, 12973, 13432, 12175, 12967], [19897, 12973, 17749, 12175, 2665], [9535, 12553, 2206, 12967, 2665], [19897, 2611, 12640, 12175, 12967], [19897, 2683, 13432, 12175, 12967], [19993, 12973, 3142, 12175, 12967]], 'aut_group': '576.8659', 'aut_hash': 8659, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 576, 'aut_permdeg': 18, 'aut_perms': [1697536220492304, 12659391753383, 2773196409565901, 17977061912323, 18582077496836, 5143352656056318], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 12, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 24, 2, 1], [12, 12, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2:D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 1], [2, 18, 1], [2, 36, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [4, 12, 2], [4, 36, 1], [6, 2, 1], [6, 6, 2], [6, 8, 1], [6, 16, 1], [6, 24, 2], [12, 12, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '144.183', 'commutator_count': 1, 'commutator_label': '72.47', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 858, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [4, 12, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 1], [6, 16, 1, 1], [6, 24, 2, 1], [12, 12, 2, 2]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 18, 'exponent': 12, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '144.183', 'hash': 858, 'hyperelementary': 1, 'id': 537847, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 3, 2, 2], 'inner_gens': [[19897, 2731, 13432, 12175, 12967], [9631, 12973, 7459, 12175, 2665], [19897, 17734, 13432, 2665, 12175], [19897, 12973, 3142, 12175, 12967], [19897, 2611, 2206, 12175, 12967]], 'inner_hash': 183, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3\\times S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 9], [3, 4], [4, 2], [6, 5]], 'label': '288.858', 'linC_count': 8, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 16, 'linQ_dim': 7, 'linQ_dim_count': 16, 'linR_count': 8, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'D6:S4', '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': 21, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 24, 'number_divisions': 21, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 134, 'number_subgroups': 942, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 67], [3, 26], [4, 60], [6, 86], [12, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [1729, 1729], 'outer_gens': [[19897, 12973, 7459, 12175, 2665], [19897, 13021, 13432, 12175, 12967]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [3, 4], [4, 4], [6, 3], [12, 1]], 'representations': {'PC': {'code': 2442231820234069288079130157836, 'gens': [1, 2, 5, 6, 7], 'pres': [7, -2, -2, -2, -3, -3, -2, 2, 309, 36, 422, 58, 451, 851, 411, 5305, 181]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 1765, 18685, 9565, 2665, 1777, 1801]}, 'Perm': {'d': 11, 'gens': [265, 363744, 1680, 403200, 3, 3669120, 7983360]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6:S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}