Query:
/api/gps_groups/?_offset=0
Table gps_groups
Finite groups
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '112.22', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 12], 'aut_gens': [[1, 2], [1, 30], [1, 82], [57, 2], [57, 75]], 'aut_group': '96.221', 'aut_hash': 221, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 96, 'aut_permdeg': 11, 'aut_perms': [1680, 744, 766080, 10887148], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 2, 2], [7, 1, 6, 1], [8, 1, 8, 1], [14, 1, 6, 1], [14, 1, 12, 1], [28, 1, 12, 2], [56, 1, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{12}:C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '96.221', 'autcent_hash': 221, 'autcent_nilpotent': True, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{12}:C_2^3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 1, 4], [7, 1, 6], [8, 1, 8], [14, 1, 18], [28, 1, 24], [56, 1, 48]], 'center_label': '112.22', 'center_order': 112, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 22, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['7.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [7, 1, 6, 1], [8, 1, 4, 2], [14, 1, 6, 3], [28, 1, 12, 2], [56, 1, 24, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 48, 'exponent': 56, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '28.4', 'hash': 22, 'hyperelementary': 2, 'id': 14657, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 112]], 'label': '112.22', 'linC_count': 2304, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 48, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C56', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 112, 'number_divisions': 16, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 22, 'number_subgroups': 22, 'old_label': None, 'order': 112, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 3], [4, 4], [7, 6], [8, 8], [14, 18], [28, 24], [56, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 30], [1, 82], [57, 2], [57, 75]], 'outer_group': '96.221', 'outer_hash': 221, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 11, 'outer_perms': [1680, 744, 766080, 10887148], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}:C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 2], [6, 4], [12, 2], [24, 2]], 'representations': {'PC': {'code': 1699797379397, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -2, -7, 26, 42, 58]}, 'GLFp': {'d': 2, 'p': 113, 'gens': [118317561, 161604576]}, 'Perm': {'d': 17, 'gens': [649685836800, 20922789888000, 4320, 274000527360, 87660961920]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 56], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{56}', 'transitive_degree': 112, 'wreath_data': None, 'wreath_product': False}