Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 4, 4, 4, 12, 2, 2], 'aut_gens': [[1, 2, 24, 48], [17, 506, 240, 552], [17, 22, 720, 888], [25, 514, 24, 936], [25, 506, 504, 816], [497, 482, 240, 840], [493, 250, 504, 456], [481, 22, 504, 552]], 'aut_group': '1536.408640917', 'aut_hash': 5803646388267248920, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 32, 'aut_perms': [20293075767285478076517588650182116, 3883320942832210188793011225933864, 175846324868347200611540522685346882, 258030100034240311328376462292058637, 250318274922038582403257206276523079, 228438120960164784153576475574475013, 195775235403294334289447642839386595], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 8, 1, 1], [4, 1, 4, 1], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 2, 2], [5, 1, 4, 1], [6, 8, 1, 3], [8, 6, 4, 2], [10, 1, 4, 3], [12, 8, 4, 1], [15, 8, 4, 1], [20, 1, 16, 1], [20, 6, 4, 2], [20, 6, 8, 1], [20, 12, 8, 2], [30, 8, 4, 3], [40, 6, 16, 2], [60, 8, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4\\times C_4\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.260', 'autcent_hash': 260, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 8, 1], [4, 1, 4], [4, 6, 4], [4, 12, 4], [5, 1, 4], [6, 8, 3], [8, 6, 8], [10, 1, 12], [12, 8, 4], [15, 8, 4], [20, 1, 16], [20, 6, 16], [20, 12, 16], [30, 8, 12], [40, 6, 32], [60, 8, 16]], 'center_label': '40.9', 'center_order': 40, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '24.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 6253, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['48.28', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 8, 1, 1], [4, 1, 2, 2], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 1, 2], [4, 12, 2, 1], [5, 1, 4, 1], [6, 8, 1, 3], [8, 6, 2, 2], [8, 6, 4, 1], [10, 1, 4, 3], [12, 8, 2, 2], [15, 8, 4, 1], [20, 1, 8, 2], [20, 6, 4, 2], [20, 6, 8, 1], [20, 12, 4, 2], [20, 12, 8, 1], [30, 8, 4, 3], [40, 6, 8, 2], [40, 6, 16, 1], [60, 8, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 108, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '240.196', 'hash': 6253, 'hyperelementary': 1, 'id': 313261, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 2], 'inner_gens': [[1, 10, 504, 552], [17, 2, 240, 72], [481, 266, 24, 528], [505, 26, 504, 48]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 60], [3, 40], [4, 20]], 'label': '960.6253', 'linC_count': 768, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 14, 'linQ_dim_count': 48, 'linR_count': 208, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C4*C10.S4', 'ngens': 8, '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, 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': 34, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 160, 'number_divisions': 42, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 120, 'number_subgroup_classes': 140, 'number_subgroups': 446, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 76], [5, 4], [6, 24], [8, 48], [10, 12], [12, 32], [15, 32], [20, 304], [30, 96], [40, 192], [60, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 482, 24, 48], [1, 266, 24, 528], [13, 2, 24, 48], [1, 14, 24, 48], [1, 2, 24, 816]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [10169970360836733217600826651920248070911972664852801398245574053330785997917536393354840, 1984672484343119467262649771272345903428500111764250414048908011916078552281594173027841, 4122625731263607402749469126481551044697931193140603687719519963675542013272980533354004, 6140706697235735751234176841909150705465927250674786789983341943385701419589600642564658, 8155376058102723961175341274794062984718101772372559454336167945133393064270456833133536], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 9], [6, 2], [8, 6], [12, 4], [16, 5], [24, 2], [32, 2]], 'representations': {'PC': {'code': 7906472554701253088876788589678934917639283024749289837905610998019, 'gens': [1, 2, 5, 6], 'pres': [8, -2, -2, -2, -3, -2, 2, -2, -5, 3840, 161, 41, 482, 66, 515, 20164, 4812, 2660, 1228, 836, 26501, 1741, 9525, 461, 1093, 141, 166]}, 'GLZN': {'d': 2, 'p': 35, 'gens': [43121, 686361, 184474, 839309, 343008, 1243404, 257256, 791188]}, 'Perm': {'d': 25, 'gens': [705169598127270809702407, 17, 46200, 7, 1586553884408810419200, 1348154267883920180006400, 1998649584796543304774400, 2646409506205782740371200]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times C_{10}.S_4', 'transitive_degree': 320, 'wreath_data': None, 'wreath_product': False}