Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [4, 6, 12, 18, 12, 6, 18, 12], 'aut_gens': [[1, 2, 12, 72, 864, 10368, 31104], [104477, 61258, 160500, 186336, 48600, 3456, 31104], [135129, 124450, 177996, 62160, 63072, 62208, 114048], [90025, 54794, 38460, 62280, 4320, 10368, 155520], [78537, 6146, 39108, 165552, 42120, 124416, 96768], [12913, 146786, 9132, 14184, 146016, 10368, 155520], [139349, 80282, 23172, 32568, 141048, 6912, 114048], [69485, 75794, 74532, 104880, 130680, 6912, 103680], [21965, 68242, 40884, 172224, 52056, 6912, 31104]], 'aut_group': None, 'aut_hash': 5270842697441228155, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1492992, 'aut_permdeg': 360, 'aut_perms': 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1, 1], [3, 12, 1, 3], [3, 16, 1, 1], [3, 24, 1, 3], [3, 48, 1, 2], [3, 864, 1, 1], [3, 1728, 1, 1], [4, 54, 1, 4], [4, 108, 2, 2], [4, 162, 2, 2], [4, 324, 2, 2], [6, 2, 1, 1], [6, 6, 1, 8], [6, 8, 1, 1], [6, 12, 1, 13], [6, 16, 1, 1], [6, 24, 1, 21], [6, 48, 1, 16], [6, 72, 2, 5], [6, 72, 4, 2], [6, 96, 1, 2], [6, 144, 2, 4], [6, 144, 4, 6], [6, 216, 2, 11], [6, 432, 2, 6], [6, 648, 2, 5], [6, 864, 1, 1], [6, 864, 2, 2], [6, 1296, 2, 2], [6, 1728, 1, 1], [6, 1944, 2, 1], [6, 2592, 2, 2], [6, 5184, 2, 1], [6, 7776, 2, 1], [8, 648, 2, 2], [8, 1944, 2, 2], [9, 1728, 1, 1], [9, 3456, 1, 1], [12, 108, 1, 12], [12, 216, 1, 12], [12, 216, 2, 6], [12, 432, 1, 4], [12, 432, 2, 6], [12, 648, 2, 8], [12, 864, 2, 2], [12, 1296, 2, 2], [18, 1728, 1, 1], [18, 3456, 1, 1], [18, 5184, 2, 1], [24, 1296, 2, 4], [24, 1296, 4, 2], [24, 3888, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_{12}^2.C_6.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 2201406838260405918, 'autcentquo_nilpotent': False, 'autcentquo_order': 186624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_4^2.D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 36, 4], [2, 108, 6], [2, 243, 2], [2, 324, 4], [2, 729, 2], [2, 972, 2], [3, 2, 1], [3, 6, 2], [3, 8, 1], [3, 12, 3], [3, 16, 1], [3, 24, 3], [3, 48, 2], [3, 864, 1], [3, 1728, 1], [4, 54, 4], [4, 108, 4], [4, 162, 4], [4, 324, 4], [6, 2, 1], [6, 6, 8], [6, 8, 1], [6, 12, 13], [6, 16, 1], [6, 24, 21], [6, 48, 16], [6, 72, 18], [6, 96, 2], [6, 144, 32], [6, 216, 22], [6, 432, 12], [6, 648, 10], [6, 864, 5], [6, 1296, 4], [6, 1728, 1], [6, 1944, 2], [6, 2592, 4], [6, 5184, 2], [6, 7776, 2], [8, 648, 4], [8, 1944, 4], [9, 1728, 1], [9, 3456, 1], [12, 108, 12], [12, 216, 24], [12, 432, 16], [12, 648, 16], [12, 864, 4], [12, 1296, 4], [18, 1728, 1], [18, 3456, 1], [18, 5184, 2], [24, 1296, 16], [24, 3888, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': None, 'central_quotient': '93312.iq', 'commutator_count': 1, 'commutator_label': '11664.fv', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 14, 'conjugacy_classes_known': True, 'counter': 114, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 36, 1, 4], [2, 108, 1, 6], [2, 243, 1, 2], [2, 324, 1, 4], [2, 729, 1, 2], [2, 972, 1, 2], [3, 2, 1, 1], [3, 6, 1, 2], [3, 8, 1, 1], [3, 12, 1, 3], [3, 16, 1, 1], [3, 24, 1, 3], [3, 48, 1, 2], [3, 864, 1, 1], [3, 1728, 1, 1], [4, 54, 1, 4], [4, 108, 1, 4], [4, 162, 1, 4], [4, 324, 1, 4], [6, 2, 1, 1], [6, 6, 1, 8], [6, 8, 1, 1], [6, 12, 1, 13], [6, 16, 1, 1], [6, 24, 1, 21], [6, 48, 1, 16], [6, 72, 1, 18], [6, 96, 1, 2], [6, 144, 1, 32], [6, 216, 1, 22], [6, 432, 1, 12], [6, 648, 1, 10], [6, 864, 1, 5], [6, 1296, 1, 4], [6, 1728, 1, 1], [6, 1944, 1, 2], [6, 2592, 1, 4], [6, 5184, 1, 2], [6, 7776, 1, 2], [8, 648, 1, 4], [8, 1944, 1, 4], [9, 1728, 1, 1], [9, 3456, 1, 1], [12, 108, 1, 12], [12, 216, 1, 24], [12, 432, 1, 16], [12, 648, 1, 16], [12, 864, 1, 4], [12, 1296, 1, 4], [18, 1728, 1, 1], [18, 3456, 1, 1], [18, 5184, 1, 2], [24, 1296, 1, 16], [24, 3888, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [8, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 4], [24, 1, 9], [48, 1, 13], [96, 1, 1]], 'familial': False, 'frattini_label': '12.5', 'frattini_quotient': '15552.jf', 'hash': 1212579475730342375, 'hyperelementary': 1, 'id': 380964, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [8, 6, 6, 12, 12, 3, 3], 'inner_gens': [[1, 79906, 62868, 124824, 130680, 20736, 96768], [104669, 2, 84948, 103416, 143208, 3456, 114048], [62425, 12770, 12, 66168, 71712, 10368, 31104], [125017, 180986, 131772, 72, 139104, 10368, 155520], [2377, 24410, 126156, 89928, 864, 20736, 155520], [20737, 17282, 12, 72, 21600, 10368, 31104], [131329, 134786, 12, 62280, 63072, 10368, 31104]], 'inner_hash': 9073412677889748987, 'inner_nilpotent': False, 'inner_order': 93312, 'inner_split': None, 'inner_tex': 'C_6^2.S_3^3:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 56], [8, 8], [12, 96], [16, 8], [24, 72], [32, 2], [48, 46], [96, 2]], 'label': '186624.ej', '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': None, 'name': 'C3^4.C4^2:D6^2', 'ngens': 14, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 3, 1, 0, 1, 0, 1, 1, 0, 3, 1, 0, 0, 1, 0, 2, 3, 0, 3, 0, 0, 3, 2, 0, 2, 0, 1, 7, 0, 3, 0, 0, 9, 1, 0, 0, 15, 0, 1, 14, 0, 15, 2, 35, 0, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 221, 'number_characteristic_subgroups': 67, 'number_conjugacy_classes': 342, 'number_divisions': 342, 'number_normal_subgroups': 159, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 186624, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 5983], [3, 2834], [4, 2592], [6, 75422], [8, 10368], [9, 5184], [12, 32400], [18, 15552], [24, 36288]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [5616, 89880, 158888, 141940], 'outer_gens': [[104477, 61258, 160500, 186336, 48600, 3456, 31104], [135129, 124450, 177996, 62160, 63072, 62208, 114048], [78537, 6146, 39108, 165552, 42120, 124416, 96768], [139349, 80282, 23172, 32568, 141048, 6912, 114048]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1327912203241, 2966658509284, 4396538203938, 5800737348096], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 16], [2, 16], [3, 16], [4, 4], [6, 56], [8, 8], [12, 96], [16, 8], [24, 72], [32, 2], [48, 46], [96, 2]], 'representations': {'PC': {'code': '172845776961604419206746023664460921840096195213461578911959056824226479312213300044238792178823725927873478147048065977659348664577680951794595303615384615853124030643381652095842974514081176574611411261899780937731234609122003243118791363901350090967309633819211059793954632970860283445525032186759387928995313721252198295803000510735895117', 'gens': [1, 2, 4, 6, 9, 12, 13], 'pres': [14, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 3, 9072, 2237369, 71, 1797602, 3520611, 2378561, 747127, 157, 9194644, 2541858, 2238212, 10485221, 4343491, 1299345, 463223, 435769, 243, 12265686, 3996068, 3687970, 286, 7037191, 8549205, 2040899, 16465688, 9022126, 5354784, 753026, 657784, 243510, 18992, 5020, 372, 18204489, 9102263, 740917, 100851, 16879, 415, 9580042, 4790040, 399206, 88756, 14864, 3483659, 290329, 2612775, 4155, 17611788, 10378394, 4560232, 393202, 32884, 544, 1354765, 1016091, 169385, 338771, 28349]}, 'Perm': {'d': 30, 'gens': [632021031330091425166959854159, 9779492920819391314041087412319, 17717821138833586958901190621807, 9474529402019617745711932852295]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 18, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^4.C_4^2:D_6^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}