Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 60, 'aut_gen_orders': [12, 6, 12, 30, 10, 5], 'aut_gens': [[1, 2, 24, 144, 4320, 21600], [90577, 25114, 32424, 84528, 90720, 95040], [88665, 48170, 26472, 26328, 73440, 74304], [100945, 34442, 57912, 35568, 12960, 47520], [14257, 2186, 42360, 34704, 17280, 34560], [53569, 52778, 24, 15696, 4320, 21600], [2593, 59618, 2616, 144, 4320, 21600]], 'aut_group': '216000.d', 'aut_hash': 4125830444204071041, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 216000, 'aut_permdeg': 540, 'aut_perms': 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'aut_phi_ratio': 7.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [2, 75, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 450, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 600, 1, 1], [3, 1200, 1, 1], [4, 450, 1, 3], [4, 1125, 1, 2], [4, 2250, 1, 3], [4, 3375, 1, 2], [5, 12, 1, 1], [5, 16, 1, 1], [5, 24, 1, 2], [5, 48, 1, 1], [6, 30, 1, 2], [6, 60, 1, 1], [6, 150, 1, 2], [6, 180, 1, 1], [6, 250, 1, 1], [6, 300, 1, 1], [6, 750, 1, 1], [6, 900, 1, 1], [6, 3000, 1, 1], [6, 6000, 1, 1], [10, 120, 1, 3], [10, 300, 1, 1], [10, 360, 1, 2], [10, 720, 1, 2], [10, 1800, 1, 1], [12, 900, 1, 3], [12, 4500, 1, 3], [12, 9000, 1, 2], [15, 12, 2, 1], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 3], [15, 48, 1, 2], [15, 48, 2, 3], [15, 96, 1, 2], [15, 96, 2, 1], [15, 2400, 1, 1], [15, 2400, 2, 1], [20, 1800, 1, 3], [30, 120, 2, 6], [30, 240, 1, 2], [30, 240, 2, 2], [30, 300, 2, 1], [30, 360, 2, 2], [30, 600, 1, 1], [30, 600, 2, 1], [30, 720, 2, 2], [30, 1800, 2, 1], [60, 1800, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'D_5^3:\\He_3.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '216000.d', 'autcentquo_hash': 4125830444204071041, 'autcentquo_nilpotent': False, 'autcentquo_order': 216000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_5^3:\\He_3.C_2^3', 'cc_stats': [[1, 1, 1], [2, 15, 1], [2, 75, 1], [2, 90, 1], [2, 125, 1], [2, 450, 1], [3, 2, 1], [3, 6, 1], [3, 600, 1], [3, 1200, 1], [4, 450, 3], [4, 1125, 2], [4, 2250, 3], [4, 3375, 2], [5, 12, 1], [5, 16, 1], [5, 24, 2], [5, 48, 1], [6, 30, 2], [6, 60, 1], [6, 150, 2], [6, 180, 1], [6, 250, 1], [6, 300, 1], [6, 750, 1], [6, 900, 1], [6, 3000, 1], [6, 6000, 1], [10, 120, 3], [10, 300, 1], [10, 360, 2], [10, 720, 2], [10, 1800, 1], [12, 900, 3], [12, 4500, 3], [12, 9000, 2], [15, 12, 2], [15, 16, 2], [15, 24, 7], [15, 48, 8], [15, 96, 4], [15, 2400, 3], [20, 1800, 3], [30, 120, 12], [30, 240, 6], [30, 300, 2], [30, 360, 4], [30, 600, 3], [30, 720, 4], [30, 1800, 2], [60, 1800, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '108000.p', 'commutator_count': 1, 'commutator_label': '13500.j', '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', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [2, 75, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 450, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 600, 1, 1], [3, 1200, 1, 1], [4, 450, 1, 1], [4, 450, 2, 1], [4, 1125, 2, 1], [4, 2250, 1, 1], [4, 2250, 2, 1], [4, 3375, 2, 1], [5, 12, 1, 1], [5, 16, 1, 1], [5, 24, 1, 2], [5, 48, 1, 1], [6, 30, 1, 2], [6, 60, 1, 1], [6, 150, 1, 2], [6, 180, 1, 1], [6, 250, 1, 1], [6, 300, 1, 1], [6, 750, 1, 1], [6, 900, 1, 1], [6, 3000, 1, 1], [6, 6000, 1, 1], [10, 120, 1, 3], [10, 300, 1, 1], [10, 360, 1, 2], [10, 720, 1, 2], [10, 1800, 1, 1], [12, 900, 1, 1], [12, 900, 2, 1], [12, 4500, 1, 1], [12, 4500, 2, 1], [12, 9000, 2, 1], [15, 12, 2, 1], [15, 16, 2, 1], [15, 24, 1, 1], [15, 24, 2, 3], [15, 48, 1, 2], [15, 48, 2, 3], [15, 96, 1, 2], [15, 96, 2, 1], [15, 2400, 1, 1], [15, 2400, 2, 1], [20, 1800, 1, 1], [20, 1800, 2, 1], [30, 120, 2, 6], [30, 240, 1, 2], [30, 240, 2, 2], [30, 300, 2, 1], [30, 360, 2, 2], [30, 600, 1, 1], [30, 600, 2, 1], [30, 720, 2, 2], [30, 1800, 2, 1], [60, 1800, 2, 1], [60, 1800, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6696, 'exponent': 60, 'exponents_of_order': [5, 3, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[12, 0, 8], [24, 0, 18], [48, -1, 1], [48, 0, 16], [48, 1, 1], [96, 0, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '36000.n', 'hash': 4258704782512683748, 'hyperelementary': 1, 'id': 136746, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [4, 12, 6, 30, 5, 5], 'inner_gens': [[1, 79330, 35016, 86256, 56160, 43200], [95849, 2, 75648, 69864, 3456, 7776], [38449, 93002, 24, 58896, 4320, 95040], [47809, 25466, 75192, 144, 17280, 86400], [77761, 5186, 24, 8784, 4320, 21600], [86401, 39746, 56184, 43344, 4320, 21600]], 'inner_hash': 4258704782512683748, 'inner_nilpotent': False, 'inner_order': 108000, 'inner_split': True, 'inner_tex': 'D_5^3.C_3^2:D_6', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 8], [3, 8], [4, 2], [6, 12], [12, 14], [16, 2], [24, 39], [32, 4], [48, 22], [96, 3]], 'label': '108000.p', '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': 'D5^3.C3^2:D6', 'ngens': 11, '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, 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, 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, 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': 94, 'number_characteristic_subgroups': 28, 'number_conjugacy_classes': 122, 'number_divisions': 85, 'number_normal_subgroups': 28, 'number_subgroup_autclasses': 1470, 'number_subgroup_classes': 1470, 'number_subgroups': 380384, 'old_label': None, 'order': 108000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 755], [3, 1808], [4, 17100], [5, 124], [6, 11800], [10, 4620], [12, 34200], [15, 8192], [20, 5400], [30, 13200], [60, 10800]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [81228], 'outer_gens': [[83377, 66962, 38904, 91728, 8640, 82080]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [3, 4], [4, 4], [6, 12], [12, 7], [16, 2], [24, 13], [32, 2], [48, 19], [64, 1], [96, 10], [192, 1]], 'representations': {'PC': {'code': '9338506972852959753507913429740177953148245690545072543705763588401886144047912519833141814887387124558571325229456809341016903555590080143194254580513995495376039739281548828676512221938744999818413949196590119534167344255', 'gens': [1, 2, 5, 7, 10, 11], 'pres': [11, 2, 2, 2, 3, 2, 3, 2, 3, 5, 5, 5, 403920, 1745261, 56, 672278, 90, 77795, 1925884, 2080335, 386456, 698647, 158, 3184, 6641718, 2689781, 876442, 518172, 189008, 226, 354823, 4057170, 444605, 650536, 4275, 348, 342152, 2779939, 213870, 481181, 14308, 6177609, 190100, 2019631, 23802, 13275, 5227210, 470469, 2326136, 222199, 479214, 72676]}, 'Perm': {'d': 24, 'gens': [1129258880240916907469, 28210018194475458612661]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_5^3.C_3^2:D_6', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}