Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [4, 8, 8, 6, 12, 18], 'aut_gens': [[135540556145936650, 264007973278023976], [987100619697934573, 1154361499522122976], [989297513118442093, 890353731351143656], [974332772221536850, 749080627401265207], [627935145656288530, 310600210867038016], [1379027632391151850, 129873448459198816], [917422778537002933, 1135483912385591767]], 'aut_group': '2654208.qn', 'aut_hash': 7403131247758471170, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2654208, 'aut_permdeg': 360, 'aut_perms': 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2086833616932690100171859464953957578669382415875322260300920042496735895041201819169628455229258109604177738748022148876150601690851917205870200269622945354943471660156488338578433899158164778686835353350454202601162459011073225300031282958505603102761553753513135005577936789012134717764485635573756109095250128015455635339299734254556253302895863518075965060504578589122767296880966620772860019343829444899262453004557937918588546084352212107595439498347422973297152919312846251499588276738540931477611825605853018806203513687103546391411184754974174860586500028270547033463313314437696657649705646300384346264556111742373927424774310156124180714606653271021408152505249942452836295603204337252415374314298658793208515383697109143535586734604264400357463194676062], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 4], [2, 18, 1, 2], [2, 27, 1, 6], [2, 54, 1, 2], [2, 81, 1, 2], [2, 108, 2, 2], [2, 216, 1, 2], [2, 288, 1, 1], [2, 324, 2, 2], [2, 648, 1, 2], [2, 864, 1, 1], [2, 1728, 1, 1], [3, 24, 1, 1], [3, 192, 1, 1], [3, 512, 1, 1], [3, 4608, 1, 1], [4, 36, 2, 4], [4, 108, 2, 2], [4, 108, 4, 4], [4, 216, 1, 2], [4, 216, 2, 4], [4, 288, 1, 1], [4, 324, 2, 6], [4, 432, 1, 2], [4, 648, 1, 2], [4, 648, 2, 4], [4, 864, 1, 3], [4, 1296, 1, 6], [4, 1296, 2, 2], [4, 1728, 1, 3], [4, 1728, 2, 1], [4, 2592, 1, 2], [4, 5184, 1, 4], [4, 5184, 2, 1], [4, 10368, 2, 2], [6, 24, 1, 3], [6, 48, 1, 2], [6, 144, 1, 8], [6, 192, 1, 3], [6, 216, 1, 4], [6, 384, 1, 2], [6, 432, 1, 2], [6, 512, 1, 1], [6, 576, 1, 4], [6, 864, 2, 2], [6, 1152, 1, 2], [6, 1152, 2, 1], [6, 1536, 1, 2], [6, 1728, 1, 2], [6, 2304, 1, 1], [6, 4608, 1, 1], [6, 6912, 1, 1], [6, 9216, 2, 1], [6, 13824, 1, 3], [8, 1728, 2, 1], [8, 5184, 2, 1], [8, 10368, 2, 2], [9, 36864, 1, 1], [12, 288, 4, 4], [12, 864, 2, 2], [12, 864, 4, 4], [12, 1152, 2, 1], [12, 1728, 1, 2], [12, 1728, 2, 4], [12, 2304, 1, 1], [12, 2304, 2, 4], [12, 3456, 2, 2], [12, 6912, 1, 1], [12, 6912, 4, 1], [12, 9216, 2, 1], [12, 13824, 1, 3], [12, 27648, 2, 2], [18, 36864, 1, 1], [24, 6912, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4^3.C_2^6:S_4', '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': 72, 'autcentquo_group': '663552.iu', 'autcentquo_hash': 3515361455959397683, 'autcentquo_nilpotent': False, 'autcentquo_order': 663552, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^9.S_3\\wr S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 9, 4], [2, 18, 2], [2, 27, 6], [2, 54, 2], [2, 81, 2], [2, 108, 4], [2, 216, 2], [2, 288, 1], [2, 324, 4], [2, 648, 2], [2, 864, 1], [2, 1728, 1], [3, 24, 1], [3, 192, 1], [3, 512, 1], [3, 4608, 1], [4, 36, 8], [4, 108, 20], [4, 216, 10], [4, 288, 1], [4, 324, 12], [4, 432, 2], [4, 648, 10], [4, 864, 3], [4, 1296, 10], [4, 1728, 5], [4, 2592, 2], [4, 5184, 6], [4, 10368, 4], [6, 24, 3], [6, 48, 2], [6, 144, 8], [6, 192, 3], [6, 216, 4], [6, 384, 2], [6, 432, 2], [6, 512, 1], [6, 576, 4], [6, 864, 4], [6, 1152, 4], [6, 1536, 2], [6, 1728, 2], [6, 2304, 1], [6, 4608, 1], [6, 6912, 1], [6, 9216, 2], [6, 13824, 3], [8, 1728, 2], [8, 5184, 2], [8, 10368, 4], [9, 36864, 1], [12, 288, 16], [12, 864, 20], [12, 1152, 2], [12, 1728, 10], [12, 2304, 9], [12, 3456, 4], [12, 6912, 5], [12, 9216, 2], [12, 13824, 3], [12, 27648, 4], [18, 36864, 1], [24, 6912, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '331776.k', 'commutator_count': 2, 'commutator_label': '165888.q', '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', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 17, 'conjugacy_classes_known': True, 'counter': 217, 'cyclic': False, 'derived_length': 5, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 4], [2, 18, 1, 2], [2, 27, 1, 6], [2, 54, 1, 2], [2, 81, 1, 2], [2, 108, 1, 4], [2, 216, 1, 2], [2, 288, 1, 1], [2, 324, 1, 4], [2, 648, 1, 2], [2, 864, 1, 1], [2, 1728, 1, 1], [3, 24, 1, 1], [3, 192, 1, 1], [3, 512, 1, 1], [3, 4608, 1, 1], [4, 36, 1, 4], [4, 36, 2, 2], [4, 108, 1, 4], [4, 108, 2, 8], [4, 216, 1, 10], [4, 288, 1, 1], [4, 324, 1, 8], [4, 324, 2, 2], [4, 432, 1, 2], [4, 648, 1, 10], [4, 864, 1, 3], [4, 1296, 1, 6], [4, 1296, 2, 2], [4, 1728, 1, 5], [4, 2592, 1, 2], [4, 5184, 1, 6], [4, 10368, 1, 4], [6, 24, 1, 3], [6, 48, 1, 2], [6, 144, 1, 8], [6, 192, 1, 3], [6, 216, 1, 4], [6, 384, 1, 2], [6, 432, 1, 2], [6, 512, 1, 1], [6, 576, 1, 4], [6, 864, 1, 4], [6, 1152, 1, 2], [6, 1152, 2, 1], [6, 1536, 1, 2], [6, 1728, 1, 2], [6, 2304, 1, 1], [6, 4608, 1, 1], [6, 6912, 1, 1], [6, 9216, 2, 1], [6, 13824, 1, 3], [8, 1728, 1, 2], [8, 5184, 1, 2], [8, 10368, 1, 4], [9, 36864, 1, 1], [12, 288, 2, 8], [12, 864, 1, 4], [12, 864, 2, 8], [12, 1152, 2, 1], [12, 1728, 1, 10], [12, 2304, 1, 5], [12, 2304, 2, 2], [12, 3456, 2, 2], [12, 6912, 1, 1], [12, 6912, 2, 2], [12, 9216, 2, 1], [12, 13824, 1, 3], [12, 27648, 2, 2], [18, 36864, 1, 1], [24, 6912, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [13, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 0, 10], [18, 1, 2], [36, 0, 12], [54, 0, 14], [54, 1, 2], [72, 0, 2], [72, 1, 1], [108, 0, 4], [108, 1, 1], [162, 0, 2], [162, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '331776.k', 'hash': 4679071451459104948, 'hyperelementary': 1, 'id': 496237, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [12, 4], 'inner_gens': [[135540556145936650, 1008488174786628607], [365777905839873133, 264007973278023976]], 'inner_hash': 3604168331467219802, 'inner_nilpotent': False, 'inner_order': 331776, 'inner_split': True, 'inner_tex': 'S_4^3.S_4', 'inner_used': [1, 2], 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 4], [2, 5], [3, 12], [6, 23], [8, 4], [9, 16], [12, 20], [16, 2], [18, 28], [24, 10], [27, 20], [36, 40], [54, 49], [72, 6], [81, 12], [108, 12], [162, 7]], 'label': '663552.ii', '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': 'C2^9.S3wrS3', 'ngens': 2, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 174, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 270, 'number_divisions': 226, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 663552, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 6847], [3, 5336], [4, 118080], [6, 95528], [8, 55296], [9, 36864], [12, 281088], [18, 36864], [24, 27648]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[520817078836833130, 289991375312891176], [135540556145946130, 264007973278028296], [137025026531372170, 758414794589627176]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 3], [3, 12], [4, 1], [6, 13], [8, 2], [9, 16], [12, 17], [16, 3], [18, 16], [24, 10], [27, 20], [36, 30], [48, 2], [54, 27], [72, 12], [81, 12], [108, 15], [144, 1], [162, 5], [216, 4], [324, 1]], 'representations': {'PC': {'code': '25367991057763605129803956792213467232219850194697138952002262422980749237823944213706976233898629845582385902116959852230697301729225363205893481036946882038337982720316147037770469017129907248792676481261284461869494634581897799043739805062773075772648308771940773494735457355645219315929582747875849083746614987538285412063176771460642308874489515508212277496838976400053220814330833025395279592173462744836941607416645181376340997053345248934213319107753172191622999086635879463333775948256209943665876660640057221163510814138680561067701669881365199831872649087269759837558912611564137478604995362271110715948297013409093319803633067239548224', 'gens': [1, 2, 5, 6, 8, 10, 12, 13, 14, 15, 16, 17], 'pres': [17, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 4775640, 20000093, 86, 22505486, 138, 35377955, 54111004, 19883901, 1774328, 1917145, 17300021, 24185038, 2125515, 6939830, 1093, 294, 3427206, 239927, 325624, 428457, 1026, 1605895, 4647960, 2428457, 1060858, 4172, 398, 71559944, 14713, 308490, 7355075, 3765, 82921929, 36613946, 15071563, 2768340, 2749997, 1392394, 691671, 502, 2064490, 1032267, 480260, 10795945, 58422, 27023, 616924, 1057581, 154286, 1982976, 330610, 161715, 54020, 27721, 85924812, 1145693, 334198, 286479, 5823872, 2911993, 83703, 40625, 81430285, 6785886, 925391, 1696528, 3135969, 1546622, 861199, 81562, 42309, 50453294, 40318591, 15532608, 9281045, 5012362, 82719, 236501, 82753, 165390, 55247, 7069, 125729295, 12807968, 17273137, 2996418, 5522771, 176356, 166598, 293911, 5064, 15689, 93136624, 93636033, 30712658, 22659979, 3870372, 3220139, 158779, 124983, 67778, 83401, 44403]}, 'Perm': {'d': 20, 'gens': [135540556145936650, 264007973278023976]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^9.S_3\\wr S_3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}