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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '2916.ea', 'ambient_counter': 105, 'ambient_order': 2916, 'ambient_tex': 'C_3^4:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '2916.ea.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '2916.ea', 'aut_centralizer_order': 27, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '648.734', 'aut_weyl_index': 54, 'centralizer': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.j1.a1', '18.c1.b1', '18.e1.a1', '18.t1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.g1.b1', '108.w1.b1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3087, 6462, 8124, 1442, 3396, 6682, 6084, 2573], 'generators': [1866513559823997, 711468341383203, 93448857844, 80788], 'label': '2916.ea.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['108.a1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '2916.ea', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.167'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '27.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [9, 8, 4], 'aut_gens': [[2920, 1045, 1231, 784], [2974, 5371, 736, 784], [2920, 5392, 3178, 757], [5110, 5134, 5626, 784]], 'aut_group': '23328.dt', 'aut_hash': 3628243401347822157, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23328, 'aut_permdeg': 27, 'aut_perms': [10030436526526919275772371736, 174626025659862093766770675, 585362951684203343265783677], 'aut_phi_ratio': 432.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [3, 1, 6, 1], [3, 3, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(S_3\\times \\GL(2,3))', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '486.183', 'autcent_hash': 183, 'autcent_nilpotent': False, 'autcent_order': 486, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^4:S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '48.29', 'autcentquo_hash': 29, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\GL(2,3)', 'cc_stats': [[1, 1, 1], [3, 1, 8], [3, 3, 24]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '9.2', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['27.3', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4], [3, 3, 2, 12]], 'element_repr_type': 'GLZq', 'elementary': 3, 'eulerian_function': 13, 'exponent': 3, 'exponents_of_order': [4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '27.5', 'hash': 12, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [1, 3, 3, 1], 'inner_gens': [[2920, 1045, 1231, 784], [2920, 1045, 1258, 784], [2920, 1018, 1231, 784], [2920, 1045, 1231, 784]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 9, 'inner_split': False, 'inner_tex': 'C_3^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 27], [3, 6]], 'label': '81.12', 'linC_count': 108, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 27, 'linQ_dim': 8, 'linQ_dim_count': 27, 'linR_count': 27, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3*He3', 'ngens': 3, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 33, 'number_divisions': 17, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 56, 'number_subgroups': 104, 'old_label': None, 'order': 81, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [6, 6, 8], 'outer_gen_pows': [730, 730, 730], 'outer_gens': [[2920, 3181, 5365, 757], [5164, 733, 3238, 784], [2920, 736, 3208, 757]], 'outer_group': '2592.fv', 'outer_hash': 9019849488891309561, 'outer_nilpotent': False, 'outer_order': 2592, 'outer_permdeg': 12, 'outer_perms': [49367521, 182993909, 186219505], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_3\\times C_3^2:\\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 13], [6, 3]], 'representations': {'PC': {'code': 1088, 'gens': [1, 2, 3, 4], 'pres': [4, -3, 3, 3, -3, 258]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [1305911, 11495158, 36731395, 11225704]}, 'GLZq': {'d': 2, 'q': 9, 'gens': [757, 733, 1021, 2920]}, 'Perm': {'d': 12, 'gens': [51609744, 79974843, 135890884, 135890880]}}, 'schur_multiplier': [3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times \\He_3', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 6, 12, 3, 3, 3, 3, 3], 'aut_gens': [[3402106385166964, 355693738798535], [4557070732429469, 355693738860964], [4891835414102425, 1134209726581945], [5247690931883523, 2999898405589945], [3402106385247363, 355693738798535], [4113655597986484, 20929020721652], [4113574726549824, 355868051835476], [3778891003359363, 21010008280195], [3402106385166964, 732478233496195]], 'aut_group': '34992.ns', 'aut_hash': 5395324004515259423, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 34992, 'aut_permdeg': 66, 'aut_perms': [521858103572185645447050180455616673563732069150414642098195715988820082788877203883719873574, 252893273483599920512736537502011762813601131386804065519710048079796999482028331140981625666, 339741019892978225485262972555278559868953308913752257885788132370529163232895968912461919481, 511526758187999293166803681543972911173765034631327466405398968680077922805058341903881231595, 387397890476933702914495819672759095480527224819386767865365965952073438328001652815462233916, 512098958896568963577190920609372738180805453999699390290320731738753467130324367288049349190, 49655496793879140035657359570583540425955454862178352468397224110764560101237321609003034528, 27925373836691748990250507851931783081465872884898484823812000057615235197572578986329], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 27, 2, 1], [2, 81, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 6, 2, 1], [3, 9, 2, 1], [3, 12, 2, 1], [3, 12, 3, 1], [3, 12, 6, 1], [3, 18, 1, 1], [3, 18, 2, 1], [3, 18, 4, 1], [3, 36, 2, 4], [3, 36, 4, 1], [6, 54, 2, 1], [6, 81, 2, 1], [6, 81, 4, 1], [6, 162, 1, 1], [6, 162, 2, 2], [6, 162, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_3^2:(S_3\\times D_4)', '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': 12, 'autcentquo_group': '34992.ns', 'autcentquo_hash': 5395324004515259423, 'autcentquo_nilpotent': False, 'autcentquo_order': 34992, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_3^2:(S_3\\times D_4)', 'cc_stats': [[1, 1, 1], [2, 27, 2], [2, 81, 1], [3, 2, 2], [3, 4, 1], [3, 6, 2], [3, 9, 2], [3, 12, 11], [3, 18, 7], [3, 36, 12], [6, 54, 2], [6, 81, 6], [6, 162, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2916.ea', 'commutator_count': 1, 'commutator_label': '243.37', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 105, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 27, 1, 2], [2, 81, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 2, 1], [3, 9, 2, 1], [3, 12, 1, 3], [3, 12, 2, 4], [3, 18, 1, 3], [3, 18, 2, 2], [3, 36, 1, 2], [3, 36, 2, 5], [6, 54, 1, 2], [6, 81, 2, 3], [6, 162, 1, 3], [6, 162, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 24, 'exponent': 6, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 6], [12, 1, 3]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '324.167', 'hash': 3693867090096231779, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 6], 'inner_gens': [[3402106385166964, 1510645587937949], [4557070732394186, 355693738798535]], 'inner_hash': 3693867090096231779, 'inner_nilpotent': False, 'inner_order': 2916, 'inner_split': True, 'inner_tex': 'C_3^4:S_3^2', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 18], [4, 15], [12, 9], [18, 4]], 'label': '2916.ea', 'linC_count': 9, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 3, 'linQ_dim': 12, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^4:S3^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 58, 'number_divisions': 39, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 328, 'number_subgroup_classes': 641, 'number_subgroups': 14367, 'old_label': None, 'order': 2916, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 135], [3, 728], [6, 2052]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [2623194826070403, 355693738665145], 'outer_gens': [[4912751973381123, 1845410269656362], [3423209842125482, 2999898405589945]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [55, 49], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 9], [8, 6], [12, 3], [18, 4], [24, 3]], 'representations': {'PC': {'code': '481245547502042790880504336723567231414345347817122110007200265995615', 'gens': [1, 3, 5, 6, 7, 8], 'pres': [8, -2, -3, -2, -3, -3, -3, -3, -3, 16, 46514, 31618, 66, 83715, 10571, 105124, 20172, 4820, 2308, 25925, 10381, 17301, 8237, 36294, 6070, 20759]}, 'Perm': {'d': 18, 'gens': [3402106385166964, 355693738798535]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:S_3^2', 'transitive_degree': 18, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 3, 3], 'aut_gens': [[475, 450, 148, 244], [450, 475, 147, 243], [572, 450, 148, 147], [572, 693, 243, 147], [719, 693, 148, 244], [572, 693, 148, 244]], 'aut_group': '72.40', 'aut_hash': 40, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 72, 'aut_permdeg': 6, 'aut_perms': [450, 1, 25, 243, 244], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 2, 1], [2, 9, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [6, 6, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\SOPlus(4,2)', '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': 12, 'autcentquo_group': '72.40', 'autcentquo_hash': 40, 'autcentquo_nilpotent': False, 'autcentquo_order': 72, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)', 'cc_stats': [[1, 1, 1], [2, 3, 2], [2, 9, 1], [3, 2, 2], [3, 4, 1], [6, 6, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '36.10', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['6.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [6, 6, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '36.10', 'hash': 10, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 3, 3], 'inner_gens': [[475, 450, 148, 147], [475, 450, 243, 244], [475, 598, 148, 244], [572, 450, 148, 244]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': True, 'inner_tex': 'S_3^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 4], [4, 1]], 'label': '36.10', 'linC_count': 5, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 5, 'linQ_dim': 4, 'linQ_dim_count': 5, 'linR_count': 5, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'S3^2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 9, 'number_divisions': 9, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 22, 'number_subgroups': 60, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 15], [3, 8], [6, 12]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [25], 'outer_gens': [[450, 475, 147, 148]], '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': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 1]], 'representations': {'PC': {'code': 415852963, 'gens': [1, 2, 4], 'pres': [4, -2, -2, -3, -3, 81, 21, 98, 199]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [11780519, 20465590, 35990610]}, 'Lie': [{'d': 4, 'q': 2, 'gens': [51450, 44940], 'family': 'OmegaPlus'}, {'d': 4, 'q': 2, 'gens': [51450, 44940], 'family': 'POmegaPlus'}, {'d': 4, 'q': 2, 'gens': [33827, 33841, 35873, 50209], 'family': 'SpinPlus'}], 'GLFp': {'d': 3, 'p': 3, 'gens': [11017, 14041, 8101, 8183]}, 'Perm': {'d': 6, 'gens': [475, 450, 148, 244]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3^2', 'transitive_degree': 6, 'wreath_data': None, 'wreath_product': False}
