-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.400', 'ambient_counter': 400, 'ambient_order': 672, 'ambient_tex': 'C_{24}:D_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': True, 'core_order': 168, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.400.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '672.400', 'aut_centralizer_order': 336, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 336, 'centralizer': '4.d1.a1', 'complements': ['168.f1.a1', '168.f1.b1', '168.f1.c1', '168.f1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '12.b1.a1', '28.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7977, 1873, 8121, 7900, 8264, 8523, 7679, 5190], 'generators': [84, 96, 168, 224, 336], 'label': '672.400.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '12.b1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '336.150', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '168.6', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 2, 6], 'aut_gens': [[1], [43], [85], [113], [73]], 'aut_group': '48.52', 'aut_hash': 52, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 48, 'aut_permdeg': 11, 'aut_perms': [3628800, 40320, 720, 27], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [8, 1, 4, 1], [12, 1, 4, 1], [14, 1, 6, 1], [21, 1, 12, 1], [24, 1, 8, 1], [28, 1, 12, 1], [42, 1, 12, 1], [56, 1, 24, 1], [84, 1, 24, 1], [168, 1, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times C_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [4, 1, 2], [6, 1, 2], [7, 1, 6], [8, 1, 4], [12, 1, 4], [14, 1, 6], [21, 1, 12], [24, 1, 8], [28, 1, 12], [42, 1, 12], [56, 1, 24], [84, 1, 24], [168, 1, 48]], 'center_label': '168.6', 'center_order': 168, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['7.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [8, 1, 4, 1], [12, 1, 4, 1], [14, 1, 6, 1], [21, 1, 12, 1], [24, 1, 8, 1], [28, 1, 12, 1], [42, 1, 12, 1], [56, 1, 24, 1], [84, 1, 24, 1], [168, 1, 48, 1]], 'element_repr_type': 'PC', 'elementary': 42, 'eulerian_function': 1, 'exponent': 168, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[1, 0, 48]], 'familial': True, 'frattini_label': '4.1', 'frattini_quotient': '42.6', 'hash': 6, 'hyperelementary': 42, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 2, 'irrep_stats': [[1, 168]], 'label': '168.6', 'linC_count': 48, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 4, 'linQ_dim': 12, 'linQ_dim_count': 4, 'linR_count': 24, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C168', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 168, 'number_divisions': 16, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 168, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 2], [6, 2], [7, 6], [8, 4], [12, 4], [14, 6], [21, 12], [24, 8], [28, 12], [42, 12], [56, 24], [84, 24], [168, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[43], [85], [113], [73]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [3628800, 40320, 720, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [8, 3, 7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [6, 2], [8, 1], [12, 3], [24, 2], [48, 1]], 'representations': {'PC': {'code': 629718704572331, 'gens': [1], 'pres': [5, -2, -2, -2, -3, -7, 10, 26, 42, 78]}, 'GLFp': {'d': 2, 'p': 13, 'gens': [18169]}, 'Perm': {'d': 18, 'gens': [2620928146636800, 725760, 4320, 1108927503129600, 357001369401600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [168], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{168}', 'transitive_degree': 168, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 168, 'aut_gen_orders': [8, 6, 84, 12, 6, 28, 2], 'aut_gens': [[1, 2, 4], [421, 662, 388], [225, 434, 76], [393, 74, 340], [85, 38, 524], [113, 530, 212], [85, 230, 172], [169, 170, 668]], 'aut_group': None, 'aut_hash': 1056978791311958020, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 66, 'aut_perms': [460271701484987493118343093141459509346848493999603145959521622666888472039059764323127314997, 359582851960818770803426957201948515830323831527894407371745196745399647638776266974367529117, 268698740613233956281223815801315232884243720486414463771755866130712063505285007620475886470, 27972142255943225921918258622990451910614505733191484915583868911350307752334539019858133490, 44549043383823917852407104671055496663983968359374798462021522307327237361779075354812142995, 32476696764580893068014717377527324867060061494985181637230797302038347103114765726140360964, 149740555610164558160020871041164812544115408095068580471366832244695867445850922937314818809], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 2, 1], [2, 21, 2, 1], [2, 28, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [6, 2, 1, 1], [6, 56, 2, 1], [7, 2, 3, 1], [8, 2, 2, 1], [8, 42, 2, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 24, 6, 1], [21, 4, 3, 1], [24, 4, 2, 1], [28, 4, 3, 1], [42, 4, 3, 1], [56, 4, 6, 1], [84, 4, 6, 1], [168, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{84}.(C_2^5\\times C_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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '2016.eo', 'autcentquo_hash': 2236184988062812809, 'autcentquo_nilpotent': False, 'autcentquo_order': 2016, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times D_4\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 12, 2], [2, 21, 2], [2, 28, 2], [3, 2, 1], [4, 2, 1], [4, 42, 1], [6, 2, 1], [6, 56, 2], [7, 2, 3], [8, 2, 2], [8, 42, 2], [12, 4, 1], [14, 2, 3], [14, 24, 6], [21, 4, 3], [24, 4, 2], [28, 4, 3], [42, 4, 3], [56, 4, 6], [84, 4, 6], [168, 4, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '336.150', 'commutator_count': 1, 'commutator_label': '84.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 400, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 12, 1, 2], [2, 21, 1, 2], [2, 28, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [6, 2, 1, 1], [6, 56, 1, 2], [7, 2, 3, 1], [8, 2, 2, 1], [8, 42, 2, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 24, 3, 2], [21, 4, 3, 1], [24, 4, 2, 1], [28, 4, 3, 1], [42, 4, 3, 1], [56, 4, 6, 1], [84, 4, 6, 1], [168, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 5376, 'exponent': 168, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '168.50', 'hash': 400, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 84], 'inner_gens': [[1, 2, 284], [1, 2, 220], [393, 458, 4]], 'inner_hash': 150, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': False, 'inner_tex': 'C_{12}:D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 22], [4, 36]], 'label': '672.400', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 32, 'linR_count': 264, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24:D14', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 66, 'number_divisions': 28, 'number_normal_subgroups': 40, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 152, 'number_subgroups': 1528, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 123], [3, 2], [4, 44], [6, 114], [7, 6], [8, 88], [12, 4], [14, 150], [21, 12], [24, 8], [28, 12], [42, 12], [56, 24], [84, 24], [168, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 588], 'outer_gens': [[1, 2, 452], [337, 2, 4], [1, 2, 340], [85, 86, 356]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [24, 3628800, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 3], [6, 4], [8, 1], [12, 3], [24, 2], [48, 1]], 'representations': {'PC': {'code': 1595096711701001329865943697180244206125405276683, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 5966, 2319, 58, 15907, 6170, 80, 16244, 3651, 102, 10757, 8748, 166, 14125]}, 'Perm': {'d': 18, 'gens': [21010447185976, 368056, 10692, 18191, 24338, 3991680, 397707843456000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:D_{14}', 'transitive_degree': 168, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
