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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.4293', 'ambient_counter': 4293, 'ambient_order': 864, 'ambient_tex': '(C_3\\times C_6^2).D_4', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 3, 'counter': 222, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.4293.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.887', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 887, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '864.4293', 'aut_centralizer_order': 3456, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3456, 'centralizer': '2.b1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.c1.a1', '144.a1.a1', '144.f1.a1', '144.l1.a1'], 'contains': ['864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3588, 1309, 4871, 3270, 1526, 7279, 8642, 7226], 'generators': [76], 'label': '864.4293.288.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['32.a1.a1', '144.a1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '864.4293', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.152', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [2]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 3]], 'label': '3.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], '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': 1, 'perfect': False, 'permutation_degree': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 4, 6, 2, 4], 'aut_gens': [[1, 2, 12, 144], [627, 370, 420, 144], [77, 706, 666, 480], [11, 346, 306, 552], [413, 410, 780, 720], [323, 658, 588, 720], [11, 346, 306, 480]], 'aut_group': None, 'aut_hash': 6073603236452683435, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 60, 'aut_perms': [4178128518715523396996815224249257167305666829044799566637071976613102465040987456, 4145199378424106117960392471550764608439140963177503639830362241554390487787675517, 6778720347295979875119745052457225743676793799060735985933830510683953699364277616, 2391056424201550727625405245441172963355698297134542865982291758240401172118913343, 7084148203470973092240795941451232294394939720153812036874799222718742042341581791, 7194688649094039626695647713344565060708700932814093639613660511416918097087170543], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 4, 2, 1], [3, 8, 1, 1], [4, 12, 2, 1], [4, 18, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 4, 1, 2], [6, 4, 2, 2], [6, 4, 4, 1], [6, 8, 1, 2], [6, 8, 2, 1], [6, 72, 1, 1], [8, 108, 2, 1], [12, 12, 4, 2], [12, 12, 8, 1], [12, 36, 1, 2], [12, 72, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_2^6.C_2^2', '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': 12, 'autcentquo_group': '864.4686', 'autcentquo_hash': 4686, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^3:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 36, 1], [3, 2, 1], [3, 4, 4], [3, 8, 1], [4, 12, 2], [4, 18, 2], [4, 36, 1], [6, 2, 3], [6, 4, 10], [6, 8, 4], [6, 72, 1], [8, 108, 2], [12, 12, 16], [12, 36, 2], [12, 72, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '432.755', 'commutator_count': 1, 'commutator_label': '108.33', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4293, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 36, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 4, 2, 1], [3, 8, 1, 1], [4, 12, 1, 2], [4, 18, 1, 2], [4, 36, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 4, 1, 4], [6, 4, 2, 3], [6, 8, 1, 2], [6, 8, 2, 1], [6, 72, 1, 1], [8, 108, 1, 2], [12, 12, 2, 4], [12, 12, 4, 2], [12, 36, 1, 2], [12, 72, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 26880, 'exponent': 24, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 8], [8, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '432.755', 'hash': 4293, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 82, 690, 552], [5, 2, 132, 720], [631, 26, 12, 720], [601, 290, 300, 144]], 'inner_hash': 755, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'S_3^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 31], [8, 5]], 'label': '864.4293', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 44, 'linQ_dim': 12, 'linQ_dim_count': 8, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C3*C6^2).D4', 'ngens': 8, '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': 31, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 54, 'number_divisions': 38, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 196, 'number_subgroup_classes': 230, 'number_subgroups': 1656, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 39], [3, 26], [4, 96], [6, 150], [8, 216], [12, 336]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 10, 12, 216], [1, 74, 492, 720], [1, 10, 84, 144], [1, 2, 84, 144]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 289, 1, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 25, '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, 11], [8, 10], [16, 3]], 'representations': {'PC': {'code': 634661142934568111255825513042926451529957302455617116517175385637, 'gens': [1, 2, 4, 7], 'pres': [8, 2, 2, 3, 2, 2, 3, 2, 3, 1313, 41, 1922, 450, 22083, 2123, 91, 14404, 2412, 116, 27653, 2317, 30918, 20174, 3390, 166, 6151, 18447, 3103]}, 'Perm': {'d': 25, 'gens': [627611488411430498174642, 1348154140464135949190536, 130438705001374548979200, 2024501127865677000288023, 2620557702965668311014400, 56, 333, 45360]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_6^2).D_4', 'transitive_degree': 48, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 3, 3], 'aut_gens': [[1, 2, 4, 48], [1, 26, 148, 48], [1, 106, 198, 176], [235, 10, 20, 48], [25, 2, 4, 72], [1, 2, 28, 48], [25, 2, 4, 48], [25, 130, 44, 240], [225, 226, 196, 48], [113, 34, 4, 48]], 'aut_group': '1152.43028', 'aut_hash': 4712047025162441457, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1152, 'aut_permdeg': 36, 'aut_perms': [115226926169335543358846874364217954129028, 176927079293062840970409315456451774592709, 9200660175058472259572538628057947499033, 2133021479288939171813665537814193, 102168690740511874172442328235406241493116, 77377505082410618771693171162688115470, 164241255766181191085468449464944180420092, 359611555872149446111814971103074065440794, 8138667937467830000009813977439882269711], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 1], [3, 4, 1, 2], [4, 12, 1, 1], [4, 12, 2, 1], [4, 18, 1, 2], [6, 4, 1, 2], [6, 4, 2, 1], [6, 8, 1, 1], [6, 24, 1, 1], [8, 36, 2, 1], [12, 12, 4, 1], [12, 24, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_6^2:D_4', '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': 12, 'autcentquo_group': '144.186', 'autcentquo_hash': 186, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 12, 1], [3, 4, 2], [4, 12, 3], [4, 18, 2], [6, 4, 4], [6, 8, 1], [6, 24, 1], [8, 36, 2], [12, 12, 4], [12, 24, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '144.186', 'commutator_count': 1, 'commutator_label': '36.7', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 887, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 12, 1, 1], [3, 4, 1, 2], [4, 12, 1, 3], [4, 18, 1, 2], [6, 4, 1, 4], [6, 8, 1, 1], [6, 24, 1, 1], [8, 36, 1, 2], [12, 12, 2, 2], [12, 24, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6720, 'exponent': 24, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, -1, 4], [8, -1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '144.186', 'hash': 887, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 6], 'inner_gens': [[1, 26, 6, 184], [25, 2, 236, 240], [131, 106, 4, 240], [201, 98, 100, 48]], 'inner_hash': 186, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3^2:C_2^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 2], [4, 13], [8, 1]], 'label': '288.887', 'linC_count': 4, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 11, 'linQ_dim': 12, 'linQ_dim_count': 8, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.D4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 24, 'number_divisions': 22, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 84, 'number_subgroup_classes': 99, 'number_subgroups': 464, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 15], [3, 8], [4, 72], [6, 48], [8, 72], [12, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 130, 20, 264], [1, 106, 188, 264]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [7, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 9], [8, 3]], 'representations': {'PC': {'code': 38753452843574455277405611371683211251571144783621, 'gens': [1, 2, 3, 6], 'pres': [7, 2, 2, 2, 2, 3, 2, 3, 365, 176, 128, 2487, 58, 3363, 570, 80, 6724, 571, 7733, 5052, 2539, 124, 1574, 4717, 2372]}, 'Perm': {'d': 22, 'gens': [13161783886837819, 51212945946893891804, 442670293840, 256099439727888991, 5721228051186, 5000609551601664000, 104864478926118912000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.D_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
