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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '576.5407', 'ambient_counter': 5407, 'ambient_order': 576, 'ambient_tex': 'C_6^2:\\SD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 576, 'characteristic': True, 'core_order': 2, 'counter': 279, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '576.5407.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.c1.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': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '576.5407', 'aut_centralizer_order': 9216, 'aut_label': '288.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 9216, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.f1.a1', '144.a1.a1', '144.j1.a1', '144.k1.a1'], 'contains': ['576.a1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6790, 2783, 2197, 4712, 3270, 2098, 2501, 1927], 'generators': [56], 'label': '576.5407.288.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.c1.a1', 'normal_contained_in': ['32.c1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '288.887', 'quotient_action_image': '1.1', 'quotient_action_kernel': '288.887', 'quotient_action_kernel_order': 288, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': [4, 2, 6, 4, 4, 12, 4], 'aut_gens': [[1, 2, 16, 96], [341, 306, 400, 496], [433, 414, 400, 536], [249, 254, 400, 536], [53, 34, 400, 504], [181, 178, 400, 552], [537, 510, 400, 480], [421, 394, 400, 504]], 'aut_group': None, 'aut_hash': 4786845279730575862, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9216, 'aut_permdeg': 72, 'aut_perms': [12014444639527782678780837700506046265866038494863895816636057065121811325461616416524883655270035532528, 23107165531805318531516034055515283702285807611068290697898549669406324248352852943892082749714914650577, 31295472438273438306349361992058864151072082462598891832013218556992108182772770633188113470109049441003, 3394264839365083730145702902240926820812608461183577344732817887322054833640814769216016375453994303735, 17116117405998199850246667113413517812683336040006747441405248550160293907955751144802070410595865554130, 38296921043657960405239632257670790946923722249317048287809049415607177394684445079219030164301428124643, 29263119154451341836465670910819869010632452825153657121263967218610811103157614483483245017467899830769], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 24, 1, 1], [3, 4, 1, 2], [4, 12, 4, 1], [4, 18, 2, 1], [4, 24, 1, 1], [4, 36, 1, 1], [6, 4, 1, 6], [6, 4, 4, 1], [6, 8, 2, 1], [6, 24, 2, 1], [8, 36, 4, 1], [12, 12, 8, 1], [12, 24, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2.C_2^6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', '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, 3], [2, 2, 2], [2, 24, 1], [3, 4, 2], [4, 12, 4], [4, 18, 2], [4, 24, 1], [4, 36, 1], [6, 4, 10], [6, 8, 2], [6, 24, 2], [8, 36, 4], [12, 12, 8], [12, 24, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '144.186', 'commutator_count': 1, 'commutator_label': '72.34', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5407, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 24, 1, 1], [3, 4, 1, 2], [4, 12, 1, 4], [4, 18, 1, 2], [4, 24, 1, 1], [4, 36, 1, 1], [6, 4, 1, 10], [6, 8, 1, 2], [6, 24, 2, 1], [8, 36, 2, 2], [12, 12, 2, 4], [12, 24, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6720, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '144.186', 'hash': 5407, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3, 6], 'inner_gens': [[1, 6, 400, 480], [13, 2, 272, 176], [193, 418, 16, 96], [193, 18, 16, 96]], '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': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10], [4, 25], [8, 2]], 'label': '576.5407', 'linC_count': 80, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 12, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:SD16', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 24, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 45, 'number_divisions': 37, 'number_normal_subgroups': 39, 'number_subgroup_autclasses': 167, 'number_subgroup_classes': 283, 'number_subgroups': 1626, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 31], [3, 8], [4, 144], [6, 104], [8, 144], [12, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 4, 0, 0, 0], 'outer_gens': [[9, 2, 16, 104], [5, 10, 272, 136], [9, 2, 16, 96], [9, 10, 16, 96], [293, 290, 272, 136]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [363001, 5040, 368040, 367927, 811456], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 4, '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, 15], [8, 8]], 'representations': {'PC': {'code': 429939873299182848437363801947645398593550270744576660934088453, 'gens': [1, 2, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 3, 2, 3, 64, 97, 41, 290, 66, 16004, 5452, 820, 116, 10757, 10765, 789, 26886, 4942, 6742, 166, 24583, 8207, 6167]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1394809, 78193, 1127136, 385244, 793169, 622537, 70633, 46745]}, 'Perm': {'d': 18, 'gens': [180594974887, 357001374285365, 94484885, 2789837498896, 16, 94484880, 43333837747200, 735000173107200]}}, 'schur_multiplier': [2, 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:\\SD_{16}', 'transitive_degree': 96, '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}
