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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.18798', 'ambient_counter': 18798, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.18798.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.735', 'subgroup_hash': 735, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.18798', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '64.a1.a1', 'complements': ['128.e1.a1', '128.e1.b1', '128.g1.a1', '128.j1.a1', '128.i1.a1', '128.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.k1.a1', '4.l1.a1', '4.u1.a1', '4.v1.a1', '4.bd1.a1', '4.bg1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4113, 5606, 6854, 4111, 4116, 5625, 6851, 4090], 'generators': [1, 2, 8], 'label': '256.18798.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.u1.a1', '4.v1.a1', '4.k1.a1', '4.l1.a1', '4.bd1.a1', '4.bg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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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': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 4, 2, 4, 2, 2, 2, 4], 'aut_gens': [[1, 2, 8, 32], [1, 2, 76, 32], [1, 2, 88, 96], [1, 98, 8, 32], [1, 66, 56, 32], [49, 50, 8, 32], [1, 2, 72, 32], [1, 70, 88, 96], [69, 2, 56, 32], [81, 114, 8, 32]], 'aut_group': None, 'aut_hash': 1969822349860123513, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 40, 'aut_perms': [673777779497349571727523436671391081358761514912, 714697415532235800411050728096363960867948500857, 423680442335402938388032195383034577986247256753, 112547356024288585214239445986650820569380259281, 2634478127881703133696880564169928124409830137, 408756710183083329334536532586101736231540718728, 718893449254738388032815381148239699097330931161, 102602600244697212989182363534175631708189086448, 12580019553536340942097877122778737224262165407], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 8, 1, 1], [2, 8, 2, 1], [4, 2, 1, 4], [4, 4, 4, 1], [4, 8, 1, 1], [4, 8, 2, 2], [8, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 32, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 8, 3], [4, 2, 4], [4, 4, 4], [4, 8, 5], [8, 8, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '32.27', 'commutator_count': 1, 'commutator_label': '16.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 735, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 8, 1, 3], [4, 2, 1, 4], [4, 4, 2, 2], [4, 8, 1, 5], [8, 8, 1, 2], [8, 8, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 336, 'exponent': 8, 'exponents_of_order': [7], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '8.5', 'hash': 735, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 2], 'inner_gens': [[1, 70, 88, 96], [69, 2, 56, 32], [81, 114, 8, 32], [65, 2, 8, 32]], 'inner_hash': 27, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': None, 'inner_tex': 'C_2^2\\wr C_2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [4, 4]], 'label': '128.735', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 12, 'linQ_dim': 10, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.D4', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 26, 'number_divisions': 23, 'number_normal_subgroups': 46, 'number_subgroup_autclasses': 131, 'number_subgroup_classes': 191, 'number_subgroups': 448, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 64], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 80, 48, 0, 0], 'outer_gens': [[1, 34, 40, 96], [49, 18, 92, 96], [49, 82, 120, 32], [49, 82, 40, 96], [49, 50, 24, 96], [1, 34, 108, 96]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 32, 'outer_perms': [142770030496520159055520294035537821, 151369820601870972414918434890868297, 254871050731657768847415004253141614, 236779228226318440747519362622433741, 176887477315135814149506605866948699, 219696133684568153371739763564713977], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 1], [8, 2]], 'representations': {'PC': {'code': 10125367706293065585026411, 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 448, 981, 36, 2467, 794, 80, 1411, 4037, 124]}, 'Perm': {'d': 20, 'gens': [124204339896780965, 26156160292511647, 276589640699740927, 406268411663923336, 534786978009191176, 45194814527385720, 534786978009191160]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.D_4', 'transitive_degree': 32, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 2, 4, 4, 4, 4, 4, 2, 4], 'aut_gens': [[1, 2, 8, 16, 32], [81, 86, 24, 144, 240], [213, 214, 72, 16, 176], [145, 82, 216, 16, 224], [5, 150, 88, 144, 176], [1, 86, 200, 16, 48], [17, 198, 216, 16, 48], [65, 6, 152, 144, 176], [193, 146, 216, 144, 112], [81, 210, 216, 144, 32], [197, 66, 136, 16, 96]], 'aut_group': None, 'aut_hash': 261240470784066402, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 40, 'aut_perms': [65928502075761605829657821786046005788139404229, 725401368978702882354823778920894112439726632046, 449546160415304695358027651549501451525495678571, 245468385487826408573953361959380478575331234093, 426560569514868831593613454500754621348147455624, 15182123153159687244934643078518745138709436704, 454281015119697789646402194929152344461365646790, 469970454317961686829968613874549923113089568311, 510739062619922584896148221790263383419285978050, 648423406397565345616250935155950787240010461775], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 4, 2, 1], [2, 8, 1, 2], [2, 8, 2, 2], [2, 16, 1, 1], [4, 2, 1, 4], [4, 4, 2, 1], [4, 8, 1, 2], [4, 8, 2, 2], [4, 16, 1, 1], [8, 4, 2, 2], [8, 8, 2, 3], [8, 16, 1, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4.C_2^6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '32.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 2], [2, 8, 6], [2, 16, 1], [4, 2, 4], [4, 4, 2], [4, 8, 6], [4, 16, 1], [8, 4, 4], [8, 8, 6], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.226', 'commutator_count': 1, 'commutator_label': '16.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 18798, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 2], [2, 8, 1, 6], [2, 16, 1, 1], [4, 2, 1, 4], [4, 4, 1, 2], [4, 8, 1, 6], [4, 16, 1, 1], [8, 4, 1, 4], [8, 8, 1, 6], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 161280, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '16.14', 'hash': 18798, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2, 1, 4], 'inner_gens': [[1, 214, 152, 16, 32], [85, 2, 88, 16, 160], [145, 210, 8, 16, 96], [1, 2, 8, 16, 32], [1, 130, 200, 16, 32]], 'inner_hash': 226, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4^2', 'inner_used': [1, 2, 3, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 2], [8, 2]], 'label': '256.18798', 'linC_count': 24, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 24, 'linQ_dim': 10, 'linQ_dim_count': 24, 'linR_count': 24, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4.D4^2', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, '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': 28, 'number_characteristic_subgroups': 95, 'number_conjugacy_classes': 40, 'number_divisions': 40, 'number_normal_subgroups': 143, 'number_subgroup_autclasses': 457, 'number_subgroup_classes': 749, 'number_subgroups': 2215, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 79], [4, 80], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 212, 0, 212, 0, 0], 'outer_gens': [[145, 82, 216, 16, 224], [213, 82, 136, 16, 224], [1, 198, 24, 16, 48], [69, 146, 152, 16, 32], [1, 130, 8, 16, 160], [65, 146, 200, 144, 224]], 'outer_group': '128.2163', 'outer_hash': 2163, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 32, 'outer_perms': [18836680831018073910268279277814188, 108540795961807695392326196335711866, 140107420029934944470543502155462008, 252421630022100634455461687736846952, 146753387256988241034375500874848300, 105201460008225407396074098333115162], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 20], [4, 2], [8, 2]], 'representations': {'PC': {'code': 10717063633963901122677965963668915171, 'gens': [1, 2, 4, 5, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 128, 3425, 41, 3170, 4867, 1419, 1107, 3853, 605, 141, 1374, 166]}, 'Perm': {'d': 20, 'gens': [148874048047121881, 256920473621026207, 275437109718707777, 405700221078917287, 534708799915414440, 7, 541466860864094040, 668224274133201120]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4.D_4^2', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
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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}
