-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.2160', 'ambient_counter': 2160, 'ambient_order': 384, 'ambient_tex': 'C_4^2.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 192, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.2160.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.817', 'subgroup_hash': 817, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:C_{12}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '384.2160', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.a1.a1', 'complements': ['192.h1.a1', '192.h1.b1', '192.h1.c1', '192.h1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.c1.b1', '4.i1.a1', '4.j1.a1', '6.a1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4328, 8002, 8617, 6550, 4170, 8036, 7701, 4407], 'generators': [5, 16, 2, 8, 192, 96, 128], 'label': '384.2160.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.b1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 4, 16], [9, 4, 24], [1, 4, 18], [57, 6, 16], [3, 4, 16], [105, 12, 80], [105, 4, 92], [145, 60, 176], [1, 6, 16], [97, 4, 16], [97, 100, 16], [9, 4, 16], [3, 4, 80], [1, 12, 112]], 'aut_group': '24576.bdd', 'aut_hash': 4333428238501561947, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 26, 'aut_perms': [615052870917408000, 849654, 222980923791090031742844840, 374406, 3754270086756455185920000, 65821485538602400193033040, 233524050962347042323170088, 1275486, 79496126941841092197792000, 1266749198301187099699200, 65876561695514626477344000, 1, 3754270208402950487328000], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 3, 2], [3, 1, 2, 1], [4, 2, 12, 1], [4, 4, 8, 1], [6, 1, 2, 1], [6, 1, 6, 2], [12, 2, 24, 1], [12, 4, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^8.\\GL(2,\\mathbb{Z}/4)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '1024.djt', 'autcent_hash': 1957374279625110839, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 1, 2], [4, 2, 12], [4, 4, 8], [6, 1, 14], [12, 2, 24], [12, 4, 16]], 'center_label': '24.15', 'center_order': 24, 'central_product': True, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 817, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.65', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 2, 1, 12], [4, 4, 2, 4], [6, 1, 2, 7], [12, 2, 2, 12], [12, 4, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 91, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '24.15', 'hash': 817, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 2], 'inner_gens': [[1, 12, 112], [9, 4, 16], [97, 4, 16]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 36]], 'label': '192.817', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:C12', 'ngens': 7, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 84, 'number_divisions': 48, 'number_normal_subgroups': 130, 'number_subgroup_autclasses': 42, 'number_subgroup_classes': 186, 'number_subgroups': 258, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 56], [6, 14], [12, 112]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 6, 4, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[53, 54, 38], [151, 150, 68], [151, 108, 118], [147, 14, 90]], 'outer_group': None, 'outer_hash': 388097117244947847, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 16, 'outer_perms': [443599400183, 2790747153496, 6832126833863, 9441720288023], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2.C_2^6.D_6.C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 24], [4, 16]], 'representations': {'PC': {'code': 18210518702818232195713, 'gens': [1, 3, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 14, 254, 58, 3924, 102, 124]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [111169, 111361, 111745, 110617, 1299761, 2821273, 2130091]}, 'Perm': {'d': 15, 'gens': [12937075224, 93884314344, 93884315304, 4, 186810624000, 186810624744, 7983360]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:C_{12}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 2, 2, 2, 12, 12, 12, 2, 12], 'aut_gens': [[1, 2, 4, 32], [145, 2, 238, 368], [345, 2, 228, 368], [321, 2, 342, 160], [81, 2, 70, 354], [19, 2, 14, 32], [265, 2, 278, 242], [345, 2, 342, 32], [267, 2, 174, 240], [1, 2, 222, 160], [257, 2, 180, 226]], 'aut_group': None, 'aut_hash': 4979065055114158367, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 80, 'aut_perms': [45614644686373578598229118235066906926932256595506574239414546654320961604441080546420567275891772477058665046704751611, 17812505039456794929921071816506220479247566035527359577743289187502472032049216777696790969479809288069424213474147310, 22253503903726804588150160903860925716464573481750229216335812035769102561511895372535115000461993538566611499698403717, 53426764277050549751511516789285311821400063762798777396607599939869812411664150909725534348211189202138087215815058400, 59649005194869240662884901566927805961195371107760908081113790162547882254759593190683707040301284251563150573449825220, 60076067131448594864447405893065460021626675348074234653489336073728865472341211378340644037951982619821760726160059329, 28543856584316971641974653383965232702167135716069959577487966746935516631948627666107732818845593886789363389042827816, 57448680542233615646567736185272305840844210195725795574508217495124877212885531987516793566902452906018720525372405915, 9856049119534776284854748272485683330152352384575649940681874437134143047465909274514366917454467430726022949442301787, 8659405527963482537536586630599534167524982534164084160460649767412286541071244877707242259942080839733817483258777117], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 12, 4, 1], [3, 2, 1, 1], [4, 2, 1, 4], [4, 2, 4, 1], [4, 4, 2, 1], [4, 8, 4, 1], [4, 12, 4, 1], [6, 2, 1, 7], [8, 12, 8, 1], [12, 4, 1, 4], [12, 4, 4, 2], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^7.C_2^6)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '512.10494213', 'autcent_hash': 1718285292446712970, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '48.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 12, 4], [3, 2, 1], [4, 2, 8], [4, 4, 2], [4, 8, 4], [4, 12, 4], [6, 2, 7], [8, 12, 8], [12, 4, 12], [12, 8, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '48.43', 'commutator_count': 2, 'commutator_label': '24.9', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2160, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 12, 1, 4], [3, 2, 1, 1], [4, 2, 1, 8], [4, 4, 1, 2], [4, 8, 2, 2], [4, 12, 2, 2], [6, 2, 1, 7], [8, 12, 4, 2], [12, 4, 1, 8], [12, 4, 2, 2], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2160, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 4, 6], 'inner_gens': [[1, 2, 30, 160], [1, 2, 4, 32], [11, 2, 4, 352], [257, 2, 68, 32]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'C_6:D_4', 'inner_used': [1, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 36], [4, 14]], 'label': '384.2160', 'linC_count': 512, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 112, 'linQ_dim': 8, 'linQ_dim_count': 24, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4^2.D12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 33, 'number_characteristic_subgroups': 67, 'number_conjugacy_classes': 66, 'number_divisions': 48, 'number_normal_subgroups': 125, 'number_subgroup_autclasses': 218, 'number_subgroup_classes': 372, 'number_subgroups': 1358, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 55], [3, 2], [4, 104], [6, 14], [8, 96], [12, 112]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4, 4, 2, 2, 2, 2], 'outer_gen_pows': [0, 8, 256, 256, 128, 8, 136, 0], 'outer_gens': [[3, 2, 12, 226], [9, 2, 20, 354], [139, 2, 238, 50], [131, 2, 60, 34], [147, 2, 324, 226], [153, 2, 134, 160], [345, 2, 132, 226], [65, 2, 92, 354]], 'outer_group': '512.10493082', 'outer_hash': 7367214181469736260, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [241945406377195251199007896399371348891513254983498228208485601986344234714252560191573275391911717438683939115736739867207690973859010893294819532064442088341482809068467551996522656079275765856994555230098409598025, 19729178442714674298716287251801787506344693302482873601689356124264910443842740110664019574841331095581288891648969714204053275961393608806717117672224780413139146661409325726813116722403299216658525193501959080232, 263487153581488943357809440207759215068338845388082960785236540382018103061901754410197355462943945954278956713158855660395036562733669540536313130804032157769871272238588846465667192914813167077442275241422254660741, 110275836833946303159811649913599447561664434101111764127021147774545754823392206900228529754076333229866625696889611357291475649715447454911335005131160699189026813681796049937661389318177326996980275014405196785420, 239481545531689915277568509799485271264829892557996036817725203976020855820851539425028781982118304207072410313770188246063153204490675152912342165892269752025319598947845248921877181141354107312434746562739300488786, 161300425637997586227107239429303861453112191648092075476369232993872561000349317253282170613445992943191483154803511556209344000915613160523199333670867035582346813836638271497442966703384728996462111851788343126270, 160007026417474388270153256300984424317632886088840883746794870829103320325564381779498507507229324560427977746218991131429888196552009646128601970189693739926272669564045632508234213677712804036305213035127859824578, 365056651117011043030731957209451693895495916114774055900899414331091840048589133660439094132485677002675687136871476444523410118174317342342934480941240614833084503436928935616682046117793916957328794146178306484529], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 22], [8, 2]], 'representations': {'PC': {'code': 236703140071689459151177434891727689968641, 'gens': [1, 2, 3, 6], 'pres': [8, -2, -2, 2, -2, -2, -2, -2, -3, 722, 66, 771, 91, 7685, 4245, 141, 17926, 4502, 166, 16391, 4119]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [1230625, 3207749, 1287821, 1494181, 2764825, 774151, 111745, 111361]}, 'Perm': {'d': 19, 'gens': [732297647668329, 6778983964435336, 6317903656, 13516122267648000, 135772680, 16, 40723320, 93405312000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2.D_{12}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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}
