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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1024.dlx', 'ambient_counter': 2338, 'ambient_order': 1024, 'ambient_tex': '(C_2\\times C_4).C_2^7', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 256, 'counter': 2647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1024.dlx.4._.DSW', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.DSW', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, '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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.54597', 'subgroup_hash': None, 'subgroup_order': 256, 'subgroup_tex': 'D_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1024.dlx', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 66, 8, 512, 16], 'label': '1024.dlx.4._.DSW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4.DSW', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4._.DSW', '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': '32.51', '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, 2, 2, 2, 2, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 4, 8, 32], [1, 2, 20, 8, 32], [1, 18, 4, 8, 32], [1, 2, 4, 8, 160], [1, 2, 4, 136, 32], [1, 2, 132, 8, 32], [129, 2, 4, 8, 32], [1, 2, 4, 24, 32], [1, 2, 4, 8, 224], [1, 2, 4, 136, 48], [1, 66, 20, 8, 32], [17, 2, 132, 8, 32]], 'aut_group': None, 'aut_hash': 2510969609100918654, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 28, 'aut_perms': [8377348379541671567049878880, 87534155720586762727788575921, 1888321223398679546400080, 294418951164999715945403566239, 403291461126605635584000720, 294420813634205999129711796713, 87530918445264350174682833713, 7472923978017687200576888, 294423321591490130144459925527, 149941392008673468502582022896, 87937447181745505768519342721], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 4, 1, 4], [2, 4, 2, 2], [2, 8, 1, 6], [4, 2, 1, 2], [4, 4, 1, 9], [4, 8, 1, 8], [8, 4, 2, 2], [8, 8, 1, 6]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9\\times D_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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{10}', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '4.2', 'autcentquo_hash': 2, 'autcentquo_nilpotent': True, 'autcentquo_order': 4, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 8], [2, 8, 6], [4, 2, 2], [4, 4, 9], [4, 8, 8], [8, 4, 4], [8, 8, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.261', 'commutator_count': 1, 'commutator_label': '8.2', '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': 54597, '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, 8], [2, 8, 1, 6], [4, 2, 1, 2], [4, 4, 1, 9], [4, 8, 1, 8], [8, 4, 2, 2], [8, 8, 1, 6]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 79994880, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '32.51', 'hash': 54597, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2, 4], 'inner_gens': [[1, 2, 4, 24, 32], [1, 2, 4, 8, 224], [1, 2, 4, 136, 48], [17, 2, 132, 8, 32], [1, 66, 20, 8, 32]], 'inner_hash': 261, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4\\times C_2^3', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 8], [8, 1]], 'label': '256.54597', 'linC_count': 16, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 12, 'linQ_dim': 12, 'linQ_dim_count': 12, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D4^2:C2^2', 'ngens': 5, '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': 44, 'number_characteristic_subgroups': 431, 'number_conjugacy_classes': 49, 'number_divisions': 47, 'number_normal_subgroups': 437, 'number_subgroup_autclasses': 996, 'number_subgroup_classes': 1145, 'number_subgroups': 3079, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 87], [4, 104], [8, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 20, 8, 32], [1, 18, 4, 8, 32], [1, 2, 4, 8, 160], [1, 2, 4, 136, 32], [1, 2, 132, 8, 32], [129, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32], [1, 2, 4, 8, 32]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320, 0, 0, 0, 0, 0], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 8], [4, 4], [8, 3]], 'representations': {'PC': {'code': 19816750261390677843285246568, 'gens': [1, 2, 3, 4, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 771, 1107, 91, 5389, 597, 141, 5390, 166]}, 'Perm': {'d': 24, 'gens': [4550136867791389330533, 12293038852329323527, 26066995649832716772480, 57336848392004920588098, 84607377413819029879103, 24338, 108279001164147378969600, 57336848392004920569600]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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': 'D_4^2:C_2^2', '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': '128.2328', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [8, 2, 4, 4, 2, 8, 2, 4, 8], 'aut_gens': [[1, 2, 8, 16, 64, 256, 512], [991, 278, 920, 216, 708, 928, 948], [165, 166, 8, 176, 96, 288, 512], [891, 590, 952, 772, 312, 252, 72], [893, 714, 1012, 260, 340, 180, 200], [1, 38, 8, 176, 96, 288, 544], [591, 894, 652, 772, 440, 220, 476], [33, 166, 136, 176, 96, 416, 544], [991, 750, 920, 900, 408, 92, 72], [859, 274, 792, 88, 708, 896, 916]], 'aut_group': None, 'aut_hash': 244215383496412165, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 524288, 'aut_permdeg': 40, 'aut_perms': [586582227851723849979123441275645128831710922639, 751797712032688645616982509090016946238241112060, 180893945714875331328745743073126365461111954607, 528956185902531660976567072639056048297736011432, 363531185522493463301315909891582424118721590538, 494862169942736509553702457926707607247960011720, 669918552231597700318269105715941942459907286516, 429740688895060662781761513435101732638176665449, 496608822074829819567669461579632286441396474159], 'aut_phi_ratio': 1024.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 8, 1], [2, 4, 1, 1], [2, 4, 2, 1], [2, 4, 4, 3], [2, 8, 2, 1], [2, 8, 4, 3], [2, 8, 8, 1], [4, 2, 1, 2], [4, 2, 4, 2], [4, 4, 1, 1], [4, 4, 2, 3], [4, 4, 4, 8], [4, 4, 8, 1], [4, 8, 2, 5], [4, 8, 4, 5], [4, 8, 8, 1], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 8, 4, 6]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5.C_2^6.C_2^6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 7584652362103600381, 'autcent_nilpotent': True, 'autcent_order': 16384, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{14}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '32.27', 'autcentquo_hash': 27, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 8], [2, 4, 15], [2, 8, 22], [4, 2, 10], [4, 4, 47], [4, 8, 38], [8, 4, 4], [8, 8, 30]], 'center_label': '4.2', 'center_order': 4, 'central_product': None, 'central_quotient': '256.56083', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 2338, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 8], [2, 4, 1, 15], [2, 8, 1, 22], [4, 2, 1, 6], [4, 2, 2, 2], [4, 4, 1, 43], [4, 4, 2, 2], [4, 8, 1, 38], [8, 4, 1, 2], [8, 4, 2, 1], [8, 8, 1, 30]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [10], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '128.2328', 'hash': 2812889187820196037, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2, 2, 2, 2, 2], 'inner_gens': [[1, 134, 8, 48, 64, 256, 672], [165, 2, 8, 144, 96, 256, 512], [1, 2, 8, 144, 192, 384, 544], [33, 130, 136, 16, 192, 384, 640], [1, 34, 136, 144, 64, 256, 512], [1, 2, 136, 144, 64, 256, 512], [161, 2, 40, 144, 64, 256, 512]], 'inner_hash': 56083, 'inner_nilpotent': True, 'inner_order': 256, 'inner_split': None, 'inner_tex': 'D_4\\times C_2^5', 'inner_used': [1, 2, 3, 4, 5, 6, 7], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 128], [2, 32], [4, 8], [8, 10]], 'label': '1024.dlx', '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': '(C2*C4).C2^7', 'ngens': 7, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [1, 3, 15, 77, 751, 3907, 12307, 11843, 2667, 127, 1], 'normal_index_bound': 4, 'normal_order_bound': 8, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 35, 'number_conjugacy_classes': 178, 'number_divisions': 173, 'number_normal_subgroups': 31699, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1024, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 255], [4, 512], [8, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2], 'outer_gen_pows': [0, 892, 0, 0, 132, 132, 0, 404, 0], 'outer_gens': [[1, 2, 168, 176, 192, 416, 544], [893, 718, 852, 260, 340, 20, 232], [133, 38, 168, 176, 64, 288, 544], [33, 166, 40, 176, 64, 256, 672], [1019, 618, 824, 900, 280, 220, 200], [165, 162, 40, 176, 192, 288, 544], [33, 134, 8, 176, 96, 288, 544], [129, 306, 168, 292, 372, 180, 820], [33, 6, 8, 16, 64, 416, 544]], 'outer_group': '2048.crm', 'outer_hash': 1609563553783776752, 'outer_nilpotent': True, 'outer_order': 2048, 'outer_permdeg': 256, 'outer_perms': 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10387481940188623388413923273358304535585271352362871190397211291517094778650191617024375365901368161860489501199963107150493057366416057394602867186123879355691909431350181863613294903662119188505837409114239357689405808327591746597322189006920449297387607039543529273466130941892380722126605523308605127210231845040623812401823101903231418960066397493342641145204441507762741389571685347266444350922361994428811175035556266150027262146916227752665332489239298201132460557459778080883896395435058515461562], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^8.D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 7, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 128], [2, 32], [8, 12], [16, 1]], 'representations': {'PC': {'code': '105415236529432261323222141395711485625146036839612668579113211478', 'gens': [1, 2, 4, 5, 7, 9, 10], 'pres': [10, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2681, 51, 1082, 262, 2404, 3614, 934, 144, 3376, 1716, 886, 206, 4358, 2208, 67209, 6839, 4049]}, 'Perm': {'d': 48, 'gens': [3268446104331349087664310361614242727238197105301715431295751, 10809550533572396492312888765569229897747736005240227740869031, 11192626580589141252938419615112190073348110867940782971991106, 10783472914187231411374967832638677570542163312383117322986103, 66180504862750882327952791519826500470512267710704783410208, 8101455601748391890357244498915663467258120000641798398793412, 8022983385551432818890415632676089322294232044069613166474867]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 2, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_4).C_2^7', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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}
