-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10807', 'ambient_counter': 10807, 'ambient_order': 960, 'ambient_tex': 'C_2^2:Q_8\\times C_{30}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 480, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10807.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '480.1180', 'subgroup_hash': 1180, 'subgroup_order': 480, 'subgroup_tex': 'C_2^3\\times C_{60}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '960.10807', 'aut_centralizer_order': 16, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.f1', '4.k1', '6.a1', '10.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4682, 4492, 4036, 2133], 'generators': [1, 192, 488, 240, 2, 480, 640], 'label': '960.10807.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.f1', '6.a1', '10.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '480.1180', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 168, 'aut_gen_orders': [14, 12, 4], 'aut_gens': [[1, 2, 4, 8], [7, 245, 1, 332], [6, 3, 244, 109], [3, 242, 6, 107]], 'aut_group': None, 'aut_hash': 4889981620459245880, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 172032, 'aut_permdeg': 22, 'aut_perms': [46813485817189122799, 789881643559479695093, 780124088306787821288], 'aut_phi_ratio': 1344.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 14, 1], [3, 1, 2, 1], [4, 1, 16, 1], [5, 1, 4, 1], [6, 1, 2, 1], [6, 1, 28, 1], [10, 1, 4, 1], [10, 1, 56, 1], [12, 1, 32, 1], [15, 1, 8, 1], [20, 1, 64, 1], [30, 1, 8, 1], [30, 1, 112, 1], [60, 1, 128, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5.C_2^5.\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 168, 'autcent_group': None, 'autcent_hash': 4889981620459245880, 'autcent_nilpotent': False, 'autcent_order': 172032, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^5.C_2^5.\\PSL(2,7)', '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, 15], [3, 1, 2], [4, 1, 16], [5, 1, 4], [6, 1, 30], [10, 1, 60], [12, 1, 32], [15, 1, 8], [20, 1, 64], [30, 1, 120], [60, 1, 128]], 'center_label': '480.1180', 'center_order': 480, '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', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1180, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3], ['3.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [3, 1, 2, 1], [4, 1, 2, 8], [5, 1, 4, 1], [6, 1, 2, 15], [10, 1, 4, 15], [12, 1, 4, 8], [15, 1, 8, 1], [20, 1, 8, 8], [30, 1, 8, 15], [60, 1, 16, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 93600, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.208', 'hash': 1180, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8]], '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, 480]], 'label': '480.1180', 'linC_count': None, 'linC_degree': 4, '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': 'C2^3*C60', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, '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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 480, 'number_divisions': 96, 'number_normal_subgroups': 472, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 472, 'number_subgroups': 472, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 16], [5, 4], [6, 30], [10, 60], [12, 32], [15, 8], [20, 64], [30, 120], [60, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 168, 'outer_gen_orders': [14, 4, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[6, 244, 247, 159], [245, 242, 6, 138], [1, 245, 243, 89]], 'outer_group': None, 'outer_hash': 4889981620459245880, 'outer_nilpotent': False, 'outer_order': 172032, 'outer_permdeg': 22, 'outer_perms': [441387580073874933046, 672222728069950852047, 9986644309605956155], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^5.C_2^5.\\PSL(2,7)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 3, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 24], [8, 24], [16, 8]], 'representations': {'PC': {'code': 511965599242256391, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -5, 80, 102, 166]}, 'GLZN': {'d': 2, 'p': 40, 'gens': [1504803, 1088017, 576009, 2312611, 1344021, 192003, 64321]}, 'Perm': {'d': 18, 'gens': [127008000, 355687428096000, 1307674368000, 6227020800, 10080, 96, 40279680]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 60], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3\\times C_{60}', 'transitive_degree': 480, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '240.208', '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, 4, 2, 4, 4, 4, 4], 'aut_gens': [[1, 2, 4, 16], [489, 483, 252, 24], [481, 491, 484, 944], [481, 11, 245, 273], [481, 2, 484, 504], [489, 11, 244, 696], [489, 482, 253, 312], [481, 491, 733, 784], [489, 490, 724, 473]], 'aut_group': None, 'aut_hash': 1578825338858570690, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 32768, 'aut_permdeg': 30, 'aut_perms': [40625978246357329016067542538085, 125498127070006875660656952168249, 195755592584107088828852366957058, 221567793276023425239363156909129, 218687630188130555494334083735605, 40701735695439733699550905671715, 166004957809407173367373123091271, 201382718939134187120518644828726], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 4, 1], [3, 1, 2, 1], [4, 2, 4, 2], [4, 4, 4, 2], [5, 1, 4, 1], [6, 1, 2, 3], [6, 1, 8, 1], [6, 2, 8, 1], [10, 1, 4, 3], [10, 1, 16, 1], [10, 2, 16, 1], [12, 2, 8, 2], [12, 4, 8, 2], [15, 1, 8, 1], [20, 2, 16, 2], [20, 4, 16, 2], [30, 1, 8, 3], [30, 1, 32, 1], [30, 2, 32, 1], [60, 2, 32, 2], [60, 4, 32, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^8.C_2^6.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 2851693483551186743, 'autcent_nilpotent': True, 'autcent_order': 16384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_4\\times C_2^8.C_2^3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [3, 1, 2], [4, 2, 8], [4, 4, 8], [5, 1, 4], [6, 1, 14], [6, 2, 8], [10, 1, 28], [10, 2, 16], [12, 2, 16], [12, 4, 16], [15, 1, 8], [20, 2, 32], [20, 4, 32], [30, 1, 56], [30, 2, 32], [60, 2, 64], [60, 4, 64]], 'center_label': '120.47', 'center_order': 120, '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10807, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['32.29', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 1, 2, 1], [4, 2, 1, 4], [4, 2, 2, 2], [4, 4, 1, 8], [5, 1, 4, 1], [6, 1, 2, 7], [6, 2, 2, 4], [10, 1, 4, 7], [10, 2, 4, 4], [12, 2, 2, 4], [12, 2, 4, 2], [12, 4, 2, 8], [15, 1, 8, 1], [20, 2, 4, 4], [20, 2, 8, 2], [20, 4, 4, 8], [30, 1, 8, 7], [30, 2, 8, 4], [60, 2, 8, 4], [60, 2, 16, 2], [60, 4, 8, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 7862400, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '240.208', 'hash': 10807, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2, 2], 'inner_gens': [[1, 2, 4, 16], [1, 2, 492, 16], [1, 490, 4, 496], [1, 2, 484, 16]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 240], [2, 180]], 'label': '960.10807', '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': 'C2^2:Q8*C30', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 52, 'number_conjugacy_classes': 420, 'number_divisions': 104, 'number_normal_subgroups': 388, 'number_subgroup_autclasses': 208, 'number_subgroup_classes': 644, 'number_subgroups': 900, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 48], [5, 4], [6, 30], [10, 60], [12, 96], [15, 8], [20, 192], [30, 120], [60, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 2, 4, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 240, 0, 0], 'outer_gens': [[489, 483, 252, 24], [481, 491, 484, 944], [481, 11, 245, 273], [481, 2, 484, 504], [489, 11, 244, 696], [489, 482, 253, 312], [481, 491, 733, 784], [489, 490, 724, 473]], 'outer_group': None, 'outer_hash': 1926513769237116296, 'outer_nilpotent': True, 'outer_order': 4096, 'outer_permdeg': 512, 'outer_perms': [688498291273120681770346229144857819951395446628671256998587640003353656690055293492001347442565358323354617036811670346770480217524920639201734015342843581746630942058392890195772286069458611507699709512267995243607140864931427749658397488519800672778365661021527068253276635619553329567154434136462179357018973361884682658273645327165374113664691554134542576482850881244419825681540367591288634691418680369587944014962104126355495735198161780349452668629548894040297252910917985785216294902920581797318764873642342796411571480849786880609005454965679744678555266559819888940090239820716820558039128332292984057593308536608951619067016404690169823928368962631490475761217165929083485429648839602079275948183514349660607469366273052719012175243636140841577837673939184244751133358790914210730234823796122531033679888551414131602796691374579826263119552694401343090040001392226858491261210528607717752373939459564084007010974501237779205465874578164318152858397082396692396440427015515011194345087044338679770355712636378751277301502786635991430912682238559546391136527945107793469545427489775379397467124938803966056795273771683517728023513279457699692737105976034, 1368988141967675087124973940675319378303436971272537913982780377495123830158174541745492017455013943041514676415371161831688224309065138488575390345893665176018762602681236010552132132061276377704040016281701604486454175063690737339089899673576750257931159424464903327382904302848478996165237215511553762534078042530440748962118547515092012443964046352879138765956293838026814585004664162941707096349171537588418857952883418049795535506014091895133345219697069536501573556484464337951154729616110954091220769544181284283671787230464184105155342768524904619676707363566411855197945881303821997742973533741902888160840414647644819485124597956052187093908127048260629846876904317471026008799500048761338845260910799045725027086914799599398760032399241941808959089447585570763572098729655450526785309598207183486195803197949155687314975856472854939481657692684915146764933790301929052086172332352546584712241005391628908272892582314874903643397814153639927084709473680844147189455550670277205974624378991107489894827274222407360440078901497030060266200867357408700078061784069500324328981663810561693838852376977383413938074299447856512328784999614765369401003729930963, 2049477992490895639125964480630764962526253186896857647906958088053054913977239822863206376674894175335132367848788689070674248783009955815529298904800400532378510150915613185943705082366005488819645414677350917000854431379262746460199224838369824906475112499271038560343830017377403237912657033471476283422375101443902511092396003625277979737925448275128975301877174613926230922975228296790421499884577627219561735030932242817368501871571848879004044362344756051032245161333947125314294996990622228894563953247222303376602093328136265113259396217904809137524164581947290914640920742434172542502725422808591573160942661234534974173446063946417977664269548911226721156293985854616055325510598537363854575889289918107678269749604035736622710932899537519874905397351179738198389314478067775644613641588704886507115553725493402224066051730202031422903668975849263026942157594248111368756202404246752485446188278256007444759336819067438114694387559905677076965361821862350436552771242608703775807306042218964310308221660409613631062154369626206207807192726070127786391676726986638606639513538296783275443723321975338512482025124377318820439988877413931371572000627407731, 13335192128611462638347123897437205941731341692174263217311015316270021594263405434520065680706382722330570639421195417267970461598368424438541146614123573412044898809703239262107294765500684870637694045138356625763416410283632988432364567405708518532013066448096380170042284204562872734475666779404803590124034280153372653922489773879452294304047259901245325960512756858336471514560783514067798793009484496663776677584273076377875003165482107213380526695387900835091639093238108085576679446684029902852421371338640814996980976348652446544893455046002249643378428593858734170915760739327120469046677458793946019451870592965991448798277427061767384131441269630077210739324173660734398841285733987642192609437563759007272252212031965554677895425717347141533881004890216618524876172667491117569833010046320402974001994060354530412271953145113150023435628365268677854580678187135594697450501207253308654825483831388178194154091600371654500955149384581044368775564169284903890484474771509416989101948708626264190360968876445373568186876885304748590871354336895672770223165968678835414432160358766532027507900638261178173997216423894844883745722550617820371480122218028, 2731299530816103303963827012679447472055167707230921695828730308941435708657648616728211670424925311960409128976137997011015339563534313442157298147004321646423199168369683375679729136750390321626693518717755745247578744271760786568008554242851674937944700235502496777099557879708212967886615801809099716198719406564232788827648366067425209198626800401995400024826508913580142831499059089236901560910570127584595893230423543326489392289544662647965170828384578546662729944476118472833781620567495353600442487214346122714852914313469376073603714972444588878070407115812659621267371305123853942654023256071672013453552396562166564977215472679084353438885500063296074020880939626980048896517316047271924902442007388412670201791014515707390792533356722008761800084659433779435523654437172900663177429219612762830698170693152255344070720396962613664147320045540031006207048698157975961750895826586527302746216253766149894892322557228903367891220850457781220517586718904353633226083839629290935945903638915773830368261620374683133637586390278652932211993215989160968623998582646101454840732894607984473817369331443710886951139155798421151037486805681569107483600861074792, 3411789381338567673495646368985945761542680164923837558060637193638986398372569285616262140626993908961982507700181067685522947773570123339876467167826592033054588199668654832849496197562750319959661238318279632858312016045521180089617087380830330931259451431239138827554212600408501683575518893937322017441895146678545184070555510908066642426865736255335305551998512276566917735966429499357200015538852032161756551596545745700420154101851259860356616171857570720679831136300521784842477091500340564227594755983440920520134150456515931472585058308726331490873173395994399112900399422240700809120840222044369321022816617054118393880960026975307419579040689714066216351157136236407802601409109931909172632180524867414342949859115186558112792513203771467868994275520798438702612902491748201037433088508558247367951621726982150772266279720843559563247280528247301436388933052839659540480278896907871840494359194767226614566843813725947418410356221945670100615535833310859417354607219766505179652956391813440889840032298053417801647767606401974278705511335403633676139218672334880380893109478949717336257447925716793794598901908103450396906283722944773015533498632346829, 4092279231862521814518639295945811600833141416157810684349103725687379983315162363517489198299144683521423295994936482193166265982250809664202980161467419756944072929252772914986954695266133527563356109399912815882921318130877790176617105438370592349485187084143854945796168382883118608621581771952091070035802271706537851057660759739284945099651607063717169216644296383696898351170240587942890580411954459959049665643122227788041798804002581475155105477891184856654621468600061084358778340143728866944890636022912404926537551466628893874625198055725914381377820334660853428368458360965125770113734013177056788143975076854629329744445941369048441881565566160243961378612092603944811443675628289762751239182667614041014039984393408529507620207774656688570361357370169911761874412693913847575531043409145501516324041594056201030218082361835530106518937378108824404939913968816308515411096571315149377292197668648225827151047357501156464892683881414364782421856610204182410141322747952482195857874675871459998246178154124363389470346522848819734270722303811670363529313146078464378823104511039668567319691149538356003215230423725789230001153841207082416177982181645184, 4772769082385742678862713225959364694299995668944677709923231926437261598753763516761226301097311490672447653990223017497121992908089936525576194167129817492463759458709898846458524825320945718364912193952439356157537557507277994419193170744991662744874522587867726735366280967219915455120685413337503376116046654217706291493624589707415566052554932162935672702708721144799119223633571819270488606837390311449338665195586909544723790700314585858488357948119936979477151872650751554146097694365008574031622003121757247111282916238856074978796608270016304974456553517198014876051389366565354144253872813067768012953984957951066534706214450300726459907691090002905219398905978540442906498094919157911110285170810550797467937831635242286512321741199616217551493034362046304140786970356278019600596527519187777740853800651268275975842518733589408650545018391328217634718752126516723484804320933261319735905562442069349757739066299760314805709443514697871248628426937254659156386830509708987682869104418756520343606756960477411108647831347076234240160534532321892674253223463526765294116500892250916438503776801304255354253376359822004925672251667645547174134327976711765], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^8.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 3, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 26], [8, 26], [16, 10], [32, 2]], 'representations': {'PC': {'code': 40550065741427112744954556055559, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 5914, 66, 4980, 116, 141, 222]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [30666285, 31010893, 684443, 6133257, 45664499, 685345, 49875609, 44295745]}, 'Perm': {'d': 22, 'gens': [51212944467962686080, 107047691251113271680, 4987804804190208000, 107048048350191742080, 10080, 96, 4302991486080, 107047688359772160000]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 30], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2:Q_8\\times C_{30}', 'transitive_degree': 480, '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}
