-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '8192.xx', 'ambient_counter': 622, 'ambient_order': 8192, 'ambient_tex': 'C_2^7.D_4^2', 'central': True, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 2506, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '8192.xx.4096._.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '4096.D', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4096.bqv', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 4096, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^6.D_4^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': None, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '8192.xx', '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': [534484512521564983152161587200000000], 'label': '8192.xx.4096._.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4096.D', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4096._.D', 'subgroup_fusion': None, 'weyl_group': None}
-
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}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[148003654549952611164135616309798592576, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [235264094292921594652033545744787406351, 115518257709641142880943955468986816, 104603383360418949125930412016991425683, 74522680129013267451863965930912976, 270095993023474855426996964342117516395, 131105384918941605707170826337251805115, 104710243979195473035957419903014151920, 208901841965701872255924029450844236109, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 105236236439073489436686811847989898986], [243478927627803483662066327265531227264, 287068137262493629942435716802843401593, 104603383360418949125930412016991425683, 52478822473329503451482867109213010652, 286895634483174614199964175286289581215, 191321330882099427000654014410643712815, 191321333929758159677771663257391923343, 208901841044584252571193820474483842921, 191321328447413597630503204999570107947, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 53070525388730146424769916818921059040], [131228575966822204793917063913866492867, 104488152007112857137357298827584854432, 104603383360418949125930412016991425683, 130521398732356251942351785422603161757, 131220388802529449927752677452825880955, 192003612153880869678190366329990394053, 2454061066318842910490688908400, 17868579233525312132083088843459358669, 286879113489950877933844331823120452145, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 70396109333540726826759766487497261810], [200530814684673548232684862592866782154, 131154681097455497598168943255303227546, 69976960400541544088491389813741715354, 52478822473329503451482867109213010652, 269997184164692367799726711481099974075, 131154680792163679448888565629885879970, 192069415600383138875079654114572220592, 43885863947220444705900325488954628776, 270161694306132239800343268177415333429, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 534484512521564983152161587200000000], [183262921408344221791710202195623975450, 191847324868421172499779004715410107947, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 191970786961683933223464056694232854399, 287528334200950426059925219488494656125, 70313942831666030693940656054324536930, 87220415746440026415328887900385794381, 287594133683501204811711516518683401593, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 534484512521564983152161587200000000], [182638182944251562837166152440929732786, 287405115404595176937274910210419973205, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 269594649263016960697296386539843430821, 130694397566252852257343560666304743573, 600515427134909406438615247912335056, 113377153796439445506054608758306937220, 191970785435209983115541879903841679869, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 70396109333540726826759766487497261810], [244046145867677014096873581894200899520, 69870110172570706519424380632518306428, 104603383360418949125930412016991425683, 52437824442495067811692646449428828308, 287487275171502160785574613177597575071, 191839107513329478800639817368417731815, 191444789014202408246266080188001679869, 173979555858612270107949999727189388521, 69787946410658455824664856338484536930, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [244004924048811058531342126981371227264, 191970785435209983115541879903841679869, 104603383360418949125930412016991425683, 74522680129013267451863965930912976, 270120639881466009261980845745800806469, 131055884161978059047647602298744349533, 105236240400203047905233219618854151920, 79021990789521560732074926383317267558, 287405115404595176937274910210419973205, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 105236236439073489436686811847989898986], [191921543530851855985632317275979528109, 287405109910958452803120131538960452145, 69976960400541544088491389813741715354, 130521398732356251942351785422603161757, 104529436655171507306225952981899780957, 52388246861734953260316027544870371458, 287594133683501204811711516518683401593, 44411855779545639701189305966213308420, 105014148428120432006633098543424854432, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 70396109333540726826759766487497261810], [286846235254415688184641671761394144039, 191970785435209983115541879903841679869, 104603383360418949125930412016991425683, 269454480787543400408587265814082736581, 104471446558070644403868938549144104215, 7337517575954403297187942797120, 70396106593578281388700180348358306428, 95821528928362122930699488637050388636, 70396108116810233501164071230654546524, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 70396109333540726826759766487497261810], [61597731565665438521385534531994033250, 131220390938361418093335902770070634709, 69976960400541544088491389813741715354, 115520710544026960328828245066930616, 52421308039165289964908502786574397232, 52437825060757397185575415067033671760, 53070523252091881977313014606623980986, 208778462798886500793485194540617447063, 270054987055478698859704386372034785930, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 53070525388730146424769916818921059040], [191896788427826439753649661881515603767, 131220390938361418093335902770070634709, 69976960400541544088491389813741715354, 269635695748486270050867766528618601635, 69754882167421269568345858160120752354, 58006263474432658005686148603745832, 191847324868421172499779004715410107947, 208778462798886500793485194540617447063, 53070521726036888512609271404715082330, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 53070525388730146424769916818921059040], [121895905919414138076568868261530426228, 130628679181167059829489165910721280450, 104603383360418949125930412016991425683, 115520710544026960328828245066930616, 287355601528963586674631075091209846799, 191970781472064095496665376893686306437, 104529434519339566114227982671493100153, 87220418813890754053896524309715547305, 269454476807862407642832712922308511221, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 70396109333540726826759766487497261810], [270202849056818701309971398594525316067, 104710242455963520921195121401849834448, 69976960400541544088491389813741715354, 269454480787543400408587265814082736581, 69738170311690825530352054682981236445, 1538185897245892899590899422720, 130694394517353843224060103054230634709, 218086579735819207444729563072518973251, 287068137262493629942435716802843401593, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 70396109333540726826759766487497261810], [191855728809572930241330616584304571157, 270054980939158744712639527170605278530, 104603383360418949125930412016991425683, 130694391159533314179069023930130867835, 773024317546653158488241229209269136, 105236240699848215719788714518495445246, 70313942831666030693940656054324536930, 87746412167447601284604687616225794381, 641514678717216012156743671308986816, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 105236236439073489436686811847989898986]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 268435456, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 65536.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 1, 4, 1], [2, 2, 1, 6], [2, 2, 2, 3], [2, 2, 4, 2], [2, 4, 2, 6], [2, 4, 4, 8], [2, 4, 16, 1], [2, 8, 2, 4], [2, 8, 8, 1], [2, 8, 16, 1], [2, 8, 32, 2], [2, 16, 1, 6], [2, 32, 2, 2], [2, 32, 4, 1], [4, 8, 2, 2], [4, 16, 1, 6], [4, 16, 8, 1], [4, 32, 2, 2], [4, 32, 4, 8], [4, 32, 8, 3], [4, 64, 8, 5], [4, 128, 4, 2], [8, 128, 4, 2]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 20], [2, 4, 60], [2, 8, 96], [2, 16, 6], [2, 32, 8], [4, 8, 4], [4, 16, 14], [4, 32, 60], [4, 64, 40], [4, 128, 8], [8, 128, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': None, 'central_quotient': None, 'commutator_count': 2, 'commutator_label': '256.56083', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 622, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 20], [2, 4, 1, 60], [2, 8, 1, 96], [2, 16, 1, 6], [2, 32, 1, 8], [4, 8, 1, 4], [4, 16, 1, 14], [4, 32, 1, 60], [4, 64, 1, 40], [4, 128, 1, 4], [4, 128, 2, 2], [8, 128, 1, 4], [8, 128, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [13], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '256.56083', 'frattini_quotient': '32.51', 'hash': 4184995697854063957, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 1], 'inner_gens': [[148003654549952611164135616309798592576, 269528984518151169843363727454765278530, 69976960400541544088491389813741715354, 52478822473329503451482867109213010652, 69976959179375051486687123550059333914, 69738170311690825530352054682981236445, 269454476807862407642832712922308511221, 113377153796439445506054608758306937220, 130521396289603635719422708287062270581, 130628682539375342147355686685366275010, 269528986655596094769488953651697979570, 534484512521564983152161587200000000], [243478927627803483662066327265531227264, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 165411158340182756641446577500611015479, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [148003654549952611164135616309798592576, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 78495994368513985862799126667477267558, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [182695705923354893944352794093784543852, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 278384772950495372019341083114228643490, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [200103560328498393256382948467176896698, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 95821528928362122930699488637050388636, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [200103560328498393256382948467176896698, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046373179463950212958385845737349322, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [243520149446669439227597782178360899520, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [130661632126861518389080519824607487371, 130521396289603635719422708287062270581, 104603383360418949125930412016991425683, 269454480787543400408587265814082736581, 104471446558070644403868938549144104215, 7337517575954403297187942797120, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [61162256505487825846056096118647637970, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [182695705923354893944352794093784543852, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [182695705923354893944352794093784543852, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000], [148003654549952611164135616309798592576, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 1024, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 88], [4, 120], [8, 92]], 'label': '8192.xx', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^7.D4^2', 'ngens': 12, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [1, 7, 27, 75, 163, 251, 347, 379, 363, 315, 235, 155, 31, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 78, 'number_characteristic_subgroups': 522, 'number_conjugacy_classes': 332, 'number_divisions': 328, 'number_normal_subgroups': 2350, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 8192, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 1407], [4, 5760], [8, 1024]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '10000.cu', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 262144, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2\\times C_5^4:Q_8', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, '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, 80], [4, 124], [8, 92]], 'representations': {'PC': {'code': '1466658027741249729719580353674604312410964804131006078980163433851122881748727604046482205658746303914454709536870442255152103967192706197551223504293963', 'gens': [1, 2, 4, 6, 7, 9, 10, 11, 12, 13], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 94848, 189853, 66, 381475, 1472, 341, 146, 475284, 237657, 286434, 142927, 71492, 681414, 21131, 167472, 17881, 617, 266, 93230, 33743, 1015049, 507542, 41648, 475914, 237975, 104725, 27531, 13816, 1081612, 540825, 164319, 16301, 8202]}, 'Perm': {'d': 34, 'gens': [148003654549952611164135616309798592576, 115518257709641142880943955468986816, 69976960400541544088491389813741715354, 74522680129013267451863965930912976, 247021781413461516601339839057267536, 1538185897245892899590899422720, 3980116084514130372512074510080, 35046367376906743540569686666973767200, 2454061066318842910490688908400, 269528986655596094769488953651697979570, 130628682539375342147355686685366275010, 534484512521564983152161587200000000]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 4, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^7.D_4^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 4], 'aut_gens': [[83497224460439472451969, 26015386931635918486609, 56212323387747076933280, 110322637403676413965557], [119706990015371442157436, 362454356546263046431541, 56616364659301455888426, 317177501495121958095423], [119728274942130702240741, 26325133789651165706299, 62949938912706808167200, 83334942421740224805685], [324141420255981933422053, 287246050010658423009358, 56616366921590643109280, 119317114586795429176520], [324141420841726597413889, 373696958313108552331729, 56212323387747076933280, 119298137588899225279285], [110305519883604838167169, 294552784669888521516341, 243915703279896576923429, 324140467230654649374709], [324125836173452341698096, 362162319155017147850299, 56616364659301455888426, 215214787411001363027482], [222725184410140420775036, 286696259036729298058421, 62949940607452785503687, 83334943363259538729845], [222725181457317341388289, 131566841919150968311099, 244387865493669321878826, 323937050796470599075189], [91215246831940197360769, 295116656707675844732878, 238707596264008713840426, 222725764090238109135477], [222706204460728771930341, 287246050010658422992699, 63411408747842968129829, 317190517513113501304520], [317343790192900815625573, 138313431422036358988219, 243926163266300327232800, 222705557802591310953845]], 'aut_group': None, 'aut_hash': 8240263953978922923, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 4194304, 'aut_permdeg': 256, 'aut_perms': [29102513875793174135275073851726393336696185519232581373022066269331788715868467536367576639786311745282745604814406699431791490864121876845544141799737231224724949323591373093107461533738945400969033403509167511318274396194807080632175078611326653196762054994890539696691040471153292009025945572202120242053196940179038558694692971065323914985415403743450714303265198399079062947862559577870413967884125314910751313539633040400113875506468536228094230180014247270554098382928584865343009869848604608102764, 148268998773132353460902080428814564145957339462192439238439725368870446256367488308657341256589842167578864728515825527273837449455448903714607383994052547955157408831954483163040571348858305098987455100826225847311510161903417298280738636931535777453950318504027899959880984713226392335249604272182924402710092952109650411892832933111834098841627675426918753233333964467401379872879766885784364051654244912795507268562268943237858150460601521006451405268974167876020539154386718685685949872155128250667005, 245729751781145809646289349318379648620577183960139497730641859444279919727576761374881632986058200817892203216701011769352261112509652214429274185982130950845962443442433666066536638984166201028449739833136959862797354178336677342782324239712692405547111659853745924130266386854556988346251559204138744755310250481905870431041238559544832290199783158623585126164359685062810038532818635971805422125641080287394708378813726569335470542141179061671180915083759127856792710019138877871248172563906329392410054, 838996590600698095083640277321737683122956343800511633618361997918996143169044789611428736104688852170676211693140476968439550369789340753483706584309696710863478129812340246522117339718561035692843496069471470668671359996710314988778935250101402084768548879456462494220558032531762792315523270594887486847688603528086729190353228406371581945946142808176338637681646202521112351102075054896245778676370358119143779981552023685323597744686106466435892184940976686742604815451101311485042641340629027432787157, 595701514577512682517793827799497089683725853132400515382057772488508050476027551515907639221870587609626987089665833500399070833815166831140034259561043257039177445929050600296880858956404883463879492268783167578823503435146591299170439328167046638694076721303334960633022286075016711086265660083890324732509129412594119915427849804968607040199269283759120410525355321007777720175698095064302925120755390982908885504931195927479438733201222898390898391475815552910994326701665057902746661427808676322867859, 44166941375884564708043741471249380194346292581958231025641153485283629195586631973089076192137333313966745568156494783211085072345044210223348864552906153779359639106693555442235642847394843546335107284104795937372501837104953167057071751034528227831028246398581412669891480493171724415375030729109310144498249681419218967348258602344084557910778788929424119948246931933715744888518474980092828893400586926419948890643250190120235106082779422921895604729394221367548761922134471328222008965010540224333243, 595058222784632792924478991222701843978713816730747985181701401307556084548215731476491579599552911586429275037877627161224029823499357495479666327994524673462806543036532602263487707703922215215548014157550353923047182760205009040167462894646891347369399651072708561690682658629971617044656536783331965475482426386919066081465155240880154645451041173946499133868309643487980554122633751874022346000163361610411253829666533104871905002039774348028854899061780075375591612619322668527763980048722470972042415, 777874332439849570478106067763347210220093978655077898906488091308684303807337863999242136990622894525121031904081748702072517573661288923139616960732973372319489268091632539413593492572845778158043642674394117025128867545887398183549570537746759812063628700608685028755115881435953876015984571229491893340921624169113388622872883161386648975199003726043524485100911257913637252101813643071849314921661334706391028041541418322228054871366583097071024120531073038907862411611215538669858541447642889853403994, 94404243069290916513187439898711934000378358982532330116657447681429073403109438366452489426049147874077670476617712202905535785740963642021183848785249770149707497656035758608236710508286057972447811829859569871180494957238429020191659055033299985561628855172597865193340734898374396121823069956579232313537117432263758326242471987161606965282375591499334992277195138968165524942224675739542205525299502062176694030366552133501161951002680283995035900031902370430315995568343153114871705502472781370019566, 222665165988981444751352360102172413482962570489340006725721712713713043171778549629044355107324507948489419503393444275504605559420205448558018259455410667915062813782402620470762341115485544995738547250930263462732339249597496233188598954037592502323242997229419557140322547874461487613407111951915064129168369212182233243194713458394764932718444254231579665404425008227141880315408454336337208428341241454326049498882219834229944428468984183323755804629858975326919029068876427589933057144043767951889028, 297557852437730651974715936828057424888895393043787700770806887557711685494242753443452378076166462478734860056165112431592297456736901766818129585990992029676489327694831076178020655927652485852698405081485090326193219094724633984166753393327237180058028087020151937625707273310111596759363741657848835372107516919052163127064693414522570231539270914993215474377328815333736043050043117584583341481301927231342974702578193993861180382551360355246284245245744784795971764683721491139190305503626801679657468], 'aut_phi_ratio': 2048.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 6], [2, 2, 4, 1], [2, 4, 2, 5], [2, 4, 4, 3], [2, 4, 8, 1], [2, 8, 2, 2], [2, 8, 4, 1], [2, 8, 8, 1], [2, 8, 16, 2], [2, 16, 1, 3], [2, 32, 1, 2], [2, 32, 2, 1], [4, 8, 2, 1], [4, 16, 1, 3], [4, 16, 4, 1], [4, 32, 1, 2], [4, 32, 2, 8], [4, 32, 4, 3], [4, 64, 4, 5], [4, 128, 2, 2], [8, 128, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^{12}.C_2^6.C_2^4', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': None, 'autcentquo_hash': 976262430540764400, 'autcentquo_nilpotent': True, 'autcentquo_order': 16384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^9.C_2^5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 10], [2, 4, 30], [2, 8, 48], [2, 16, 3], [2, 32, 4], [4, 8, 2], [4, 16, 7], [4, 32, 30], [4, 64, 20], [4, 128, 4], [8, 128, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': None, 'central_quotient': None, 'commutator_count': 2, 'commutator_label': '256.56083', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 1114, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 10], [2, 4, 1, 30], [2, 8, 1, 48], [2, 16, 1, 3], [2, 32, 1, 4], [4, 8, 1, 2], [4, 16, 1, 7], [4, 32, 1, 30], [4, 64, 1, 20], [4, 128, 1, 2], [4, 128, 2, 1], [8, 128, 1, 2], [8, 128, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': None, 'exponent': 8, 'exponents_of_order': [12], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '256.56083', 'frattini_quotient': '16.14', 'hash': 2336288734402960954, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [4, 4, 4, 4], 'inner_gens': [[83497224460439472451969, 294552784669888521509329, 243926163266300327253029, 214837587672838268110325], [215195221422098175658369, 26015386931635918486609, 56212323387747076953509, 317331592729466860710682], [324125836173452341693061, 26015386931635918493621, 56212323387747076933280, 214837584720015105669685], [91215247773459467784956, 138313431422036358988219, 63411408747842968129829, 110322637403676413965557]], 'inner_hash': 1200386431280143996, 'inner_nilpotent': True, 'inner_order': 1024, 'inner_split': None, 'inner_tex': 'C_2^6.C_2^4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 44], [4, 60], [8, 46]], 'label': '4096.bqv', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^6.D4^2', 'ngens': 4, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [1, 3, 11, 23, 43, 55, 71, 67, 63, 55, 35, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 58, 'number_characteristic_subgroups': 199, 'number_conjugacy_classes': 166, 'number_divisions': 164, 'number_normal_subgroups': 443, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 4096, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 703], [4, 2880], [8, 512]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 4, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[214838045709143138926896, 295116656707675844732878, 56212325772945595583687, 317331593315211568277877], [222706207767931684848769, 373709743076465876517941, 244378742107215716200229, 323921467426623577831925], [110305519883604838162131, 132132291775888781225809, 238295755022155532352800, 323921467426623577831925], [119297487647272369916156, 286696259036729298058421, 244387865493669321878826, 323937050796470599077685], [223137055465579096954341, 36185071275614611941941, 63411410989209847766826, 323937049603690951559240], [324141420255981933422053, 138878686341068924287541, 56212325772945595574826, 110322639851730484524960], [215195224204922632453221, 287261380240821326167099, 243915703279896576903200, 91203115630979890168309]], 'outer_group': None, 'outer_hash': 7414810045752927898, 'outer_nilpotent': True, 'outer_order': 4096, 'outer_permdeg': 256, 'outer_perms': [396164439841949511162910710516336467600862705263397648225397327613434295068894103251621576845149233115192154034740028673348057593667497022588920107834553987105920319895561305357985254626436776150927160936526198567451604502514470700330849826655957912554012856578346244088604797910689336867496532640736096883496938985301324414123874998787060623985004734580251959669118961021790524614021674727336453774527435459741508112433250933306201539398746944699270133409804079128210508091648408071037191729462755723770111, 813388477511592359397786493850040667031841137025486206958219626483583658197418100935143922451271319555863248424055580101148429838225942140927024607497448960875119320506597721459187891425706416722531444365748660824780762521379054593879935266594070157997038538676428382550111716652226628645736366940691543743635883918190287444456998370333732892707523186166548073810509807422316731219315813897573869398783015612466746716722862101535284433599859475308464331266263987190868623571053795073710526590005272991663618, 52470560201780777113051120946247892268173186810868751342482673369153130768194893243485218057409083390792253529393786995386847562752706907864232929574001698117143543104243789809365485916538939586702836970140684323487626225399773130013480899730143645183675688372771852238545168511721834598158196988873081823232688795458044405020328467455273875357206265094414124984821066353801950488626980945830394073072499164717549331955600244998221999131923588268160105966445480002666647541339327013356564965794141827336820, 88417456764762390631635245272260302121359692146290960712168086087945837538113829954608973928790444765143422235672243870087035989497014119733688199660620674214347763159908150041576178194896254867728375850872279237000618046448574010054561027630746140330279725722248986468783956896860279856922861039940130074332471120319067459357980092042493172977239831181883355977180324703933349883924464686182002118601005388519386565451615764838254766562712998519294828664133918892103393685091855637212909923890046289250686, 702779262684706108958075795817335376580530591117229890506867746877816116233772270965597543990314635387663576583335237878003733954242405408465542385852691836855131876065488339128535020236555906014078510601284506339446240042807387712699756120806336158949096999022361580780952228033848899499738949876334986900138841207175440625349349256362633290239579524402428964929271877959120762542877903681757396716476651043401571890366992858157197955079301620946490346510568238386351536342561859160252859119629558867732014, 794531097081865392065668083989291086726420589551727072024015386016598123510215097914066659402649406358528704706649863106747367892946783833065679136384699905684909239379585494143660576039287047585313491303521388821299751595277555830473971759013065643475999266046078221271851140047163055159140674273669618373368050136474872684999401549217655249538400480250958188889053933306008128307044468768315107753156399522513251394970275601068552311059256922771807934638378434891336330078855654678758664385392322493085533, 58167676405104524969484572412631473529541287484676247985380080828547203870675145994374674385240900010656668290742360670131989203660344318422746113447842335978092554501018595350719346799073338044344120836237039817645156358781014919535352408683552683511904109546394603254658599786498515759988357720013402937510301112699937505479958274372534774576729853414921382541688075852298860252814447073717044693929205455616124146230184758782189332930188359777449739370126243745506199086928040649716243155853971853002184], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^8.C_2^4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 40], [4, 62], [8, 46]], 'representations': {'PC': {'code': '6866474045395989188840041136781226191653642488309807781103633590556601054036495851073849760405717855814312098073939622290778636020316255870984316458179868779', 'gens': [1, 2, 4, 6, 7, 9, 10, 11, 12], 'pres': [12, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 192, 72337, 61, 722, 74115, 32847, 315, 135, 65776, 150917, 72017, 37469, 14441, 4673, 17478, 104178, 4062, 16506, 5946, 246, 98323, 24619, 96788, 24236, 307209, 90261, 76833, 39885, 9669, 4881, 405514, 65494, 101410, 52318, 12742, 6418, 9239, 2351]}, 'Perm': {'d': 24, 'gens': [83497224460439472451969, 26015386931635918486609, 56212323387747076933280, 110322637403676413965557]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 8, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^6.D_4^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
