LMFDB - Abstract group data

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Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
abelian_quotient	text
all_subgroups_known	boolean
almost_simple	boolean
aut_abelian	boolean
aut_cyclic	boolean
aut_derived_length	smallint
aut_exponent	numeric
aut_gen_orders	numeric[]
aut_gens	numeric[]
aut_group	text
aut_hash	bigint
aut_nilpotency_class	smallint
aut_nilpotent	boolean
aut_order	numeric
aut_permdeg	integer
aut_perms	numeric[]
aut_phi_ratio	double precision
aut_solvable	boolean
aut_stats	numeric[]
aut_supersolvable	boolean
aut_tex	text
autcent_abelian	boolean
autcent_cyclic	boolean
autcent_exponent	numeric
autcent_group	text
autcent_hash	bigint
autcent_nilpotent	boolean
autcent_order	numeric
autcent_solvable	boolean
autcent_split	boolean
autcent_supersolvable	boolean
autcent_tex	text
autcentquo_abelian	boolean
autcentquo_cyclic	boolean
autcentquo_exponent	numeric
autcentquo_group	text
autcentquo_hash	bigint
autcentquo_nilpotent	boolean
autcentquo_order	numeric
autcentquo_solvable	boolean
autcentquo_supersolvable	boolean
autcentquo_tex	text
cc_stats	numeric[]
center_label	text
center_order	numeric
central_product	boolean
central_quotient	text
commutator_count	integer
commutator_label	text
complements_known	boolean
complete	boolean
complex_characters_known	boolean
composition_factors	text[]
composition_length	smallint
conjugacy_classes_known	boolean
counter	integer
cyclic	boolean
derived_length	smallint
dihedral	boolean
direct_factorization	jsonb
direct_product	boolean
div_stats	numeric[]
element_repr_type	text
elementary	integer
eulerian_function	numeric
exponent	numeric
exponents_of_order	smallint[]
factors_of_aut_order	integer[]
factors_of_order	smallint[]
faithful_reps	numeric[]
familial	boolean
frattini_label	text
frattini_quotient	text
hash	bigint
hyperelementary	integer
inner_abelian	boolean
inner_cyclic	boolean
inner_exponent	numeric
inner_gen_orders	numeric[]
inner_gens	numeric[]
inner_hash	bigint
inner_nilpotent	boolean
inner_order	numeric
inner_split	boolean
inner_tex	text
inner_used	smallint[]
irrC_degree	integer
irrQ_degree	integer
irrQ_dim	integer
irrR_degree	integer
irrep_stats	numeric[]
label	text
linC_count	numeric
linC_degree	integer
linFp_degree	integer
linFq_degree	integer
linQ_degree	integer
linQ_degree_count	numeric
linQ_dim	integer
linQ_dim_count	numeric
linR_count	numeric
linR_degree	integer
maximal_subgroups_known	boolean
metabelian	boolean
metacyclic	boolean
monomial	boolean
name	text
ngens	smallint
nilpotency_class	smallint
nilpotent	boolean
normal_counts	integer[]
normal_index_bound	numeric
normal_order_bound	numeric
normal_subgroups_known	boolean
number_autjugacy_classes	integer
number_characteristic_subgroups	integer
number_conjugacy_classes	integer
number_divisions	integer
number_normal_subgroups	integer
number_subgroup_autclasses	integer
number_subgroup_classes	integer
number_subgroups	numeric
old_label	text
order	numeric
order_factorization_type	integer
order_stats	numeric[]
outer_abelian	boolean
outer_cyclic	boolean
outer_equivalence	boolean
outer_exponent	numeric
outer_gen_orders	numeric[]
outer_gen_pows	numeric[]
outer_gens	numeric[]
outer_group	text
outer_hash	bigint
outer_nilpotent	boolean
outer_order	numeric
outer_permdeg	integer
outer_perms	numeric[]
outer_solvable	boolean
outer_supersolvable	boolean
outer_tex	text
pc_rank	smallint
perfect	boolean
permutation_degree	integer
pgroup	smallint
primary_abelian_invariants	integer[]
quasisimple	boolean
rank	smallint
rational	boolean
rational_characters_known	boolean
ratrep_stats	numeric[]
representations	jsonb
schur_multiplier	integer[]
semidirect_product	boolean
simple	boolean
smith_abelian_invariants	integer[]
solvability_type	smallint
solvable	boolean
subgroup_inclusions_known	boolean
subgroup_index_bound	numeric
supersolvable	boolean
sylow_subgroups_known	boolean
tex_name	text
transitive_degree	integer
wreath_data	text[]
wreath_product	boolean

gps_groups • Show schema

{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '64.26', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [48, 24, 64, 48], 'aut_gens': [[1, 16], [4273, 3856], [5809, 9008], [3601, 464], [529, 8816]], 'aut_group': None, 'aut_hash': 2013647253270866901, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 296448, 'aut_permdeg': 772, 'aut_perms': [166406514259950795693920368248954736540967271155686351680047657529296457433325983294469233337708988255359577840171958019232667324849424574645511161950002024950291774585827141564053997754016037791146883649120511603332802568632659516471768191744587732678663690253888410247359058388632478489966948148998751361744505810934894037476859732947714264662762285542349246770778834559051996851376961814053726813032559842314927244306083543860087238780697453711739766698654601940904147693343753639029858930554919315756491497159647207054461733993917915091768848871872506770587877811756028983490143172468298489204580538593242448654795749629449582433383486799610789926105163560449874998366417191365941848796582581166577787180434622605580598986900617468622970115984746628885066661160483839886487995783282525482635730315843761954135778842974409956047604552434715287363759351072478657286340271983599952601559324611871960644709758984763130374436076264595793211919845310099865776972031885347342425407501374204108935428633835419152427711644849198809225100317177523639222005935320139381397354352697591385263697942368423779222169918998014112075138548254387879002631507818690503853962362310524641815389492016703056454693022710822049679619024180438554777152640488724921000918749550764760827973341234424813103073597511595325096317359597547475360089019158141150530451217612828119717983016617465339272020976581281482179408746509851638537537158907782914183773236820805334186248573009830174208552375766905349996885754290254867278900588267057175467706652999001965268773129916836914972367505111954603938564597149427656131416554974182560610994089781552083248952967464806172923238826364627993978175383659400246087410320325661665826907566023263981773543272123477598379777721833693278565421808456473376435373232893839178376381683453665500707740874014266484050622509598104149490311062687101151821701468662555057507815894750271998243804, 555696059771055038650973820535451550639619718201129449418117885874270582397844732988663989077429193861697070029911010272853574091442218887278627283268194679185801811129443946350002929470826524240053625233033713894740727200665033566584634919689003857470330577129787895909363104978413596568316711182691750615956435305726237858080556097073112303277313854284879589597930309542892319499051879074762641160963316173677386763449663508011354849248512919493115119594716269065911205738682352109996035389215167659841431662706314123461160018325799392371271265940212467551642559852666051223955277635367047326365607530254683423777708459005534828700984133293712438399274147701651815180576690674933396031130785046759916782898783040552426678540294732344496539524185233550158559229691728349407600730337494260694526731471190339148374433516228794711441923997964755364271064987312079809970430016066192889986195812075123476613338766285344649028860893626504305575791035437329135462320553478327221117391413039781190074071540634051421883313646794447133159678128527117524758760352300287629011877811665075227838164967618111103567913393629487898708122057938514058088978533588667918668620433539691911740158982435132358170949774231839576990481821377724452792749326838274074484697054742572682981610538968514202975552543744626730357967989777557813634343624529472042330798264659523587164899931713672349716830876373083522337432615609358491805698116873008013908952032054332700167863600028898021875707191257254892969072856200607049457200426784336165912906447144429862271768678893687614768493946982262517464103142590421725002902786400627931103476129131190320026328703661277387340284130736673755015491837492351388158563167709054335613283861246386063193327277708346155597379199972636814775075914358110151691357843817339619095850936276808760985960182877389894154921135758479240953143219901186847310910124838031896692248677072563896359331, 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'aut_phi_ratio': 48.25, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [4, 1, 2, 1], [4, 193, 1, 4], [4, 193, 2, 3], [8, 193, 2, 8], [16, 193, 4, 8], [193, 16, 12, 1], [386, 16, 12, 1], [772, 16, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{386}.C_{96}.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 193, 2], [4, 1, 2], [4, 193, 10], [8, 193, 16], [16, 193, 32], [193, 16, 12], [386, 16, 12], [772, 16, 24]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '3088.54', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '193.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1674, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3088.54', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [4, 1, 2, 1], [4, 193, 2, 5], [8, 193, 4, 4], [16, 193, 8, 4], [193, 16, 12, 1], [386, 16, 12, 1], [772, 16, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 192, 'exponent': 3088, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 193], 'faithful_reps': [[16, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '6176.246', 'hash': 1674, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 3088, 'inner_gen_orders': [16, 193], 'inner_gens': [[1, 12304], [65, 16]], 'inner_hash': 54, 'inner_nilpotent': False, 'inner_order': 3088, 'inner_split': False, 'inner_tex': 'C_{193}:C_{16}', 'inner_used': [1, 2], 'irrC_degree': 16, 'irrQ_degree': 384, 'irrQ_dim': 384, 'irrR_degree': 32, 'irrep_stats': [[1, 64], [16, 48]], 'label': '12352.1674', 'linC_count': 24, 'linC_degree': 16, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 194, 'linQ_degree_count': 8, 'linQ_dim': 194, 'linQ_dim_count': 8, 'linR_count': 384, 'linR_degree': 18, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C772:C16', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 112, 'number_divisions': 21, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 44, 'number_subgroup_classes': 58, 'number_subgroups': 5050, 'old_label': None, 'order': 12352, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 387], [4, 1932], [8, 3088], [16, 6176], [193, 192], [386, 192], [772, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 4, 12], 'outer_gen_pows': [0, 5, 12], 'outer_gens': [[1, 12336], [1, 7312], [3089, 11408]], 'outer_group': '96.165', 'outer_hash': 165, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 11, 'outer_perms': [767760, 2160, 4032004], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 197, 'pgroup': 0, 'primary_abelian_invariants': [4, 16], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [8, 4], [192, 2], [384, 1]], 'representations': {'PC': {'code': '72407528335999452377277843788303020815094084830022278204159326426892925831612632776520499391', 'gens': [1, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -193, 14, 36, 58, 430644, 2531, 11358, 26975, 102, 514757, 6060, 27235, 64706, 124, 595846, 14125, 63524, 75291]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1365920873, 582313729]}, 'Perm': {'d': 197, 'gens': [5290273345984864897683944123082956631220066364900253396726259059766269559200235413715177147698004284025594961028822560923834716647335335646782683178127927701850149621311947644736352530825831559089639200063438532790427221928341897546834098797438127745470625459344068218749828555758253110619759250004403483806498954818604823553161926087080150002071074875160801725560, 9, 7896146472218856502393881215272180448607715302217823038480840402592075442888782334598101578804469491722017008442403110034580758066612966193062153191003165794662509714205876275508506316534606456485998062120044681800379766614251220802300702017288411488349582440302601260771679149486482287636140697371705750316485130991060173970329479343368418131379968662762330588240, 16, 10461532913094680818289408021199360182337152438568301470075869865765861863574813452987192156277912935756095880952558744287790336020715603557128987402820322664978709376847114195610925734074225539086790955889736488207604978092986805271850954882804263039468151199343278442654273620917630499833139965503217978033223387903829743037492645791738257574229789666158530438440, 2592381132973149765779289246531185296419382784883920013901222755849351293628592008151691890954402788253039663753020082609107439334904412326282239603261948437302473854804655963712088645187779112731793528834357671948713737992400807244149705391268119111136677134958116230430763311877262318184849472983323284357135732667011753861924031209391791363940984026715737429240, 520972671180291378873378228799679326959717638111606330328292901165986473129410184711055071299345784828690369857414184422249346580994648235923978424589548271404017967409610673350600057073095348109955036142474517622285973437735974016368518172307132793835132086153054465008777445548393143686583542501166362214033044187300451811977217876794123160958270890813465818123440]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 16], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{772}:C_{16}', 'transitive_degree': 772, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema

id: 106239665
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1674, 'group_order': 12352, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 106239689
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1674, 'group_order': 12352, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 6176, 'size': 1}
id: 106239700
{'aut_label': '2B', 'centralizer': '193.a1.a1', 'counter': 3, 'group_counter': 1674, 'group_order': 12352, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 4744, 'size': 193}
id: 106239711
{'aut_label': '2C', 'centralizer': '193.a1.a1', 'counter': 4, 'group_counter': 1674, 'group_order': 12352, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 7720, 'size': 193}
id: 106239722
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{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 95, 'group_counter': 1674, 'group_order': 12352, 'label': '772A11', 'order': 772, 'powers': [80, 96, 6], 'representative': 176, 'size': 16}
id: 106239773
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 96, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-11', 'order': 772, 'powers': [80, 95, 5], 'representative': 464, 'size': 16}
id: 106239774
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 97, 'group_counter': 1674, 'group_order': 12352, 'label': '772A13', 'order': 772, 'powers': [81, 98, 5], 'representative': 208, 'size': 16}
id: 106239775
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 98, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-13', 'order': 772, 'powers': [81, 97, 6], 'representative': 560, 'size': 16}
id: 106239776
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 99, 'group_counter': 1674, 'group_order': 12352, 'label': '772A17', 'order': 772, 'powers': [82, 100, 5], 'representative': 272, 'size': 16}
id: 106239667
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 100, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-17', 'order': 772, 'powers': [82, 99, 6], 'representative': 816, 'size': 16}
id: 106239668
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 101, 'group_counter': 1674, 'group_order': 12352, 'label': '772A23', 'order': 772, 'powers': [83, 102, 6], 'representative': 368, 'size': 16}
id: 106239669
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 102, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-23', 'order': 772, 'powers': [83, 101, 5], 'representative': 1104, 'size': 16}
id: 106239670
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 103, 'group_counter': 1674, 'group_order': 12352, 'label': '772A25', 'order': 772, 'powers': [84, 104, 5], 'representative': 400, 'size': 16}
id: 106239671
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 104, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-25', 'order': 772, 'powers': [84, 103, 6], 'representative': 1200, 'size': 16}
id: 106239672
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 105, 'group_counter': 1674, 'group_order': 12352, 'label': '772A31', 'order': 772, 'powers': [85, 106, 6], 'representative': 496, 'size': 16}
id: 106239673
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 106, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-31', 'order': 772, 'powers': [85, 105, 5], 'representative': 1040, 'size': 16}
id: 106239674
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 107, 'group_counter': 1674, 'group_order': 12352, 'label': '772A37', 'order': 772, 'powers': [86, 108, 5], 'representative': 592, 'size': 16}
id: 106239675
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 108, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-37', 'order': 772, 'powers': [86, 107, 6], 'representative': 752, 'size': 16}
id: 106239676
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 109, 'group_counter': 1674, 'group_order': 12352, 'label': '772A49', 'order': 772, 'powers': [87, 110, 5], 'representative': 784, 'size': 16}
id: 106239678
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 110, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-49', 'order': 772, 'powers': [87, 109, 6], 'representative': 880, 'size': 16}
id: 106239679
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 111, 'group_counter': 1674, 'group_order': 12352, 'label': '772A61', 'order': 772, 'powers': [88, 112, 5], 'representative': 976, 'size': 16}
id: 106239680
{'aut_label': '772A1', 'centralizer': '16.b1.a1', 'counter': 112, 'group_counter': 1674, 'group_order': 12352, 'label': '772A-61', 'order': 772, 'powers': [88, 111, 6], 'representative': 1264, 'size': 16}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 3676711
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 3676722
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 3676725
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 3676726
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 3676727
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, -2, 2, -2, 0, 2, -2, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, -2, 0, 2, 0, 2, 0, -2, 0, -2, 0, 2, 0, 2, 0, 0, 2, -2, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676728
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, -2, 2, -2, 0, 2, -2, 2, 0, 0, 0, -2, 0, 0, 0, 2, 0, 2, 0, 2, 0, -2, 0, -2, 0, 2, 0, 2, 0, -2, 0, -2, 0, 0, -2, 2, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676729
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 2, -2, 2, 0, -2, 2, -2, 0, 0, 0, 2, 0, 0, 0, -2, -2, 0, 2, 0, -2, 0, -2, 0, 2, 0, 2, 0, 2, 0, -2, 0, -2, -2, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676730
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1h', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 2, 0, 2, -2, 2, 0, -2, 2, -2, 0, 0, 0, 2, 0, 0, 0, -2, 2, 0, -2, 0, 2, 0, 2, 0, -2, 0, -2, 0, -2, 0, 2, 0, 2, 2, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676731
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 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, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
id: 3676712
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 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, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 3676713
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1k', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 0, 0, -4, 4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 4, 0, 0, 0, 4, -4, -4, 0, -4, 4, 4, 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, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676714
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1l', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 0, 0, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, -4, 0, 0, 0, -4, 4, 4, 0, 4, -4, -4, 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, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676715
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, 4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4], 'schur_index': 1}
id: 3676716
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1n', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 4, -4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4], 'schur_index': 1}
id: 3676717
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1o', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, -8, 8, 0, 0, -8, 0, 0, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676718
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1p', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 3676719
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1q', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8, -8], 'schur_index': 1}
id: 3676720
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.1r', 'multiplicity': 8, 'nt': [16, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, -8, -8, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], 'schur_index': 1}
id: 3676721
{'cdim': 16, 'counter': 19, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.16a', 'multiplicity': 12, 'nt': [193, 0], 'qdim': 192, 'qvalues': [192, 192, 0, 0, 192, 192, 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, 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, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 3676723
{'cdim': 16, 'counter': 20, 'faithful': False, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.16b', 'multiplicity': 12, 'nt': [386, 0], 'qdim': 192, 'qvalues': [192, 192, 0, 0, -192, -192, 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, 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, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 3676724
{'cdim': 16, 'counter': 21, 'faithful': True, 'group': '12352.1674', 'group_order': 12352, 'image': None, 'label': '12352.1674.16c', 'multiplicity': 24, 'nt': [772, 0], 'qdim': 384, 'qvalues': [384, -384, 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, 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, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema

id: 5249977
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id: 5250001
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id: 5250012
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 6176, 'label': '12352.1674.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 5250023
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id: 5250034
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 3088, 'label': '12352.1674.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
id: 5250045
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 3088, 'label': '12352.1674.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 5250056
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.b1', 'kernel_order': 3088, 'label': '12352.1674.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
id: 5250067
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id: 5250078
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id: 5249978
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id: 5249989
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.c1', 'kernel_order': 3088, 'label': '12352.1674.1h1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
id: 5249993
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.c1', 'kernel_order': 3088, 'label': '12352.1674.1h2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 5249994
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 3088, 'label': '12352.1674.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 5249995
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 3088, 'label': '12352.1674.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 5249996
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 3088, 'label': '12352.1674.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 5249997
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 12352, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 3088, 'label': '12352.1674.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 5249998
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id: 5249999
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id: 5250000
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id: 5250002
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id: 5250003
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id: 5250004
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id: 5250005
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id: 5250006
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id: 5250007
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id: 5250008
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id: 5250009
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id: 5250010
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id: 5250011
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id: 5250013
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id: 5250014
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id: 5250015
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id: 5250016
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id: 5250017
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id: 5250018
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id: 5250019
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id: 5250020
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id: 5250021
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id: 5250022
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id: 5250024
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id: 5250025
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id: 5250026
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id: 5250027
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id: 5250028
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id: 5250029
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id: 5250030
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id: 5250031
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id: 5250032
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id: 5250033
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id: 5250035
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id: 5250036
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id: 5250037
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id: 5250038
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id: 5250039
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id: 5250040
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id: 5250041
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id: 5250042
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id: 5250043
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id: 5250044
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id: 5250046
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id: 5250047
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id: 5250048
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id: 5250049
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id: 5250050
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id: 5250051
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id: 5250061
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id: 5250062
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id: 5250063
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id: 5250052
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id: 5250053
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id: 5250054
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id: 5250055
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id: 5250057
{'center': '3088.a1.a1', 'center_index': 3088, 'center_order': 4, 'counter': 70, 'cyclotomic_n': 193, 'dim': 16, 'faithful': False, 'field': [6561, 40095, -144990, 25812, 136836, -16656, -31612, 1105, 2617, 3, -88, -1, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '3088.54', 'image_order': 3088, 'indicator': 1, 'kernel': '3088.a1.a1', 'kernel_order': 4, 'label': '12352.1674.16a6', 'nt': [193, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 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, 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, 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, 0]], [[0, 0]], [[0, 0]], [[0, 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id: 5250058
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id: 5250059
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id: 5250060
{'center': '3088.a1.a1', 'center_index': 3088, 'center_order': 4, 'counter': 73, 'cyclotomic_n': 193, 'dim': 16, 'faithful': False, 'field': [6561, 40095, -144990, 25812, 136836, -16656, -31612, 1105, 2617, 3, -88, -1, 1], 'group': '12352.1674', 'group_counter': 1674, 'group_order': 12352, 'image': None, 'image_isoclass': '3088.54', 'image_order': 3088, 'indicator': 1, 'kernel': '3088.a1.a1', 'kernel_order': 4, 'label': '12352.1674.16a9', 'nt': [193, 0], 'q_character': None, 'values': [[[16, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 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, 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, 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, 0]], [[0, 0]], [[0, 0]], [[0, 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id: 5250064
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id: 5250074
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id: 5250075
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id: 5250076
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id: 5250065
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id: 5250066
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id: 5250068
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id: 5250069
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id: 5250070
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id: 5250071
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id: 5250072
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id: 5250073
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id: 5250077
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id: 5250087
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id: 5250088
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id: 5249979
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id: 5249980
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id: 5249981
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id: 5249982
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id: 5249983
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id: 5249984
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id: 5249985
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id: 5249986
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id: 5250079
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id: 5249987
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id: 5249988
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id: 5249990
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id: 5249991
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id: 5249992
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id: 5250080
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id: 5250081
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id: 5250082
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id: 5250083
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id: 5250084
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id: 5250085
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id: 5250086
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Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 60102132
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 12352, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 386, 'label': '12352.1674.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12352.1674', 'subgroup_hash': 1674, 'subgroup_order': 12352, 'subgroup_tex': 'C_{772}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102143
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 6176, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6176.237', 'subgroup_hash': 237, 'subgroup_order': 6176, 'subgroup_tex': 'C_{772}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102154
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6176, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6176.246', 'subgroup_hash': 246, 'subgroup_order': 6176, 'subgroup_tex': 'C_{386}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102165
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6176, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6176.246', 'subgroup_hash': 246, 'subgroup_order': 6176, 'subgroup_tex': 'C_{386}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102176
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 3088, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3088.44', 'subgroup_hash': 44, 'subgroup_order': 3088, 'subgroup_tex': 'C_{772}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102186
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 3088, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3088.53', 'subgroup_hash': 53, 'subgroup_order': 3088, 'subgroup_tex': 'C_{386}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102187
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 3088, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3088.53', 'subgroup_hash': 53, 'subgroup_order': 3088, 'subgroup_tex': 'C_{386}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102188
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3088, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12352.1674.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3088.54', 'subgroup_hash': 54, 'subgroup_order': 3088, 'subgroup_tex': 'C_{193}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102189
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3088, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12352.1674.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3088.54', 'subgroup_hash': 54, 'subgroup_order': 3088, 'subgroup_tex': 'C_{193}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102133
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3088, 'counter': 10, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12352.1674.4.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3088.54', 'subgroup_hash': 54, 'subgroup_order': 3088, 'subgroup_tex': 'C_{193}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102134
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3088, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12352.1674.4.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3088.54', 'subgroup_hash': 54, 'subgroup_order': 3088, 'subgroup_tex': 'C_{193}:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102135
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 1544, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.7', 'subgroup_hash': 7, 'subgroup_order': 1544, 'subgroup_tex': 'C_4\\times D_{193}', 'supersolvable': True, 'sylow': 0}
id: 60102136
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 1544, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.14', 'subgroup_hash': 14, 'subgroup_order': 1544, 'subgroup_tex': 'C_{386}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102137
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 1544, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.14', 'subgroup_hash': 14, 'subgroup_order': 1544, 'subgroup_tex': 'C_{386}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102138
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1544, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.15', 'subgroup_hash': 15, 'subgroup_order': 1544, 'subgroup_tex': 'C_{193}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102139
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1544, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.15', 'subgroup_hash': 15, 'subgroup_order': 1544, 'subgroup_tex': 'C_{193}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102140
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1544, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.15', 'subgroup_hash': 15, 'subgroup_order': 1544, 'subgroup_tex': 'C_{193}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102141
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1544, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1544.15', 'subgroup_hash': 15, 'subgroup_order': 1544, 'subgroup_tex': 'C_{193}:C_8', 'supersolvable': True, 'sylow': 0}
id: 60102142
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 772, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '772.4', 'subgroup_hash': 4, 'subgroup_order': 772, 'subgroup_tex': 'D_{386}', 'supersolvable': True, 'sylow': 0}
id: 60102144
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 772, 'characteristic': True, 'core_order': 772, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '12352.1674.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '772.2', 'subgroup_hash': 2, 'subgroup_order': 772, 'subgroup_tex': 'C_{772}', 'supersolvable': True, 'sylow': 0}
id: 60102145
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 772, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '772.1', 'subgroup_hash': 1, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102146
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 772, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '772.3', 'subgroup_hash': 3, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102147
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 772, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '772.3', 'subgroup_hash': 3, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102148
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 772, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '772.3', 'subgroup_hash': 3, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102149
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 772, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '772.3', 'subgroup_hash': 3, 'subgroup_order': 772, 'subgroup_tex': 'C_{193}:C_4', 'supersolvable': True, 'sylow': 0}
id: 60102150
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 772, 'characteristic': True, 'core_order': 386, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '12352.1674.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '386.2', 'subgroup_hash': 2, 'subgroup_order': 386, 'subgroup_tex': 'C_{386}', 'supersolvable': True, 'sylow': 0}
id: 60102151
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 386, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.3', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '386.1', 'subgroup_hash': 1, 'subgroup_order': 386, 'subgroup_tex': 'D_{193}', 'supersolvable': True, 'sylow': 0}
id: 60102152
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 386, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12352.1674.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '386.1', 'subgroup_hash': 1, 'subgroup_order': 386, 'subgroup_tex': 'D_{193}', 'supersolvable': True, 'sylow': 0}
id: 60102153
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 772, 'characteristic': True, 'core_order': 193, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 193, 'label': '12352.1674.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.26', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '193.1', 'subgroup_hash': 1, 'subgroup_order': 193, 'subgroup_tex': 'C_{193}', 'supersolvable': True, 'sylow': 193}
id: 60102155
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '12352.1674.193.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '193.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 193, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.26', 'subgroup_hash': 26, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times C_{16}', 'supersolvable': True, 'sylow': 2}
id: 60102156
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.386.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '386.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 386, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 60102157
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.386.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '386.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 386, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102158
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.386.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '386.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 386, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102159
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.772.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 60102160
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.772.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 60102161
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.772.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 60102162
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.772.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102163
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.772.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102164
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.772.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102166
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.772.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '772.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 772, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 60102167
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 60102168
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 60102169
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 60102170
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 60102171
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 60102172
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 60102173
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.1544.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1544.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1544, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 60102174
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 12352, 'characteristic': True, 'core_order': 4, 'counter': 48, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '12352.1674.3088.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3088.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3088.54', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3088, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{193}:C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102175
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 60102177
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102178
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102179
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102180
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102181
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.3088.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3088.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3088, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 60102182
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 12352, 'characteristic': True, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '12352.1674.6176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '6176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6176.246', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 246, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{386}:C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 60102183
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.6176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6176.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 60102184
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12352.1674.6176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6176.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 60102185
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12352.1674', 'ambient_counter': 1674, 'ambient_order': 12352, 'ambient_tex': 'C_{772}:C_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 12352, 'characteristic': True, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '12352.1674.12352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12352.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '12352.1674', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1674, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{772}:C_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

Column	Type
ambient	text
aut_centralizer_order	numeric
aut_label	text
aut_quo_index	numeric
aut_stab_index	numeric
aut_weyl_group	text
aut_weyl_index	numeric
centralizer	text
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
diagramx	smallint[]
generators	numeric[]
label	text
mobius_quo	bigint
mobius_sub	bigint
normal_closure	text
normal_contained_in	text[]
normal_contains	text[]
normalizer	text
old_label	text
projective_image	text
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_fusion	jsonb
short_label	text
subgroup_fusion	integer[]
weyl_group	text

gps_subgroup_data • Show schema

id: 60102171
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '1544.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '193.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '772.b1.a1'], 'contains': ['3088.d1.a1'], 'core': '12352.a1.a1', 'coset_action_label': None, 'count': 193, 'diagramx': [5061, -1, 5555, -1, 3428, -1, 5588, -1], 'generators': [146], 'label': '12352.1674.1544.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '193.a1.a1', 'old_label': '1544.d1.b1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1544.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 60102172
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '1544.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '193.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '772.c1.a1', '772.d1.a1', '772.d1.b1'], 'contains': ['3088.e1.a1'], 'core': '12352.a1.a1', 'coset_action_label': None, 'count': 193, 'diagramx': [8993, -1, 7134, -1, 1913, -1, 8108, -1], 'generators': [34], 'label': '12352.1674.1544.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '193.a1.a1', 'old_label': '1544.e1.a1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1544.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 60102173
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '1544.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '193.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '772.c1.a1', '772.d1.c1', '772.d1.d1'], 'contains': ['3088.e1.a1'], 'core': '12352.a1.a1', 'coset_action_label': None, 'count': 193, 'diagramx': [8993, -1, 8988, -1, 1913, -1, 6654, -1], 'generators': [2], 'label': '12352.1674.1544.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '193.a1.a1', 'old_label': '1544.e1.b1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1544.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 60102132
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': ['12352.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '193.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7407, 6578, 7952, 3844, 2748, 6376, 6958, 3923], 'generators': [6176, 4, 8, 2, 3088, 1, 64], 'label': '12352.1674.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '3088.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102133
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': ['3088.a1.a1', '3088.c1.a1', '3088.f1.b1', '3088.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.e1.b1', '772.d1.c1'], 'core': '4.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [9697, 9569, 8822, 2610, 444, 9275, 6047, 2664], 'generators': [9288, 64, 11716, 12290, 33], 'label': '12352.1674.4.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.c1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.c1', 'projective_image': '12352.1674', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.d1.c1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102170
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '1544.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '193.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '772.b1.a1'], 'contains': ['3088.d1.a1'], 'core': '12352.a1.a1', 'coset_action_label': None, 'count': 193, 'diagramx': [5061, -1, 4450, -1, 3428, -1, 5256, -1], 'generators': [178], 'label': '12352.1674.1544.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '193.a1.a1', 'old_label': '1544.d1.a1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1544.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 60102134
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': ['3088.a1.a1', '3088.c1.a1', '3088.f1.b1', '3088.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['8.e1.b1', '772.d1.d1'], 'core': '4.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9697, 9569, 9646, 5079, 444, 9275, 6760, 5183], 'generators': [8, 64, 4, 2, 1], 'label': '12352.1674.4.d1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.d1', 'normal_contained_in': ['2.b1.b1'], 'normal_contains': ['8.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.d1', 'projective_image': '12352.1674', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.d1.d1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102135
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '1544.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1169, 1130, 1251, 9009, 8427, 1095, 2235, 9194], 'generators': [8, 3088, 64, 6176], 'label': '12352.1674.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '3088.54', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102136
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '1544.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5904, 5398, 4217, 5424, 5358, 5233, 3481, 5535], 'generators': [4, 6176, 64, 8], 'label': '12352.1674.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '6176.246', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102137
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.f1.b1', '1544.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3008, 3182, 2256, 7714, 7209, 3085, 1370, 7871], 'generators': [1300, 6176, 64, 7464], 'label': '12352.1674.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.f1.a1', '16.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '6176.246', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102138
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.d1.a1', '1544.d1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4632, 7211, 3334, 6568, 4283, 6989, 4245, 6703], 'generators': [178, 1764, 64, 8456], 'label': '12352.1674.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102139
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.d1.a1', '1544.d1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4632, 7211, 5098, 4279, 4283, 6989, 4833, 4367], 'generators': [146, 1444, 64, 6920], 'label': '12352.1674.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102140
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.e1.a1', '1544.e1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9406, 8608, 6867, 2031, 1693, 8344, 8604, 2073], 'generators': [34, 324, 64, 1544], 'label': '12352.1674.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.d1.b1', '4.d1.a1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102141
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.c1', '4.d1.d1'], 'contains': ['16.e1.a1', '1544.e1.b1'], 'core': '8.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9406, 8608, 8749, 3396, 1693, 8344, 6047, 3466], 'generators': [2, 4, 64, 8], 'label': '12352.1674.8.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.b1', 'normal_contained_in': ['4.c1.a1', '4.d1.c1', '4.d1.d1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.b1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102142
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id: 60102143
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id: 60102144
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id: 60102145
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id: 60102146
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.b1.a1', '3088.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4624, 5530, 4456, 5424, 4956, 5360, 4171, 5535], 'generators': [2596, 2568, 64], 'label': '12352.1674.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '12352.1674', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102147
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id: 60102148
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id: 60102149
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id: 60102150
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id: 60102151
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id: 60102152
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id: 60102153
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'contains': ['12352.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1912, 2823, 1820, 7389, 7048, 2852, 2474, 7956], 'generators': [64], 'label': '12352.1674.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['12352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '12352.1674', 'quotient_action_image': '16.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.1'}
id: 60102154
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.d1.b1', '386.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9069, 7757, 7590, 1900, 1473, 7519, 8319, 1939], 'generators': [12036, 10824, 64, 12322, 6176, 17], 'label': '12352.1674.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '6176.246', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102155
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id: 60102156
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id: 60102157
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '386.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '193.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '193.a1.a1'], 'contains': ['772.c1.a1', '772.d1.a1', '772.d1.b1'], 'core': '6176.a1.a1', 'coset_action_label': None, 'count': 193, 'diagramx': [9376, -1, 6963, -1, 1473, -1, 8241, -1], 'generators': [17, 6176], 'label': '12352.1674.386.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '193.a1.a1', 'old_label': '386.b1.a1', 'projective_image': '6176.246', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '386.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 60102158
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id: 60102159
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id: 60102160
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id: 60102161
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id: 60102162
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id: 60102163
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id: 60102164
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id: 60102165
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id: 60102166
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id: 60102167
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id: 60102168
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id: 60102169
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id: 60102174
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id: 60102175
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id: 60102176
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id: 60102177
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id: 60102178
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id: 60102179
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id: 60102180
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id: 60102181
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id: 60102182
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id: 60102183
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id: 60102184
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id: 60102185
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id: 60102186
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1', '772.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6050, 5398, 4541, 6312, 4859, 5233, 3661, 6443], 'generators': [6920, 64, 1444, 6176, 146], 'label': '12352.1674.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '6176.246', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102187
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id: 60102188
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': ['3088.a1.a1', '3088.c1.a1', '3088.f1.b1', '3088.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '772.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9697, 9569, 6767, 1541, 444, 9275, 8972, 1573], 'generators': [7752, 64, 11396, 12258, 49], 'label': '12352.1674.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '12352.1674', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}
id: 60102189
{'ambient': '12352.1674', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3088.a1.a1', 'complements': ['3088.a1.a1', '3088.c1.a1', '3088.f1.b1', '3088.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '772.d1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9697, 9569, 7590, 473, 444, 9275, 9685, 482], 'generators': [10824, 64, 12036, 12322, 17], 'label': '12352.1674.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '12352.1674', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '3088.54'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.