LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-10-16T04:42:14.768667

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': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 113460, 'aut_gen_orders': [60, 3], 'aut_gens': [[7036413, 223381], [7539168, 7740074], [8306179, 3718055]], 'aut_group': '226920.b', 'aut_hash': 6642875333164673378, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 226920, 'aut_permdeg': 1891, 'aut_perms': [8995639990287663455756575306160351758076860337072598253395805850771359894103284047088129314640623837348328358923523415283237782333661905316132641736692741347890420458835215139162644989046734544554135002272902986631225085963771394370330888486662460205458136931663292176744148063476419205132548989105952240332931310202395226847360666260579363470906715452952023828919134397249140210790993057888473089483883863316660233868922797413317688333511196494473213867397975399263860823033770711270875750202942812351346240455224853161306013423231079015218314662063864392383444848052043169291313460453564284246659064119058629944996853956041642453779101638351661514567749358622715186202350061753102749020779100126340563766673166805265391511510450238232155417252559374389957782828359568621662668077024262182318034637163011455253946738481454203235445633138695020625085234828113204628139336696190913485032893629636399335710689955291249173679022635256308935352442476034279695578467035085657262467086469694555351569399787288175903936446753286769561447443028742466612283696848340996298052134625334514924752367975032793729728476319732158348634940562183069207063306977381750039612290959068542940252882616116821919687140374885896237277413948621602408470696953032689821232889507636686355183845691801457286385850469472845095612196345596099910758892477157353086727031403016888458980201027124690013707476352731885108348380174885041131592329184840561530569362263897711522154427143746525815590319585698318458490175559113015843887985687272986183965109468338349348510737936452275213820094882581233257150666972174425494540057409142579329334913350247319445571771079876806276706526860162325836505284585497523382730486224201265921310102532826537547506904563343546545686895579682029305464603829705166047186975995506034790290328639260389615646124589092729043111472024691491012868984972689765144340130396119797479788298647920444090249496509792479037365489629317605956689280024728203171157925673641538346577970699830998818077103722219190915513428746658861619033197950813115740308326191368473341674490986522549094270641247352166282548073852791260403371389483447222264315479843643644594380014392517935809196756016084353575280431551427977527806413393474389890985580652770804520222451016740444881362733698278398296002066402540671728435808363932620022750842112304723058861786521633815558708562228592120701675519309548136767069971764712810019246994801433063088071312167115538505867831554245298563209903343577209559526760142711462772386585274712670848953324224154294067340618307260658562600321016753390087491900361321198915877688554107907816573719045631446341840261327517205322766494887398908383148531898873205626051244833629270037975005538168031326011750545779821210010828782387153329639552242436944071446780431778584252683963383063577047215026501945132300925765272275778038786875339491448579007428004410615613565734571856813498940724261074074156124329762084528957719057659444019873363983235987116362889509097667320964148814934471984554426341797952461675714448881914379579013042333607991029213274418106487305355668908155658781807575797263196036787881035232885722450277422156024230698635108819815825932391106413034807518987162484426803651419049653426704444647218620942646527370449041979179563006200631746412893328773515963188396696300527806263874648866672405176181612864717992262723756367826886156666416944683194770772293960015703723218742530006269636369373333616030115460382643455203441901743294023248482473709892176239581817725918166843933537663395313369406032221440535781222859646343337464429790949756360068761689073644151853490566868117809776467516201270767641999634109205584253186601085960370669140570398353093923421549163784314801253117830940761335427126008731253062514194130561814074258220013941865399570834076238820128110751566786784559119609233099707522520113122552184107606629939208768491773934873265765665853689884455464092625457062782602820115263384265617841864223076358590328654571285416359764728547994822875214706589416847027317799852500042884876366985713660972609282579485763107292253726151587510340843495865724690552285209872396220145664776126528394190713886349341641124970748121585408664164372454443666939367296178558263689554289999352341416855530201812750041850266226241674086100919454469961317738028485088634159874779308998846312226619247339006221223002084624227496573976373896760612933092600953897180578312271580233711566015111023305908743090860260565219840589548060993320485595990777900784324785871621309517178581282610289407240314353033868684838835334743030900283187506412194683302625553554096307946768563336993012659892292061590087575891923169564640137921013068315694733023733918916956158967494279993578241750303564565415965388904053403189643072392024774524494928524468500449274716092372958642326912832646873714512184238767413262972392798760859621460177236584415701486141219833358529928432942749719639396932983692122551652398556741531167773146531247777435029940664564903938451237127523688116171200896610624177783685944274966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'aut_phi_ratio': 7.879166666666666, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1891, 1, 1], [3, 3782, 1, 1], [5, 3782, 1, 2], [6, 3782, 1, 1], [10, 3782, 1, 2], [15, 3782, 1, 4], [30, 3782, 1, 4], [31, 3660, 1, 15], [61, 1860, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,61)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 113460, 'autcentquo_group': '226920.b', 'autcentquo_hash': 6642875333164673378, 'autcentquo_nilpotent': False, 'autcentquo_order': 226920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,61)', 'cc_stats': [[1, 1, 1], [2, 1891, 1], [3, 3782, 1], [5, 3782, 2], [6, 3782, 1], [10, 3782, 2], [15, 3782, 4], [30, 3782, 4], [31, 3660, 15], [61, 1860, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '113460.a', 'commutator_count': 1, 'commutator_label': '113460.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['113460.a'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1891, 1, 1], [3, 3782, 1, 1], [5, 3782, 2, 1], [6, 3782, 1, 1], [10, 3782, 2, 1], [15, 3782, 4, 1], [30, 3782, 4, 1], [31, 3660, 15, 1], [61, 1860, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 55729, 'exponent': 56730, 'exponents_of_order': [2, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 31, 61], 'factors_of_order': [2, 3, 5, 31, 61], 'faithful_reps': [[31, 1, 2], [60, 1, 15], [61, 1, 1], [62, 1, 14]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '113460.a', 'hash': 8024833966218457710, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 56730, 'inner_gen_orders': [30, 3], 'inner_gens': [[7036413, 214963], [561902, 223381]], 'inner_hash': 8024833966218457710, 'inner_nilpotent': False, 'inner_order': 113460, 'inner_split': True, 'inner_tex': '\\PSL(2,61)', 'inner_used': [1, 2], 'irrC_degree': 31, 'irrQ_degree': 61, 'irrQ_dim': 61, 'irrR_degree': 31, 'irrep_stats': [[1, 1], [31, 2], [60, 15], [61, 1], [62, 14]], 'label': '113460.a', 'linC_count': 2, 'linC_degree': 31, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 61, 'linQ_degree_count': 1, 'linQ_dim': 61, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 31, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,61)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 33, 'number_divisions': 10, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 32, 'number_subgroups': 91144, 'old_label': None, 'order': 113460, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1891], [3, 3782], [5, 7564], [6, 3782], [10, 7564], [15, 15128], [30, 15128], [31, 54900], [61, 3720]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [5581903], 'outer_gens': [[2231338, 6639456]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': True, 'permutation_degree': 62, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [61, 1], [62, 3], [124, 2], [248, 2], [900, 1]], 'representations': {'Lie': [{'d': 2, 'q': 61, 'gens': [223381, 7036413], 'family': 'PSL'}, {'d': 2, 'q': 61, 'family': 'PSU'}, {'d': 3, 'q': 61, 'family': 'Omega'}, {'d': 3, 'q': 61, 'family': 'POmega'}, {'d': 2, 'q': 61, 'family': 'PSigmaL'}], 'Perm': {'d': 62, 'gens': [30966583629010787847057338565450731680853780026004037616455383676527432239942243867433, 5012331917525853437857176521103221167803000886146226238684397046084314355332697916]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,61)', 'transitive_degree': 62, '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: 171203327
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1, 'group_order': 113460, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1, 1], 'representative': 226982, 'size': 1}
id: 171203338
{'aut_label': '2A', 'centralizer': '1891.b1.a1', 'counter': 2, 'group_counter': 1, 'group_order': 113460, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2, 2], 'representative': 7053399, 'size': 1891}
id: 171203349
{'aut_label': '3A', 'centralizer': '3782.a1.a1', 'counter': 3, 'group_counter': 1, 'group_order': 113460, 'label': '3A', 'order': 3, 'powers': [3, 1, 3, 3, 3], 'representative': 7323810, 'size': 3782}
id: 171203354
{'aut_label': '5A1', 'centralizer': '3782.a1.a1', 'counter': 4, 'group_counter': 1, 'group_order': 113460, 'label': '5A1', 'order': 5, 'powers': [5, 5, 1, 4, 4], 'representative': 5970427, 'size': 3782}
id: 171203355
{'aut_label': '5A2', 'centralizer': '3782.a1.a1', 'counter': 5, 'group_counter': 1, 'group_order': 113460, 'label': '5A2', 'order': 5, 'powers': [4, 4, 1, 5, 5], 'representative': 3183863, 'size': 3782}
id: 171203356
{'aut_label': '6A', 'centralizer': '3782.a1.a1', 'counter': 6, 'group_counter': 1, 'group_order': 113460, 'label': '6A', 'order': 6, 'powers': [3, 2, 6, 6, 6], 'representative': 9541692, 'size': 3782}
id: 171203357
{'aut_label': '10A1', 'centralizer': '3782.a1.a1', 'counter': 7, 'group_counter': 1, 'group_order': 113460, 'label': '10A1', 'order': 10, 'powers': [4, 8, 2, 7, 7], 'representative': 11483108, 'size': 3782}
id: 171203358
{'aut_label': '10A3', 'centralizer': '3782.a1.a1', 'counter': 8, 'group_counter': 1, 'group_order': 113460, 'label': '10A3', 'order': 10, 'powers': [5, 7, 2, 8, 8], 'representative': 5576849, 'size': 3782}
id: 171203359
{'aut_label': '15A1', 'centralizer': '3782.a1.a1', 'counter': 9, 'group_counter': 1, 'group_order': 113460, 'label': '15A1', 'order': 15, 'powers': [10, 4, 3, 9, 9], 'representative': 11158365, 'size': 3782}
id: 171203328
{'aut_label': '15A2', 'centralizer': '3782.a1.a1', 'counter': 10, 'group_counter': 1, 'group_order': 113460, 'label': '15A2', 'order': 15, 'powers': [11, 5, 3, 10, 10], 'representative': 11945520, 'size': 3782}
id: 171203329
{'aut_label': '15A4', 'centralizer': '3782.a1.a1', 'counter': 11, 'group_counter': 1, 'group_order': 113460, 'label': '15A4', 'order': 15, 'powers': [12, 4, 3, 11, 11], 'representative': 7690915, 'size': 3782}
id: 171203330
{'aut_label': '15A7', 'centralizer': '3782.a1.a1', 'counter': 12, 'group_counter': 1, 'group_order': 113460, 'label': '15A7', 'order': 15, 'powers': [9, 5, 3, 12, 12], 'representative': 19351, 'size': 3782}
id: 171203331
{'aut_label': '30A1', 'centralizer': '3782.a1.a1', 'counter': 13, 'group_counter': 1, 'group_order': 113460, 'label': '30A1', 'order': 30, 'powers': [9, 7, 6, 13, 13], 'representative': 4647176, 'size': 3782}
id: 171203332
{'aut_label': '30A7', 'centralizer': '3782.a1.a1', 'counter': 14, 'group_counter': 1, 'group_order': 113460, 'label': '30A7', 'order': 30, 'powers': [12, 8, 6, 14, 14], 'representative': 3460389, 'size': 3782}
id: 171203333
{'aut_label': '30A11', 'centralizer': '3782.a1.a1', 'counter': 15, 'group_counter': 1, 'group_order': 113460, 'label': '30A11', 'order': 30, 'powers': [11, 7, 6, 15, 15], 'representative': 1340207, 'size': 3782}
id: 171203334
{'aut_label': '30A13', 'centralizer': '3782.a1.a1', 'counter': 16, 'group_counter': 1, 'group_order': 113460, 'label': '30A13', 'order': 30, 'powers': [10, 8, 6, 16, 16], 'representative': 7118573, 'size': 3782}
id: 171203335
{'aut_label': '31A1', 'centralizer': '3660.a1.a1', 'counter': 17, 'group_counter': 1, 'group_order': 113460, 'label': '31A1', 'order': 31, 'powers': [18, 19, 21, 1, 17], 'representative': 10890227, 'size': 3660}
id: 171203336
{'aut_label': '31A2', 'centralizer': '3660.a1.a1', 'counter': 18, 'group_counter': 1, 'group_order': 113460, 'label': '31A2', 'order': 31, 'powers': [20, 22, 26, 1, 18], 'representative': 11767482, 'size': 3660}
id: 171203337
{'aut_label': '31A3', 'centralizer': '3660.a1.a1', 'counter': 19, 'group_counter': 1, 'group_order': 113460, 'label': '31A3', 'order': 31, 'powers': [22, 25, 31, 1, 19], 'representative': 8351730, 'size': 3660}
id: 171203339
{'aut_label': '31A4', 'centralizer': '3660.a1.a1', 'counter': 20, 'group_counter': 1, 'group_order': 113460, 'label': '31A4', 'order': 31, 'powers': [24, 28, 27, 1, 20], 'representative': 3003544, 'size': 3660}
id: 171203340
{'aut_label': '31A5', 'centralizer': '3660.a1.a1', 'counter': 21, 'group_counter': 1, 'group_order': 113460, 'label': '31A5', 'order': 31, 'powers': [26, 31, 22, 1, 21], 'representative': 9292785, 'size': 3660}
id: 171203341
{'aut_label': '31A6', 'centralizer': '3660.a1.a1', 'counter': 22, 'group_counter': 1, 'group_order': 113460, 'label': '31A6', 'order': 31, 'powers': [28, 29, 17, 1, 22], 'representative': 13065574, 'size': 3660}
id: 171203342
{'aut_label': '31A7', 'centralizer': '3660.a1.a1', 'counter': 23, 'group_counter': 1, 'group_order': 113460, 'label': '31A7', 'order': 31, 'powers': [30, 26, 20, 1, 23], 'representative': 9370062, 'size': 3660}
id: 171203343
{'aut_label': '31A8', 'centralizer': '3660.a1.a1', 'counter': 24, 'group_counter': 1, 'group_order': 113460, 'label': '31A8', 'order': 31, 'powers': [31, 23, 25, 1, 24], 'representative': 9774969, 'size': 3660}
id: 171203344
{'aut_label': '31A9', 'centralizer': '3660.a1.a1', 'counter': 25, 'group_counter': 1, 'group_order': 113460, 'label': '31A9', 'order': 31, 'powers': [29, 20, 30, 1, 25], 'representative': 2846537, 'size': 3660}
id: 171203345
{'aut_label': '31A10', 'centralizer': '3660.a1.a1', 'counter': 26, 'group_counter': 1, 'group_order': 113460, 'label': '31A10', 'order': 31, 'powers': [27, 17, 28, 1, 26], 'representative': 3992469, 'size': 3660}
id: 171203346
{'aut_label': '31A11', 'centralizer': '3660.a1.a1', 'counter': 27, 'group_counter': 1, 'group_order': 113460, 'label': '31A11', 'order': 31, 'powers': [25, 18, 23, 1, 27], 'representative': 2804781, 'size': 3660}
id: 171203347
{'aut_label': '31A12', 'centralizer': '3660.a1.a1', 'counter': 28, 'group_counter': 1, 'group_order': 113460, 'label': '31A12', 'order': 31, 'powers': [23, 21, 18, 1, 28], 'representative': 9797074, 'size': 3660}
id: 171203348
{'aut_label': '31A13', 'centralizer': '3660.a1.a1', 'counter': 29, 'group_counter': 1, 'group_order': 113460, 'label': '31A13', 'order': 31, 'powers': [21, 24, 19, 1, 29], 'representative': 9444884, 'size': 3660}
id: 171203350
{'aut_label': '31A14', 'centralizer': '3660.a1.a1', 'counter': 30, 'group_counter': 1, 'group_order': 113460, 'label': '31A14', 'order': 31, 'powers': [19, 27, 24, 1, 30], 'representative': 13126920, 'size': 3660}
id: 171203351
{'aut_label': '31A15', 'centralizer': '3660.a1.a1', 'counter': 31, 'group_counter': 1, 'group_order': 113460, 'label': '31A15', 'order': 31, 'powers': [17, 30, 29, 1, 31], 'representative': 4927349, 'size': 3660}
id: 171203352
{'aut_label': '61A1', 'centralizer': '1860.a1.a1', 'counter': 32, 'group_counter': 1, 'group_order': 113460, 'label': '61A1', 'order': 61, 'powers': [33, 32, 32, 33, 1], 'representative': 11733301, 'size': 1860}
id: 171203353
{'aut_label': '61A1', 'centralizer': '1860.a1.a1', 'counter': 33, 'group_counter': 1, 'group_order': 113460, 'label': '61A2', 'order': 61, 'powers': [32, 33, 33, 32, 1], 'representative': 9166798, 'size': 1860}

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: 17269935
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.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], 'schur_index': 1}
id: 17269939
{'cdim': 61, 'counter': 4, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.61a', 'multiplicity': 1, 'nt': [62, 0], 'qdim': 61, 'qvalues': [61, 1, 1, 1, 1, 1, 1, 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, 0], 'schur_index': 1}
id: 17269937
{'cdim': 31, 'counter': 2, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.31a', 'multiplicity': 2, 'nt': [124, 0], 'qdim': 62, 'qvalues': [62, -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, 1, 1], 'schur_index': 1}
id: 17269940
{'cdim': 62, 'counter': 5, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62a', 'multiplicity': 1, 'nt': [186, 0], 'qdim': 62, 'qvalues': [62, 2, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 17269941
{'cdim': 62, 'counter': 6, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62b', 'multiplicity': 1, 'nt': [372, 0], 'qdim': 62, 'qvalues': [62, -2, -1, 2, 2, 1, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 17269942
{'cdim': 62, 'counter': 7, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62c', 'multiplicity': 2, 'nt': [310, 0], 'qdim': 124, 'qvalues': [124, 4, 4, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2], 'schur_index': 1}
id: 17269943
{'cdim': 62, 'counter': 8, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62d', 'multiplicity': 2, 'nt': [620, 0], 'qdim': 124, 'qvalues': [124, -4, 4, -1, -1, -4, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2], 'schur_index': 1}
id: 17269944
{'cdim': 62, 'counter': 9, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62e', 'multiplicity': 4, 'nt': [930, 0], 'qdim': 248, 'qvalues': [248, 8, -4, -2, -2, -4, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], 'schur_index': 1}
id: 17269936
{'cdim': 62, 'counter': 10, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.62f', 'multiplicity': 4, 'nt': [1860, 0], 'qdim': 248, 'qvalues': [248, -8, -4, -2, -2, 4, 2, 2, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4], 'schur_index': 1}
id: 17269938
{'cdim': 60, 'counter': 3, 'faithful': True, 'group': '113460.a', 'group_order': 113460, 'image': None, 'label': '113460.a.60a', 'multiplicity': 15, 'nt': [1830, 0], 'qdim': 900, 'qvalues': [900, 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, -15, -15], '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: 37866996
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 113460, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 113460, 'label': '113460.a.1a', 'nt': [1, 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]]]}
id: 37867007
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 2, 'cyclotomic_n': 61, 'dim': 31, 'faithful': True, 'field': [-15, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.31a1', 'nt': [124, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0], [1, 2], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 17], [1, 18], [1, 21], [1, 23], [1, 24], [1, 26], [1, 28], [1, 29], [1, 30], [1, -30], [1, -29], [1, -28], [1, -26], [1, -24], [1, -23], [1, -21], [1, -18], [1, -17], [1, -11], [1, -10], [1, -8], [1, -7], [1, -6], [1, -2]], [[-1, 2], [-1, 6], [-1, 7], [-1, 8], [-1, 10], [-1, 11], [-1, 17], [-1, 18], [-1, 21], [-1, 23], [-1, 24], [-1, 26], [-1, 28], [-1, 29], [-1, 30], [-1, -30], [-1, -29], [-1, -28], [-1, -26], [-1, -24], [-1, -23], [-1, -21], [-1, -18], [-1, -17], [-1, -11], [-1, -10], [-1, -8], [-1, -7], [-1, -6], [-1, -2]]]}
id: 37867018
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 61, 'dim': 31, 'faithful': True, 'field': [-15, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.31a2', 'nt': [124, 0], 'q_character': None, 'values': [[[31, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2], [-1, 6], [-1, 7], [-1, 8], [-1, 10], [-1, 11], [-1, 17], [-1, 18], [-1, 21], [-1, 23], [-1, 24], [-1, 26], [-1, 28], [-1, 29], [-1, 30], [-1, -30], [-1, -29], [-1, -28], [-1, -26], [-1, -24], [-1, -23], [-1, -21], [-1, -18], [-1, -17], [-1, -11], [-1, -10], [-1, -8], [-1, -7], [-1, -6], [-1, -2]], [[1, 0], [1, 2], [1, 6], [1, 7], [1, 8], [1, 10], [1, 11], [1, 17], [1, 18], [1, 21], [1, 23], [1, 24], [1, 26], [1, 28], [1, 29], [1, 30], [1, -30], [1, -29], [1, -28], [1, -26], [1, -24], [1, -23], [1, -21], [1, -18], [1, -17], [1, -11], [1, -10], [1, -8], [1, -7], [1, -6], [1, -2]]]}
id: 37867023
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id: 37867000
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id: 37867001
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id: 37867002
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id: 37867003
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id: 37867004
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id: 37867005
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id: 37867024
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id: 37867025
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id: 37867026
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id: 37867027
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id: 37867028
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id: 37866997
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id: 37866998
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id: 37866999
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 31, 'dim': 60, 'faithful': True, 'field': [1, -8, -28, 84, 126, -252, -210, 330, 165, -220, -66, 78, 13, -14, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.60a9', 'nt': [1830, 0], 'q_character': None, 'values': [[[60, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 14], [-1, -14]], [[-1, 8], [-1, -8]], [[-1, 1], [-1, -1]], [[-1, 10], [-1, -10]], [[-1, 12], [-1, -12]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[-1, 15], [-1, -15]], [[-1, 7], [-1, -7]], [[-1, 2], [-1, -2]], [[-1, 11], [-1, -11]], [[-1, 0]], [[-1, 0]]]}
id: 37867006
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 1, 'dim': 61, 'faithful': True, 'field': [0, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.61a', 'nt': [62, 0], 'q_character': None, 'values': [[[61, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 37867008
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 1, 'dim': 62, 'faithful': True, 'field': [0, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62a', 'nt': [186, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867009
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 1, 'dim': 62, 'faithful': True, 'field': [0, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62b', 'nt': [372, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867010
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 5, 'dim': 62, 'faithful': True, 'field': [-1, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62c1', 'nt': [310, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867011
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 5, 'dim': 62, 'faithful': True, 'field': [-1, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62c2', 'nt': [310, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867012
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 5, 'dim': 62, 'faithful': True, 'field': [-1, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62d1', 'nt': [620, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-2, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867013
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 5, 'dim': 62, 'faithful': True, 'field': [-1, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62d2', 'nt': [620, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-2, 0]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867014
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62e1', 'nt': [930, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867015
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62e2', 'nt': [930, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867016
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62e3', 'nt': [930, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 4], [1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867017
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62e4', 'nt': [930, 0], 'q_character': None, 'values': [[[62, 0]], [[2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867019
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62f1', 'nt': [1860, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}
id: 37867020
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62f2', 'nt': [1860, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[-1, 0]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 0]], [[-1, 3], [-1, -3]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867021
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62f3', 'nt': [1860, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -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]], [[1, 0]], [[1, 0]]]}
id: 37867022
{'center': '113460.a1.a1', 'center_index': 113460, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 15, 'dim': 62, 'faithful': True, 'field': [1, 4, -4, -1, 1], 'group': '113460.a', 'group_counter': 1, 'group_order': 113460, 'image': None, 'image_isoclass': '113460.a', 'image_order': 113460, 'indicator': 1, 'kernel': '113460.a1.a1', 'kernel_order': 1, 'label': '113460.a.62f4', 'nt': [1860, 0], 'q_character': None, 'values': [[[62, 0]], [[-2, 0]], [[-1, 0]], [[1, 3], [1, -3]], [[1, 6], [1, -6]], [[1, 0]], [[-1, 6], [-1, -6]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0]], [[1, 0]]]}

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: 262432480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 113460, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 56730, 'label': '113460.a.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'S', 'PC', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '113460.a', 'subgroup_hash': 8024833966218457710, 'subgroup_order': 113460, 'subgroup_tex': '\\PSL(2,61)', 'supersolvable': False, 'sylow': 0}
id: 262432491
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.62.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '62.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': 62, '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': '1830.1', 'subgroup_hash': 1, 'subgroup_order': 1830, 'subgroup_tex': 'C_{61}:C_{30}', 'supersolvable': True, 'sylow': 0}
id: 262432502
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 915, 'label': '113460.a.124.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '124.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': 124, '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': '915.1', 'subgroup_hash': 1, 'subgroup_order': 915, 'subgroup_tex': 'C_{61}:C_{15}', 'supersolvable': True, 'sylow': 0}
id: 262432506
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.186.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '186.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': 186, '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': '610.1', 'subgroup_hash': 1, 'subgroup_order': 610, 'subgroup_tex': 'C_{61}:C_{10}', 'supersolvable': True, 'sylow': 0}
id: 262432507
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.310.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '310.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': 310, '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': '366.1', 'subgroup_hash': 1, 'subgroup_order': 366, 'subgroup_tex': 'C_{61}:C_6', 'supersolvable': True, 'sylow': 0}
id: 262432508
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 305, 'label': '113460.a.372.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '372.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': 372, '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': '305.1', 'subgroup_hash': 1, 'subgroup_order': 305, 'subgroup_tex': 'C_{61}:C_5', 'supersolvable': True, 'sylow': 0}
id: 262432509
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 183, 'label': '113460.a.620.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '620.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': 620, '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': '183.1', 'subgroup_hash': 1, 'subgroup_order': 183, 'subgroup_tex': 'C_{61}:C_3', 'supersolvable': True, 'sylow': 0}
id: 262432510
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.930.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '930.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': 930, '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': '122.1', 'subgroup_hash': 1, 'subgroup_order': 122, 'subgroup_tex': 'D_{61}', 'supersolvable': True, 'sylow': 0}
id: 262432511
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.1830.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1830.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': 1830, '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': '62.1', 'subgroup_hash': 1, 'subgroup_order': 62, 'subgroup_tex': 'D_{31}', 'supersolvable': True, 'sylow': 0}
id: 262432481
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 61, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 61, 'label': '113460.a.1860.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1860.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': 1860, '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': '61.1', 'subgroup_hash': 1, 'subgroup_order': 61, 'subgroup_tex': 'C_{61}', 'supersolvable': True, 'sylow': 61}
id: 262432482
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '113460.a.1891.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1891.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1891, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
id: 262432483
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '113460.a.1891.a1.a2', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1891.a1.a2', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1891, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
id: 262432484
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '113460.a.1891.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1891.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': 1891, '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': '60.12', 'subgroup_hash': 12, 'subgroup_order': 60, 'subgroup_tex': 'D_{30}', 'supersolvable': True, 'sylow': 0}
id: 262432485
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 31, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': True, 'direct': None, 'hall': 31, 'label': '113460.a.3660.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3660.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': 3660, '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': '31.1', 'subgroup_hash': 1, 'subgroup_order': 31, 'subgroup_tex': 'C_{31}', 'supersolvable': True, 'sylow': 31}
id: 262432486
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '113460.a.3782.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3782.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': 3782, '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': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
id: 262432487
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.3782.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3782.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': 3782, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
id: 262432488
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.3782.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3782.b1.a2', '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': 3782, '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': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
id: 262432489
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '113460.a.5673.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5673.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': 5673, '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': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 262432490
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '113460.a.7564.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7564.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': 7564, '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': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
id: 262432492
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '113460.a.9455.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9455.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': 9455, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
id: 262432493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '113460.a.9455.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9455.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': 9455, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 262432494
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '113460.a.11346.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11346.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': 11346, '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': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 262432495
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.11346.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11346.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': 11346, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
id: 262432496
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.11346.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11346.b1.a2', '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': 11346, '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': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
id: 262432497
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '113460.a.18910.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18910.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': 18910, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 262432498
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.18910.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18910.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': 18910, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 262432499
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113460.a.18910.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18910.b1.a2', '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': 18910, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 262432500
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '113460.a.22692.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22692.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': 22692, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 262432501
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '113460.a.28365.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28365.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': 28365, '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': 2}
id: 262432503
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '113460.a.37820.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '37820.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': 37820, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 262432504
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '113460.a.56730.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56730.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': 56730, '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: 262432505
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '113460.a', 'ambient_counter': 1, 'ambient_order': 113460, 'ambient_tex': '\\PSL(2,61)', 'central': True, 'central_factor': False, 'centralizer_order': 113460, 'characteristic': True, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '113460.a.113460.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '113460.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '113460.a', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8024833966218457710, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 113460, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,61)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'Phi', 'R', 'U0', 'C1'], '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: 262432480
{'ambient': '113460.a', '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': '113460.a1.a1', 'complements': ['113460.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['62.a1.a1', '1830.a1.a1', '1891.a1.a1', '1891.a1.a2', '1891.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6966, 5000, 3862, 5000, 7392, 5000, 2365, 5000], 'generators': [571993, 7168933], 'label': '113460.a.1.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['113460.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '113460.a', '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': '113460.a'}
id: 262432481
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '1860.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1860.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['372.a1.a1', '620.a1.a1', '930.a1.a1'], 'contains': ['113460.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [1600, -1, 8570, -1, 2645, -1, 7452, -1], 'generators': [6828247], 'label': '113460.a.1860.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '1860.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1860.a1.a1', 'subgroup_fusion': None, 'weyl_group': '30.4'}
id: 262432482
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '1891.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9455.a1.a1', '11346.b1.a1', '18910.b1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1891, 'diagramx': [7464, -1, 1830, -1, 8320, -1, 2365, -1], 'generators': [10620237, 3159176], 'label': '113460.a.1891.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1891.a1.a1', 'old_label': '1891.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1891.a1.a1', 'subgroup_fusion': None, 'weyl_group': '60.5'}
id: 262432483
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '1891.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['9455.a1.a1', '11346.b1.a2', '18910.b1.a2'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1891, 'diagramx': [7464, -1, 665, -1, 8320, -1, 1551, -1], 'generators': [150792, 2824897], 'label': '113460.a.1891.a1.a2', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1891.a1.a2', 'old_label': '1891.a1.a2', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1891.a1.a2', 'subgroup_fusion': None, 'weyl_group': '60.5'}
id: 262432484
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '1891.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56730.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['3782.a1.a1', '3782.b1.a1', '3782.b1.a2', '5673.a1.a1', '9455.b1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1891, 'diagramx': [6302, -1, 3862, -1, 6667, -1, 4010, -1], 'generators': [2818248, 6169252, 3387072, 7980290], 'label': '113460.a.1891.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1891.b1.a1', 'old_label': '1891.b1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1891.b1.a1', 'subgroup_fusion': None, 'weyl_group': '30.3'}
id: 262432485
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id: 262432486
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id: 262432487
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id: 262432488
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id: 262432489
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id: 262432490
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id: 262432491
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id: 262432492
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id: 262432493
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id: 262432494
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id: 262432495
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id: 262432496
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id: 262432497
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id: 262432498
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id: 262432499
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id: 262432500
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id: 262432501
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id: 262432502
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id: 262432503
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '37820.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3782.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['620.a1.a1', '7564.a1.a1', '9455.a1.a1', '18910.a1.a1', '18910.b1.a1', '18910.b1.a2'], 'contains': ['113460.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1891, 'diagramx': [5061, -1, 2258, -1, 5941, -1, 4466, -1], 'generators': [4007743], 'label': '113460.a.37820.a1.a1', 'mobius_quo': None, 'mobius_sub': -20, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1891.b1.a1', 'old_label': '37820.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '37820.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 262432504
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '56730.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1891.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['930.a1.a1', '1830.a1.a1', '11346.a1.a1', '11346.b1.a1', '11346.b1.a2', '18910.a1.a1', '18910.b1.a1', '18910.b1.a2', '28365.a1.a1'], 'contains': ['113460.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1891, 'diagramx': [5707, -1, 5656, -1, 6709, -1, 3500, -1], 'generators': [11314597], 'label': '113460.a.56730.a1.a1', 'mobius_quo': None, 'mobius_sub': -90, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1891.b1.a1', 'old_label': '56730.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56730.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 262432505
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '113460.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1860.a1.a1', '3660.a1.a1', '22692.a1.a1', '37820.a1.a1', '56730.a1.a1'], 'contains': [], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5061, 5000, 8824, 5000, 5941, 5000, 4466, 5000], 'generators': [], 'label': '113460.a.113460.a1.a1', 'mobius_quo': 1, 'mobius_sub': 113460, 'normal_closure': '113460.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '113460.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '113460.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 262432506
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '186.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['62.a1.a1'], 'contains': ['372.a1.a1', '930.a1.a1', '11346.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [559, -1, 7896, -1, 2240, -1, 8122, -1], 'generators': [11229789, 11314597, 6828247], 'label': '113460.a.186.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '186.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '186.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1830.1'}
id: 262432507
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '310.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['62.a1.a1'], 'contains': ['620.a1.a1', '930.a1.a1', '18910.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [4004, -1, 5246, -1, 3659, -1, 6933, -1], 'generators': [4007743, 11314597, 6828247], 'label': '113460.a.310.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '310.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '310.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1830.1'}
id: 262432508
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '372.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['124.a1.a1', '186.a1.a1'], 'contains': ['1860.a1.a1', '22692.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [1845, -1, 8788, -1, 821, -1, 8980, -1], 'generators': [11229789, 6828247], 'label': '113460.a.372.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '372.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '372.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1830.1'}
id: 262432509
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '620.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['124.a1.a1', '310.a1.a1'], 'contains': ['1860.a1.a1', '37820.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [4004, -1, 7003, -1, 2091, -1, 7917, -1], 'generators': [4007743, 6828247], 'label': '113460.a.620.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '620.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '620.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1830.1'}
id: 262432510
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '930.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['186.a1.a1', '310.a1.a1'], 'contains': ['1860.a1.a1', '56730.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 62, 'diagramx': [1922, -1, 7431, -1, 3200, -1, 6987, -1], 'generators': [11314597, 6828247], 'label': '113460.a.930.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '62.a1.a1', 'old_label': '930.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '930.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1830.1'}
id: 262432511
{'ambient': '113460.a', 'aut_centralizer_order': None, 'aut_label': '1830.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '113460.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['3660.a1.a1', '56730.a1.a1'], 'core': '113460.a1.a1', 'coset_action_label': None, 'count': 1830, 'diagramx': [8890, -1, 9726, -1, 9621, -1, 317, -1], 'generators': [1496234, 4427544], 'label': '113460.a.1830.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1830.a1.a1', 'old_label': '1830.a1.a1', 'projective_image': '113460.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1830.a1.a1', 'subgroup_fusion': None, 'weyl_group': '62.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
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.