LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-23T17:56:56.152831

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': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 4680, 'aut_gen_orders': [8, 8, 8], 'aut_gens': [[14408201, 9605495], [23793960, 32856903], [19251676, 29495479], [21546876, 29607407]], 'aut_group': None, 'aut_hash': 977983066756978958, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24261120, 'aut_permdeg': 1080, 'aut_perms': [8417408574876301959060503752192424257036451877039553279011009871748516195760662875263923588797804170781963986938300877821401353775844255706575220659705409779401740225441621248941661343844188575447252999946588826992989431340462178213724552470808842178828007381134298504203215081084465663290716386149252146095636435342935320823222238964275135256195998125501340040396624971942170313744517864883100411279210603935702069265139443260911268446510140501741677189944205753992571067721377420878074144885492842523126626594663545301000215258515313305586365510089512619624541616846160163975818506440943308842545853859572171316928121284775650018304091352463672862225095888859737344325892541180905287320721176154807231610511981800618263216823974466087828476748367461200420019178715879617876763808019241469185632632645438926028251453489063822320242186128345931906732739802618983188067530252345704416369529394214992632269035418697511631503890710297116928285864333727507787032290378484448962253808491836653739267423972890772507358459732875883451044867826956406621232788148195413993333126318660251679208259275250905801536758764891493762345796245392848183603245603831353371524889140779886472526970133556149773548148444239299451283313420075219729018069920533251859230499832223110967685736670457543361114068775682259781777261086891766112380922391816097892182517074331281643154502044650172556056161512042422654922018468257998236671938320177027031599060057024561122071181450870781511464380041180112250878423442107018701113606724257597468328715707399664660855218382535301141147397690793163173086741801281314170384197960539403289207404097317143544108123610479804980989154655794402032293175669142008553505590383210175005306707977986448873168795093970476299078867490199464942307344288742803997888538564523600691828368744028831457558497474371476601664994085952269525525096864321222918108839595957470261299733447979995387333378956534269700467380740628417725570427576277828160237763142710524476369829344203801550690067032234942187732598221266506696930224245170358799207098232484525314883954931861032109153550851886177685347026841906052455167172690152482597090014046395579169052335693839761155966570364989911206466580278355270883126936840258020847853425720478992974231289433618525953745790851682794077158273869294435065004084598967559022923185067136011411984223728002933450898362244913008354988170226453529308026691306396738627018274846878055107940913183791340340959251140337244393398937097292533732658457954051860432290886055677947033840791046241692151407613174825413164857788862580013107298604524667253002013949199169998976456862325230425747205259656279435878087891325786686639907628619493259417582352787216865056477451428672550088646214576282074081429254175161682326909035649486007570170403411994327375491100739975822739255313064028092693, 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'aut_phi_ratio': 8.125, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1080, 1, 1], [2, 2106, 1, 1], [2, 5265, 1, 1], [3, 1040, 1, 1], [3, 6240, 1, 1], [3, 74880, 1, 1], [4, 4212, 1, 1], [4, 63180, 1, 1], [4, 189540, 1, 1], [4, 379080, 1, 1], [5, 303264, 1, 1], [6, 84240, 1, 1], [6, 112320, 1, 1], [6, 168480, 1, 1], [6, 336960, 1, 1], [6, 673920, 1, 1], [8, 63180, 2, 1], [8, 151632, 2, 1], [8, 379080, 1, 1], [8, 758160, 1, 1], [9, 449280, 1, 1], [10, 303264, 1, 1], [12, 336960, 1, 1], [12, 505440, 1, 1], [13, 466560, 2, 2], [20, 303264, 2, 1], [24, 505440, 2, 1], [26, 466560, 2, 2], [40, 303264, 2, 2]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(4,3).C_2^2', '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': 4680, 'autcentquo_group': None, 'autcentquo_hash': 977983066756978958, 'autcentquo_nilpotent': False, 'autcentquo_order': 24261120, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PSL(4,3).C_2^2', 'cc_stats': [[1, 1, 1], [2, 1080, 1], [2, 2106, 1], [2, 5265, 1], [3, 1040, 1], [3, 6240, 1], [3, 74880, 1], [4, 4212, 1], [4, 63180, 1], [4, 189540, 1], [4, 379080, 1], [5, 303264, 1], [6, 84240, 1], [6, 112320, 1], [6, 168480, 1], [6, 336960, 1], [6, 673920, 1], [8, 63180, 2], [8, 151632, 2], [8, 379080, 1], [8, 758160, 1], [9, 449280, 1], [10, 303264, 1], [12, 336960, 1], [12, 505440, 1], [13, 466560, 4], [20, 303264, 2], [24, 505440, 2], [26, 466560, 4], [40, 303264, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '12130560.c', 'commutator_count': 1, 'commutator_label': '6065280.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '6065280.a'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1080, 1, 1], [2, 2106, 1, 1], [2, 5265, 1, 1], [3, 1040, 1, 1], [3, 6240, 1, 1], [3, 74880, 1, 1], [4, 4212, 1, 1], [4, 63180, 1, 1], [4, 189540, 1, 1], [4, 379080, 1, 1], [5, 303264, 1, 1], [6, 84240, 1, 1], [6, 112320, 1, 1], [6, 168480, 1, 1], [6, 336960, 1, 1], [6, 673920, 1, 1], [8, 63180, 2, 1], [8, 151632, 2, 1], [8, 379080, 1, 1], [8, 758160, 1, 1], [9, 449280, 1, 1], [10, 303264, 1, 1], [12, 336960, 1, 1], [12, 505440, 1, 1], [13, 466560, 4, 1], [20, 303264, 2, 1], [24, 505440, 2, 1], [26, 466560, 4, 1], [40, 303264, 4, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': None, 'exponent': 4680, 'exponents_of_order': [8, 6, 1, 1], 'factors_of_aut_order': [2, 3, 5, 13], 'factors_of_order': [2, 3, 5, 13], 'faithful_reps': [[39, 1, 2], [52, 0, 2], [52, 1, 1], [90, 1, 2], [130, 1, 1], [260, 1, 2], [351, 1, 2], [390, 1, 2], [416, 0, 6], [416, 1, 2], [468, 0, 2], [468, 1, 1], [520, 1, 1], [640, 0, 8], [729, 1, 2], [780, 1, 2], [1040, 0, 2], [1170, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '12130560.c', 'hash': 8461112410546189005, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4680, 'inner_gen_orders': [2, 13], 'inner_gens': [[14408201, 9605441], [29819989, 9605495]], 'inner_hash': 8461112410546189005, 'inner_nilpotent': False, 'inner_order': 12130560, 'inner_split': True, 'inner_tex': '\\PGL(4,3)', 'inner_used': [1, 2], 'irrC_degree': 39, 'irrQ_degree': 39, 'irrQ_dim': 39, 'irrR_degree': 39, 'irrep_stats': [[1, 2], [39, 2], [52, 3], [90, 2], [130, 1], [260, 2], [351, 2], [390, 2], [416, 8], [468, 3], [520, 1], [640, 8], [729, 2], [780, 2], [1040, 2], [1170, 1]], 'label': '12130560.c', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PGL(4,3)', '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 33, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 43, 'number_divisions': 30, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 929, 'number_subgroup_classes': 1228, 'number_subgroups': 51404899, 'old_label': None, 'order': 12130560, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 8451], [3, 82160], [4, 636012], [5, 303264], [6, 1375920], [8, 1566864], [9, 449280], [10, 303264], [12, 842400], [13, 1866240], [20, 606528], [24, 1010880], [26, 1866240], [40, 1213056]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [7517589], 'outer_gens': [[33540112, 34811758]], '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': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [39, 2], [52, 1], [90, 2], [104, 1], [130, 1], [260, 2], [351, 2], [390, 2], [416, 2], [468, 1], [520, 1], [729, 2], [780, 2], [832, 1], [936, 1], [1170, 1], [1664, 1], [2080, 1], [2560, 2]], 'representations': {'Lie': [{'d': 4, 'q': 3, 'gens': [14408201, 9605495], 'family': 'PGL'}, {'d': 4, 'q': 3, 'family': 'PGammaL'}], 'Perm': {'d': 40, 'gens': [612318134292892751059980015582271582240530785125, 341668435346154550866383681368759885266699329565, 65971900822765570518592262312207230347168537455]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PGL(4,3)', 'transitive_degree': 40, '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: 171432478
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3, 'group_order': 12130560, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 14408200, 'size': 1}
id: 171432489
{'aut_label': '2A', 'centralizer': '1080.a1', 'counter': 2, 'group_counter': 3, 'group_order': 12130560, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 28820251, 'size': 1080}
id: 171432500
{'aut_label': '2B', 'centralizer': '2106.a1', 'counter': 3, 'group_counter': 3, 'group_order': 12130560, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 31314840, 'size': 2106}
id: 171432511
{'aut_label': '2C', 'centralizer': '5265.a1', 'counter': 4, 'group_counter': 3, 'group_order': 12130560, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 14814384, 'size': 5265}
id: 171432516
{'aut_label': '3A', 'centralizer': '1040.D', 'counter': 5, 'group_counter': 3, 'group_order': 12130560, 'label': '3A', 'order': 3, 'powers': [5, 1, 5, 5], 'representative': 34558174, 'size': 1040}
id: 171432517
{'aut_label': '3B', 'centralizer': '6240.I', 'counter': 6, 'group_counter': 3, 'group_order': 12130560, 'label': '3B', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 14865844, 'size': 6240}
id: 171432518
{'aut_label': '3C', 'centralizer': '74880.E', 'counter': 7, 'group_counter': 3, 'group_order': 12130560, 'label': '3C', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 37005298, 'size': 74880}
id: 171432519
{'aut_label': '4A', 'centralizer': '4212.B', 'counter': 8, 'group_counter': 3, 'group_order': 12130560, 'label': '4A', 'order': 4, 'powers': [3, 8, 8, 8], 'representative': 4439084, 'size': 4212}
id: 171432520
{'aut_label': '4B', 'centralizer': '63180.C', 'counter': 9, 'group_counter': 3, 'group_order': 12130560, 'label': '4B', 'order': 4, 'powers': [4, 9, 9, 9], 'representative': 4684693, 'size': 63180}
id: 171432479
{'aut_label': '4C', 'centralizer': '189540.I', 'counter': 10, 'group_counter': 3, 'group_order': 12130560, 'label': '4C', 'order': 4, 'powers': [3, 10, 10, 10], 'representative': 30822472, 'size': 189540}
id: 171432480
{'aut_label': '4D', 'centralizer': '379080.A', 'counter': 11, 'group_counter': 3, 'group_order': 12130560, 'label': '4D', 'order': 4, 'powers': [4, 11, 11, 11], 'representative': 8083779, 'size': 379080}
id: 171432481
{'aut_label': '5A', 'centralizer': '303264.A', 'counter': 12, 'group_counter': 3, 'group_order': 12130560, 'label': '5A', 'order': 5, 'powers': [12, 12, 1, 12], 'representative': 8897587, 'size': 303264}
id: 171432482
{'aut_label': '6A', 'centralizer': '84240.E', 'counter': 13, 'group_counter': 3, 'group_order': 12130560, 'label': '6A', 'order': 6, 'powers': [5, 4, 13, 13], 'representative': 40131256, 'size': 84240}
id: 171432483
{'aut_label': '6B', 'centralizer': '112320.G', 'counter': 14, 'group_counter': 3, 'group_order': 12130560, 'label': '6B', 'order': 6, 'powers': [5, 2, 14, 14], 'representative': 22219365, 'size': 112320}
id: 171432484
{'aut_label': '6C', 'centralizer': '168480.M', 'counter': 15, 'group_counter': 3, 'group_order': 12130560, 'label': '6C', 'order': 6, 'powers': [6, 3, 15, 15], 'representative': 38987639, 'size': 168480}
id: 171432485
{'aut_label': '6D', 'centralizer': '336960.O', 'counter': 16, 'group_counter': 3, 'group_order': 12130560, 'label': '6D', 'order': 6, 'powers': [6, 4, 16, 16], 'representative': 28809558, 'size': 336960}
id: 171432486
{'aut_label': '6E', 'centralizer': '673920.A', 'counter': 17, 'group_counter': 3, 'group_order': 12130560, 'label': '6E', 'order': 6, 'powers': [7, 2, 17, 17], 'representative': 18055213, 'size': 673920}
id: 171432487
{'aut_label': '8A1', 'centralizer': '63180.C', 'counter': 18, 'group_counter': 3, 'group_order': 12130560, 'label': '8A1', 'order': 8, 'powers': [9, 18, 19, 19], 'representative': 638612, 'size': 63180}
id: 171432488
{'aut_label': '8A1', 'centralizer': '63180.C', 'counter': 19, 'group_counter': 3, 'group_order': 12130560, 'label': '8A-1', 'order': 8, 'powers': [9, 19, 18, 18], 'representative': 1848204, 'size': 63180}
id: 171432490
{'aut_label': '8B1', 'centralizer': '151632.B', 'counter': 20, 'group_counter': 3, 'group_order': 12130560, 'label': '8B1', 'order': 8, 'powers': [8, 20, 21, 21], 'representative': 28069125, 'size': 151632}
id: 171432491
{'aut_label': '8B1', 'centralizer': '151632.B', 'counter': 21, 'group_counter': 3, 'group_order': 12130560, 'label': '8B-1', 'order': 8, 'powers': [8, 21, 20, 20], 'representative': 16011468, 'size': 151632}
id: 171432492
{'aut_label': '8C', 'centralizer': '379080.P', 'counter': 22, 'group_counter': 3, 'group_order': 12130560, 'label': '8C', 'order': 8, 'powers': [9, 22, 22, 22], 'representative': 12954270, 'size': 379080}
id: 171432493
{'aut_label': '8D', 'centralizer': '758160.B', 'counter': 23, 'group_counter': 3, 'group_order': 12130560, 'label': '8D', 'order': 8, 'powers': [9, 23, 23, 23], 'representative': 31972164, 'size': 758160}
id: 171432494
{'aut_label': '9A', 'centralizer': '449280.C', 'counter': 24, 'group_counter': 3, 'group_order': 12130560, 'label': '9A', 'order': 9, 'powers': [24, 5, 24, 24], 'representative': 19273334, 'size': 449280}
id: 171432495
{'aut_label': '10A', 'centralizer': '303264.A', 'counter': 25, 'group_counter': 3, 'group_order': 12130560, 'label': '10A', 'order': 10, 'powers': [12, 25, 3, 25], 'representative': 28432850, 'size': 303264}
id: 171432496
{'aut_label': '12A', 'centralizer': '336960.M', 'counter': 26, 'group_counter': 3, 'group_order': 12130560, 'label': '12A', 'order': 12, 'powers': [15, 8, 26, 26], 'representative': 21056179, 'size': 336960}
id: 171432497
{'aut_label': '12B', 'centralizer': '505440.U', 'counter': 27, 'group_counter': 3, 'group_order': 12130560, 'label': '12B', 'order': 12, 'powers': [13, 9, 27, 27], 'representative': 19174580, 'size': 505440}
id: 171432498
{'aut_label': '13A1', 'centralizer': '466560.a1', 'counter': 28, 'group_counter': 3, 'group_order': 12130560, 'label': '13A1', 'order': 13, 'powers': [30, 28, 30, 1], 'representative': 18220846, 'size': 466560}
id: 171432499
{'aut_label': '13A1', 'centralizer': '466560.a1', 'counter': 29, 'group_counter': 3, 'group_order': 12130560, 'label': '13A-1', 'order': 13, 'powers': [31, 29, 31, 1], 'representative': 7830569, 'size': 466560}
id: 171432501
{'aut_label': '13A2', 'centralizer': '466560.a1', 'counter': 30, 'group_counter': 3, 'group_order': 12130560, 'label': '13A2', 'order': 13, 'powers': [29, 30, 29, 1], 'representative': 5247580, 'size': 466560}
id: 171432502
{'aut_label': '13A2', 'centralizer': '466560.a1', 'counter': 31, 'group_counter': 3, 'group_order': 12130560, 'label': '13A-2', 'order': 13, 'powers': [28, 31, 28, 1], 'representative': 23212223, 'size': 466560}
id: 171432503
{'aut_label': '20A1', 'centralizer': '303264.A', 'counter': 32, 'group_counter': 3, 'group_order': 12130560, 'label': '20A1', 'order': 20, 'powers': [25, 32, 8, 33], 'representative': 23669428, 'size': 303264}
id: 171432504
{'aut_label': '20A1', 'centralizer': '303264.A', 'counter': 33, 'group_counter': 3, 'group_order': 12130560, 'label': '20A-1', 'order': 20, 'powers': [25, 33, 8, 32], 'representative': 40005234, 'size': 303264}
id: 171432505
{'aut_label': '24A1', 'centralizer': '505440.U', 'counter': 34, 'group_counter': 3, 'group_order': 12130560, 'label': '24A1', 'order': 24, 'powers': [27, 18, 35, 35], 'representative': 27545016, 'size': 505440}
id: 171432506
{'aut_label': '24A1', 'centralizer': '505440.U', 'counter': 35, 'group_counter': 3, 'group_order': 12130560, 'label': '24A-1', 'order': 24, 'powers': [27, 19, 34, 34], 'representative': 21978252, 'size': 505440}
id: 171432507
{'aut_label': '26A1', 'centralizer': '466560.a1', 'counter': 36, 'group_counter': 3, 'group_order': 12130560, 'label': '26A1', 'order': 26, 'powers': [28, 36, 38, 2], 'representative': 42326138, 'size': 466560}
id: 171432508
{'aut_label': '26A1', 'centralizer': '466560.a1', 'counter': 37, 'group_counter': 3, 'group_order': 12130560, 'label': '26A-1', 'order': 26, 'powers': [29, 37, 39, 2], 'representative': 33886830, 'size': 466560}
id: 171432509
{'aut_label': '26A5', 'centralizer': '466560.a1', 'counter': 38, 'group_counter': 3, 'group_order': 12130560, 'label': '26A5', 'order': 26, 'powers': [30, 38, 37, 2], 'representative': 27917938, 'size': 466560}
id: 171432510
{'aut_label': '26A5', 'centralizer': '466560.a1', 'counter': 39, 'group_counter': 3, 'group_order': 12130560, 'label': '26A-5', 'order': 26, 'powers': [31, 39, 36, 2], 'representative': 37620420, 'size': 466560}
id: 171432512
{'aut_label': '40A1', 'centralizer': '303264.A', 'counter': 40, 'group_counter': 3, 'group_order': 12130560, 'label': '40A1', 'order': 40, 'powers': [32, 40, 20, 41], 'representative': 1259140, 'size': 303264}
id: 171432513
{'aut_label': '40A1', 'centralizer': '303264.A', 'counter': 41, 'group_counter': 3, 'group_order': 12130560, 'label': '40A-1', 'order': 40, 'powers': [33, 41, 21, 40], 'representative': 23994009, 'size': 303264}
id: 171432514
{'aut_label': '40A7', 'centralizer': '303264.A', 'counter': 42, 'group_counter': 3, 'group_order': 12130560, 'label': '40A7', 'order': 40, 'powers': [32, 42, 21, 43], 'representative': 39661025, 'size': 303264}
id: 171432515
{'aut_label': '40A7', 'centralizer': '303264.A', 'counter': 43, 'group_counter': 3, 'group_order': 12130560, 'label': '40A-7', 'order': 40, 'powers': [33, 43, 20, 42], 'representative': 6081530, 'size': 303264}

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: 17284310
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 17284321
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 17284332
{'cdim': 39, 'counter': 3, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.39a', 'multiplicity': 1, 'nt': [40, 177552], 'qdim': 39, 'qvalues': [39, 13, -1, 7, 12, 3, 3, -1, 3, -1, 1, -1, 4, 4, -1, 1, 1, 3, 3, -1, -1, -1, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
id: 17284334
{'cdim': 39, 'counter': 4, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.39b', 'multiplicity': 1, 'nt': [80, 0], 'qdim': 39, 'qvalues': [39, -13, -1, 7, 12, 3, 3, -1, 3, -1, -1, -1, 4, -4, -1, 1, -1, -3, -3, 1, 1, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
id: 17284335
{'cdim': 52, 'counter': 5, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.52a', 'multiplicity': 1, 'nt': [234, 0], 'qdim': 52, 'qvalues': [52, 0, 12, 4, -2, 7, -2, 8, 4, 0, 0, 2, -2, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, -1, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284337
{'cdim': 90, 'counter': 7, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.90a', 'multiplicity': 1, 'nt': [130, 0], 'qdim': 90, 'qvalues': [90, 12, 10, 10, 9, 9, 0, 10, -2, 2, 0, 0, 1, 3, 1, 1, 0, -2, -2, 0, 0, 2, 0, 0, 0, 1, 1, -1, -1, -1, -1, 0, 0, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
id: 17284338
{'cdim': 90, 'counter': 8, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.90b', 'multiplicity': 1, 'nt': [234, 0], 'qdim': 90, 'qvalues': [90, -12, 10, 10, 9, 9, 0, 10, -2, 2, 0, 0, 1, -3, 1, 1, 0, 2, 2, 0, 0, -2, 0, 0, 0, 1, 1, -1, -1, -1, -1, 0, 0, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
id: 17284336
{'cdim': 52, 'counter': 6, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.52b', 'multiplicity': 2, 'nt': [468, 0], 'qdim': 104, 'qvalues': [104, 0, 16, -8, -4, 14, -4, -20, 0, 4, 0, 4, 4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284339
{'cdim': 130, 'counter': 9, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.130a', 'multiplicity': 1, 'nt': [260, 0], 'qdim': 130, 'qvalues': [130, 0, 10, -14, 22, 13, 4, -10, 2, -2, 0, 0, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284311
{'cdim': 260, 'counter': 10, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.260a', 'multiplicity': 1, 'nt': [390, 0], 'qdim': 260, 'qvalues': [260, 26, 20, 4, 17, -10, -1, 0, 4, 0, 2, 0, 1, -1, 2, -2, -1, 2, 2, 0, 0, 2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284312
{'cdim': 260, 'counter': 11, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.260b', 'multiplicity': 1, 'nt': [780, 0], 'qdim': 260, 'qvalues': [260, -26, 20, 4, 17, -10, -1, 0, 4, 0, -2, 0, 1, 1, 2, -2, 1, -2, -2, 0, 0, -2, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284313
{'cdim': 351, 'counter': 12, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.351a', 'multiplicity': 1, 'nt': [520, 0], 'qdim': 351, 'qvalues': [351, 39, -9, 15, 27, 0, 0, -9, -1, -1, -1, 1, 3, 3, 0, 0, 0, -1, -1, 1, 1, -1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
id: 17284314
{'cdim': 351, 'counter': 13, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.351b', 'multiplicity': 1, 'nt': [780, 0], 'qdim': 351, 'qvalues': [351, -39, -9, 15, 27, 0, 0, -9, -1, -1, 1, 1, 3, -3, 0, 0, 0, 1, 1, -1, -1, 1, -1, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
id: 17284315
{'cdim': 390, 'counter': 14, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.390a', 'multiplicity': 1, 'nt': [780, 0], 'qdim': 390, 'qvalues': [390, -26, -10, -10, 39, 3, 3, 10, 2, 2, 2, 0, -1, 1, -1, -1, 1, -4, -4, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284316
{'cdim': 390, 'counter': 15, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.390b', 'multiplicity': 1, 'nt': [780, 0], 'qdim': 390, 'qvalues': [390, 26, -10, -10, 39, 3, 3, 10, 2, 2, -2, 0, -1, -1, -1, -1, -1, 4, 4, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284317
{'cdim': 416, 'counter': 16, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.416a', 'multiplicity': 1, 'nt': [2106, 0], 'qdim': 416, 'qvalues': [416, 0, 16, 0, -16, 2, 2, 16, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 4, 4, 0, 0, -1, 1, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
id: 17284318
{'cdim': 416, 'counter': 17, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.416b', 'multiplicity': 1, 'nt': [4212, 0], 'qdim': 416, 'qvalues': [416, 0, 16, 0, -16, 2, 2, 16, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, -4, -4, 0, 0, -1, 1, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
id: 17284322
{'cdim': 468, 'counter': 20, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.468a', 'multiplicity': 1, 'nt': [780, 0], 'qdim': 468, 'qvalues': [468, 0, 28, 4, -18, 9, 0, -8, 4, 0, 0, -2, -2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284324
{'cdim': 520, 'counter': 22, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.520a', 'multiplicity': 1, 'nt': [4212, 0], 'qdim': 520, 'qvalues': [520, 0, 0, -8, -20, 16, -2, 20, 0, -4, 0, 0, 4, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284327
{'cdim': 729, 'counter': 25, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.729a', 'multiplicity': 1, 'nt': [2080, 0], 'qdim': 729, 'qvalues': [729, 27, 9, 9, 0, 0, 0, 9, -3, 1, -1, -1, 0, 0, 0, 0, 0, -3, -3, -1, -1, 1, -1, 0, -1, 0, 0, 1, 1, 1, 1, -1, -1, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 17284328
{'cdim': 729, 'counter': 26, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.729b', 'multiplicity': 1, 'nt': [2106, 0], 'qdim': 729, 'qvalues': [729, -27, 9, 9, 0, 0, 0, 9, -3, 1, 1, -1, 0, 0, 0, 0, 0, 3, 3, 1, 1, -1, -1, 0, -1, 0, 0, 1, 1, 1, 1, -1, -1, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 17284329
{'cdim': 780, 'counter': 27, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.780a', 'multiplicity': 1, 'nt': [1560, 0], 'qdim': 780, 'qvalues': [780, 26, -20, 12, -3, 6, -3, 0, 4, 0, 2, 0, -3, -1, -2, 0, -1, -2, -2, 0, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284330
{'cdim': 780, 'counter': 28, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.780b', 'multiplicity': 1, 'nt': [2340, 0], 'qdim': 780, 'qvalues': [780, -26, -20, 12, -3, 6, -3, 0, 4, 0, -2, 0, -3, 1, -2, 0, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284319
{'cdim': 416, 'counter': 18, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.416c', 'multiplicity': 2, 'nt': [6318, 0], 'qdim': 832, 'qvalues': [832, 0, 32, 0, -32, 4, 4, -32, 0, 0, 0, 2, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 4, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284323
{'cdim': 468, 'counter': 21, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.468b', 'multiplicity': 2, 'nt': [6240, 0], 'qdim': 936, 'qvalues': [936, 0, -16, -8, -36, 18, 0, -20, 0, 4, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284333
{'cdim': 1170, 'counter': 30, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.1170a', 'multiplicity': 1, 'nt': [2340, 0], 'qdim': 1170, 'qvalues': [1170, 0, 10, 2, 36, 9, 0, -10, -6, -2, 0, 0, -4, 0, 1, -1, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284320
{'cdim': 416, 'counter': 19, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.416d', 'multiplicity': 4, 'nt': [16848, 0], 'qdim': 1664, 'qvalues': [1664, 0, -64, 0, -64, 8, 8, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284331
{'cdim': 1040, 'counter': 29, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.1040a', 'multiplicity': 2, 'nt': [9360, 0], 'qdim': 2080, 'qvalues': [2080, 0, 0, -32, 28, -8, -8, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 17284325
{'cdim': 640, 'counter': 23, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.640a', 'multiplicity': 4, 'nt': [5760, 0], 'qdim': 2560, 'qvalues': [2560, 64, 0, 0, -32, -32, 4, 0, 0, 0, 0, 0, 0, -8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
id: 17284326
{'cdim': 640, 'counter': 24, 'faithful': True, 'group': '12130560.c', 'group_order': 12130560, 'image': None, 'label': '12130560.c.640b', 'multiplicity': 4, 'nt': [11520, 0], 'qdim': 2560, 'qvalues': [2560, -64, 0, 0, -32, -32, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 37887456
{'center': None, 'center_index': 1, 'center_order': 12130560, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 12130560, 'label': '12130560.c.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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 37887467
{'center': None, 'center_index': 1, 'center_order': 12130560, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 6065280, 'label': '12130560.c.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 37887478
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 3, 'cyclotomic_n': 1, 'dim': 39, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.39a', 'nt': [40, 177552], 'q_character': None, 'values': [[[39, 0]], [[13, 0]], [[-1, 0]], [[7, 0]], [[12, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 37887489
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 4, 'cyclotomic_n': 1, 'dim': 39, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.39b', 'nt': [80, 0], 'q_character': None, 'values': [[[39, 0]], [[-13, 0]], [[-1, 0]], [[7, 0]], [[12, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-4, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 37887494
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 5, 'cyclotomic_n': 1, 'dim': 52, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.52a', 'nt': [234, 0], 'q_character': None, 'values': [[[52, 0]], [[0, 0]], [[12, 0]], [[4, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[8, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887495
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 6, 'cyclotomic_n': 8, 'dim': 52, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.52b1', 'nt': [468, 0], 'q_character': None, 'values': [[[52, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
id: 37887496
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 7, 'cyclotomic_n': 8, 'dim': 52, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.52b2', 'nt': [468, 2], 'q_character': None, 'values': [[[52, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-2, 0]], [[7, 0]], [[-2, 0]], [[-10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 37887497
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 8, 'cyclotomic_n': 1, 'dim': 90, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.90a', 'nt': [130, 0], 'q_character': None, 'values': [[[90, 0]], [[12, 0]], [[10, 0]], [[10, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887498
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 9, 'cyclotomic_n': 1, 'dim': 90, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.90b', 'nt': [234, 0], 'q_character': None, 'values': [[[90, 0]], [[-12, 0]], [[10, 0]], [[10, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[10, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887457
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 10, 'cyclotomic_n': 1, 'dim': 130, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.130a', 'nt': [260, 0], 'q_character': None, 'values': [[[130, 0]], [[0, 0]], [[10, 0]], [[-14, 0]], [[22, 0]], [[13, 0]], [[4, 0]], [[-10, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887458
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 11, 'cyclotomic_n': 1, 'dim': 260, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.260a', 'nt': [390, 0], 'q_character': None, 'values': [[[260, 0]], [[26, 0]], [[20, 0]], [[4, 0]], [[17, 0]], [[-10, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887459
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 12, 'cyclotomic_n': 1, 'dim': 260, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.260b', 'nt': [780, 0], 'q_character': None, 'values': [[[260, 0]], [[-26, 0]], [[20, 0]], [[4, 0]], [[17, 0]], [[-10, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887460
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 13, 'cyclotomic_n': 1, 'dim': 351, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.351a', 'nt': [520, 0], 'q_character': None, 'values': [[[351, 0]], [[39, 0]], [[-9, 0]], [[15, 0]], [[27, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 37887461
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 14, 'cyclotomic_n': 1, 'dim': 351, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.351b', 'nt': [780, 0], 'q_character': None, 'values': [[[351, 0]], [[-39, 0]], [[-9, 0]], [[15, 0]], [[27, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 37887462
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 15, 'cyclotomic_n': 1, 'dim': 390, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.390a', 'nt': [780, 0], 'q_character': None, 'values': [[[390, 0]], [[-26, 0]], [[-10, 0]], [[-10, 0]], [[39, 0]], [[3, 0]], [[3, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887463
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 16, 'cyclotomic_n': 1, 'dim': 390, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.390b', 'nt': [780, 0], 'q_character': None, 'values': [[[390, 0]], [[26, 0]], [[-10, 0]], [[-10, 0]], [[39, 0]], [[3, 0]], [[3, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887464
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 1, 'dim': 416, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416a', 'nt': [2106, 0], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 37887465
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 416, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416b', 'nt': [4212, 0], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 37887466
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 20, 'dim': 416, 'faithful': True, 'field': [5, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416c1', 'nt': [6318, 0], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]]]}
id: 37887468
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 20, 'dim': 416, 'faithful': True, 'field': [5, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416c2', 'nt': [6318, 2], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]]]}
id: 37887469
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 40, 'dim': 416, 'faithful': True, 'field': [9, 0, -4, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416d1', 'nt': [16848, 0], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]]]}
id: 37887470
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 40, 'dim': 416, 'faithful': True, 'field': [9, 0, -4, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416d2', 'nt': [16848, 4], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]]]}
id: 37887471
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 40, 'dim': 416, 'faithful': True, 'field': [9, 0, -4, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416d3', 'nt': [16848, 0], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5], [-2, 15]], [[2, 5], [2, 15]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6], [-1, 10], [2, 14]], [[-2, 6], [1, 10], [-2, 14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]]]}
id: 37887472
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 40, 'dim': 416, 'faithful': True, 'field': [9, 0, -4, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.416d4', 'nt': [16848, 4], 'q_character': None, 'values': [[[416, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-16, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 15]], [[-2, 5], [-2, 15]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [1, 10], [-2, 14]], [[2, 6], [-1, 10], [2, 14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [-1, 7], [1, 9]], [[1, 1], [1, 3], [-1, 5], [-1, 7], [1, 9], [-1, 15]], [[-1, 1], [-1, 3], [1, 7], [-1, 9]], [[-1, 1], [-1, 3], [1, 5], [1, 7], [-1, 9], [1, 15]]]}
id: 37887473
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 468, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.468a', 'nt': [780, 0], 'q_character': None, 'values': [[[468, 0]], [[0, 0]], [[28, 0]], [[4, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887474
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 8, 'dim': 468, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.468b1', 'nt': [6240, 0], 'q_character': None, 'values': [[[468, 0]], [[0, 0]], [[-8, 0]], [[-4, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 37887475
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 8, 'dim': 468, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.468b2', 'nt': [6240, 2], 'q_character': None, 'values': [[[468, 0]], [[0, 0]], [[-8, 0]], [[-4, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[-10, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
id: 37887476
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 1, 'dim': 520, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.520a', 'nt': [4212, 0], 'q_character': None, 'values': [[[520, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-20, 0]], [[16, 0]], [[-2, 0]], [[20, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887477
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640a1', 'nt': [5760, 0], 'q_character': None, 'values': [[[640, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887479
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640a2', 'nt': [5760, 4], 'q_character': None, 'values': [[[640, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887480
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640a3', 'nt': [5760, 0], 'q_character': None, 'values': [[[640, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887481
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640a4', 'nt': [5760, 4], 'q_character': None, 'values': [[[640, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887482
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640b1', 'nt': [11520, 0], 'q_character': None, 'values': [[[640, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -3], [-1, -1]], [[-1, 1], [-1, 3], [-1, -4]], [[-1, -6], [-1, -5], [-1, -2]], [[-1, 2], [-1, 5], [-1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887483
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640b2', 'nt': [11520, 4], 'q_character': None, 'values': [[[640, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, -4]], [[-1, 4], [-1, -3], [-1, -1]], [[-1, 2], [-1, 5], [-1, 6]], [[-1, -6], [-1, -5], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887484
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640b3', 'nt': [11520, 0], 'q_character': None, 'values': [[[640, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -3], [1, -1]], [[1, 1], [1, 3], [1, -4]], [[1, -6], [1, -5], [1, -2]], [[1, 2], [1, 5], [1, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, 5], [-1, 6]], [[-1, -6], [-1, -5], [-1, -2]], [[-1, 4], [-1, -3], [-1, -1]], [[-1, 1], [-1, 3], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887485
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 13, 'dim': 640, 'faithful': True, 'field': [3, 4, 2, -1, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.640b4', 'nt': [11520, 4], 'q_character': None, 'values': [[[640, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, -4]], [[1, 4], [1, -3], [1, -1]], [[1, 2], [1, 5], [1, 6]], [[1, -6], [1, -5], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -6], [-1, -5], [-1, -2]], [[-1, 2], [-1, 5], [-1, 6]], [[-1, 1], [-1, 3], [-1, -4]], [[-1, 4], [-1, -3], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887486
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 1, 'dim': 729, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.729a', 'nt': [2080, 0], 'q_character': None, 'values': [[[729, 0]], [[27, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 37887487
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 729, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.729b', 'nt': [2106, 0], 'q_character': None, 'values': [[[729, 0]], [[-27, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 37887488
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 780, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.780a', 'nt': [1560, 0], 'q_character': None, 'values': [[[780, 0]], [[26, 0]], [[-20, 0]], [[12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-3, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887490
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 780, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.780b', 'nt': [2340, 0], 'q_character': None, 'values': [[[780, 0]], [[-26, 0]], [[-20, 0]], [[12, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887491
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 8, 'dim': 1040, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.1040a1', 'nt': [9360, 0], 'q_character': None, 'values': [[[1040, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[14, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-4, 1], [-4, 3]], [[4, 1], [4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887492
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 8, 'dim': 1040, 'faithful': True, 'field': [2, 0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 0, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.1040a2', 'nt': [9360, 2], 'q_character': None, 'values': [[[1040, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[14, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[4, 1], [4, 3]], [[-4, 1], [-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 37887493
{'center': None, 'center_index': 12130560, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 1170, 'faithful': True, 'field': [0, 1], 'group': '12130560.c', 'group_counter': 3, 'group_order': 12130560, 'image': None, 'image_isoclass': '12130560.c', 'image_order': 12130560, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '12130560.c.1170a', 'nt': [2340, 0], 'q_character': None, 'values': [[[1170, 0]], [[0, 0]], [[10, 0]], [[2, 0]], [[36, 0]], [[9, 0]], [[0, 0]], [[-10, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 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
Showing the first 100 of 929 matching records in this table.

id: 262680638
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 12130560, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 390, 'label': '12130560.c.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12130560.c', 'subgroup_hash': 8461112410546189005, 'subgroup_order': 12130560, 'subgroup_tex': '\\PGL(4,3)', 'supersolvable': False, 'sylow': 0}
id: 262680749
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id: 262680860
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id: 262680971
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id: 262681082
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id: 262681193
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id: 262681304
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id: 262681415
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id: 262681526
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id: 262680639
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id: 262680650
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id: 262680661
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id: 262680672
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id: 262680683
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id: 262680694
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id: 262680705
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id: 262680716
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id: 262680727
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id: 262680738
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id: 262680750
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id: 262680761
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id: 262680772
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id: 262680783
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id: 262680794
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id: 262680805
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id: 262680816
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id: 262680827
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id: 262680838
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id: 262680849
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id: 262680861
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id: 262680872
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id: 262680883
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id: 262680894
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id: 262680905
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id: 262680916
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id: 262680927
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id: 262680938
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id: 262680949
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id: 262680960
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id: 262680972
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id: 262680983
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id: 262680994
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id: 262681005
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id: 262681016
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id: 262681027
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id: 262681038
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id: 262681049
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id: 262681060
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id: 262681071
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id: 262681083
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id: 262681094
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id: 262681105
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id: 262681116
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id: 262681127
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id: 262681138
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id: 262681149
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id: 262681160
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id: 262681171
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id: 262681182
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id: 262681194
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id: 262681205
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id: 262681216
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id: 262681227
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id: 262681238
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id: 262681249
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id: 262681260
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id: 262681271
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id: 262681282
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id: 262681293
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id: 262681305
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id: 262681316
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id: 262681327
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id: 262681338
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id: 262681349
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id: 262681360
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id: 262681371
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id: 262681382
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id: 262681393
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id: 262681404
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id: 262681416
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id: 262681427
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id: 262681438
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id: 262681449
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id: 262681460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4212.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4212.c1', 'outer_equivalence': True, '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': 4212, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2559216126776383709, 'subgroup_order': 2880, 'subgroup_tex': 'C_4.A_6.C_2', 'supersolvable': False, 'sylow': 0}
id: 262681471
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id: 262681482
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id: 262681493
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id: 262681504
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id: 262681515
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id: 262681527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.f1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 3219339599282734366, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.D_8:C_2', 'supersolvable': False, 'sylow': 0}
id: 262681538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.g1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 863601208845687898, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
id: 262681549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.h1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 8800710472352522369, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
id: 262681560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.i1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 8800710472352522369, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.D_4.C_2^2', 'supersolvable': False, 'sylow': 0}
id: 262681561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.j1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 4088988131338656119, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.\\SD_{16}.C_2', 'supersolvable': False, 'sylow': 0}
id: 262681562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.k1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 9019849488891309561, 'subgroup_order': 2592, 'subgroup_tex': '\\ASL(2,3).D_6', 'supersolvable': False, 'sylow': 0}
id: 262681563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.l1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 1359974926057248800, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.Q_8:C_2^2', 'supersolvable': False, 'sylow': 0}
id: 262681564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.m1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 273629761795729703, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.C_4:Q_8', 'supersolvable': False, 'sylow': 0}
id: 262681565
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.n1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 2088917612038948738, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.(C_4\\times C_8)', 'supersolvable': False, 'sylow': 0}
id: 262681566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.o1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 6438732644365265606, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.(\\OD_{16}.C_2)', 'supersolvable': False, 'sylow': 0}
id: 262680640
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12130560.c', 'ambient_counter': 3, 'ambient_order': 12130560, 'ambient_tex': '\\PGL(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12130560.c.4680.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4680.p1', 'outer_equivalence': True, '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': 4680, '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': None, 'subgroup_hash': 1515785214594576051, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4.\\OD_{16}.C_2', 'supersolvable': False, 'sylow': 0}

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
Showing the first 100 of 929 matching records in this table.

id: 262680638
{'ambient': '12130560.c', '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': '12130560.a1', 'complements': ['12130560.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '40.a1', '130.a1', '2106.a1', '5265.a1', '8424.A', '10530.B'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [9605495, 14408201], 'label': '12130560.c.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680639
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '468.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1'], 'contains': ['12636.a1', '16848.D', '18720.N', '18720.U', '21060.E'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 234, 'diagramx': None, 'generators': [33622648, 8949692], 'label': '12130560.c.468.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '234.a1', 'old_label': '468.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '468.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680640
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2340.A', '2340.C', '2340.G'], 'contains': ['9360.R', '9360.S', '9360.T', '379080.S'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 10464457, 12059806, 6496812, 29075747, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.4680.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.P', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680641
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2340.E', '2340.G', '2340.H'], 'contains': ['9360.Q', '9360.R', '9360.U', '9360.BF', '9360.BG', '42120.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [10464457, 4375630, 6272156, 30987847, 12059806, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.4680.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.Q', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680642
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2340.F', '2340.G'], 'contains': ['9360.S', '9360.U', '379080.V'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [10464457, 4375630, 6272156, 30987847, 11247527, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.4680.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.R', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680643
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.G', '2340.A', '2340.B', '2340.I'], 'contains': ['9360.P', '9360.T', '9360.Z', '379080.W'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [30888252, 6272156, 30987847, 40599884, 26838171, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.4680.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.S', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680644
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.H', '2340.B', '2340.D', '2340.G'], 'contains': ['9360.Q', '9360.S', '9360.W', '9360.Z', '9360.BD', '379080.X'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [6272156, 30987847, 26838171, 7701714, 29075747, 29691520, 14615915, 14218051, 41950063], 'label': '12130560.c.4680.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.T', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680645
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.I', '2340.A', '2340.D', '2340.G'], 'contains': ['9360.R', '9360.S', '9360.Z', '379080.Y'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [30888252, 6272156, 30987847, 26838171, 12059806, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.4680.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '4680.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.U', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680646
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.J', '2340.E', '2340.G', '2340.I'], 'contains': ['9360.T', '9360.U', '9360.Y', '9360.Z', '9360.BH', '379080.BB'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [4375630, 30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.4680.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.V', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680647
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2340.C', '2340.D', '2340.H'], 'contains': ['9360.Q', '9360.R', '9360.V', '9360.W', '9360.BB', '42120.J'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 12059806, 29075747, 41950063, 30987847, 6272156, 3196208, 26838171, 14615915], 'label': '12130560.c.4680.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.W', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680648
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2340.C', '2340.I'], 'contains': ['9360.T', '9360.BB', '379080.BG'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [29691520, 10464457, 29075747, 40599884, 41950063, 30987847, 6272156, 3196208, 14615915], 'label': '12130560.c.4680.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.X', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680649
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2340.F', '2340.H', '2340.I'], 'contains': ['9360.P', '9360.U', '9360.BA', '9360.BB', '42120.K'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [29691520, 10464457, 4375630, 29075747, 41950063, 30987847, 6272156, 3196208, 14615915], 'label': '12130560.c.4680.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '4680.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.Y', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680650
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '520.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1'], 'contains': ['1040.B', '1040.D', '1040.F', '1560.D', '2080.A', '4680.K'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 520, 'diagramx': None, 'generators': [14409276, 35721160, 28222666, 28817147, 28821548, 14497917, 14408363, 14850717, 19420862, 14463520, 23764951], 'label': '12130560.c.520.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '520.A', 'old_label': '520.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '520.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680651
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '4680.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1560.K', '1560.L', '2340.D', '2340.I'], 'contains': ['9360.Z', '9360.BB', '379080.BK'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 130, 'diagramx': None, 'generators': [30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 14218051, 41950063], 'label': '12130560.c.4680.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '130.a1', 'old_label': '4680.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4680.Z', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680652
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '5265.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['10530.A', '10530.C', '10530.D', '47385.a1', '84240.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 5265, 'diagramx': None, 'generators': [12662683, 37718412, 33021920, 26685532, 23596896, 26472940, 6688714, 33204274, 38421150, 16061816], 'label': '12130560.c.5265.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5265.a1', 'old_label': '5265.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5265.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680653
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '5760.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1'], 'contains': ['11520.a1', '17280.a1', '74880.K', '155520.a1'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 11520, 'diagramx': None, 'generators': [29227503, 30882930, 31086262, 4514243, 38787609, 41257047], 'label': '12130560.c.5760.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5760.a1', 'old_label': '5760.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5760.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680654
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.A', '3120.J'], 'contains': ['12480.A', '12480.L', '12480.O', '18720.D', '56160.B'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 6240, 'diagramx': None, 'generators': [10120304, 23617626, 29227503, 24298787, 30882930, 4514243, 30183917, 37911058], 'label': '12130560.c.6240.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.J', 'old_label': '6240.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680655
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.K'], 'contains': ['12480.B', '12480.M', '12480.P', '56160.A', '56160.B'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [5313187, 28316667, 14497917, 28817147, 14463520, 28821548, 28222746, 14409276], 'label': '12130560.c.6240.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.K', 'old_label': '6240.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680656
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.B', '3120.B', '3120.D', '3120.J'], 'contains': ['12480.A', '12480.J', '18720.F', '56160.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [14409276, 29022779, 28817147, 4401128, 28821548, 14463600, 14790979, 14676671], 'label': '12130560.c.6240.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680657
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.C', '3120.E', '3120.K'], 'contains': ['12480.B', '12480.K', '56160.C', '56160.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [9832222, 28316667, 14463600, 14497917, 28817147, 28821548, 28222746, 14409276], 'label': '12130560.c.6240.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.b2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680658
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.E', '3120.F', '3120.H', '3120.J'], 'contains': ['12480.G', '12480.J', '12480.L', '18720.C', '56160.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [29227503, 24298787, 30882930, 7265832, 31086262, 4514243, 27975829, 37911058], 'label': '12130560.c.6240.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.E', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680659
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.G', '3120.I', '3120.K'], 'contains': ['12480.H', '12480.K', '12480.M', '56160.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [14409276, 35721160, 28222666, 28817147, 28821548, 14497917, 14408363, 19420862], 'label': '12130560.c.6240.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.c2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.F', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680660
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.F', '2080.A', '3120.J'], 'contains': ['12480.A', '12480.E', '12480.F', '12480.G', '12480.O', '18720.G', '18720.H'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 6240, 'diagramx': None, 'generators': [14409276, 35721160, 28222666, 14497917, 14849997, 14408363, 14410441, 14463520], 'label': '12130560.c.6240.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.J', 'old_label': '6240.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.G', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680661
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '520.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1', '130.a1'], 'contains': ['1040.A', '1040.C', '1040.E', '1560.C', '1560.F', '2080.A', '4680.K'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1040, 'diagramx': None, 'generators': [24298787, 5744874, 29227503, 20767024, 4514243, 7265832, 37911058, 27975829, 30801585, 30882930, 31086262], 'label': '12130560.c.520.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '520.B', 'old_label': '520.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '520.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680662
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2080.A', '3120.K'], 'contains': ['12480.B', '12480.D', '12480.H', '12480.P', '18720.H'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [14409276, 35721160, 28222666, 28817147, 28821548, 14497917, 14408363, 14463520], 'label': '12130560.c.6240.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.K', 'old_label': '6240.d2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.H', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680663
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.N'], 'contains': ['12480.I', '18720.O', '18720.Q', '24960.J', '168480.J'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [4375630, 40218391, 29075747, 14356646, 41950063, 6272156, 1608369, 14615915], 'label': '12130560.c.6240.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.N', 'old_label': '6240.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.I', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680664
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.N'], 'contains': ['12480.I', '18720.M', '18720.N', '18720.P', '24960.K', '168480.K'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [40218391, 29075747, 4346324, 14356646, 41950063, 6272156, 1608369, 14615915], 'label': '12130560.c.6240.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.N', 'old_label': '6240.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.J', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680665
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1560.K', '3120.N'], 'contains': ['12480.I', '18720.R', '18720.T', '24960.N', '168480.T'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [13363104, 29075747, 14356646, 41950063, 30987847, 6272156, 1610305, 14615915], 'label': '12130560.c.6240.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.N', 'old_label': '6240.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.K', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680666
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.K', '2080.B', '3120.P'], 'contains': ['18720.BC', '24960.N', '56160.U'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2080, 'diagramx': None, 'generators': [25816757, 40447218, 31293946, 4514243, 33839636, 27792121, 17621843, 38119169], 'label': '12130560.c.6240.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1040.E', 'old_label': '6240.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.L', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680667
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.H', '3120.B', '3120.H', '3120.Q'], 'contains': ['12480.J', '12480.L', '18720.X', '56160.V'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [23617626, 29227503, 24298787, 30882930, 30801585, 4514243, 27975829, 37911058], 'label': '12130560.c.6240.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.M', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680668
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.C', '3120.I', '3120.R'], 'contains': ['12480.K', '12480.M', '56160.R', '56160.V'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [14409276, 28817147, 28821548, 28316667, 14497917, 28222746, 19420862, 23764951], 'label': '12130560.c.6240.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.i2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.N', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680669
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.I', '3120.D', '3120.F', '3120.Q'], 'contains': ['12480.J', '18720.Z', '56160.W'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [23617626, 29227503, 24298787, 30882930, 4514243, 31664856, 37911058, 17967176], 'label': '12130560.c.6240.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.O', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680670
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.E', '3120.G', '3120.R'], 'contains': ['12480.K', '56160.W'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [9832222, 28316667, 14497917, 28817147, 28821548, 28222746, 38564206, 14409276], 'label': '12130560.c.6240.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.j2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.P', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680671
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.G', '3120.B', '3120.F', '3120.S'], 'contains': ['12480.J', '18720.BB', '56160.X'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [19068860, 14409276, 29022779, 28817147, 4401128, 28821548, 14790979, 14676671], 'label': '12130560.c.6240.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.Q', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680672
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '520.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['260.A', '260.B'], 'contains': ['1560.K', '1560.L', '2080.B', '42120.H'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 130, 'diagramx': None, 'generators': [15477724, 30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 14218051, 26325238, 41950063], 'label': '12130560.c.520.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '130.a1', 'old_label': '520.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '520.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680673
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.C', '3120.G', '3120.T'], 'contains': ['12480.K', '56160.P', '56160.S', '56160.T', '56160.X'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [9832222, 28316667, 19548957, 14497917, 28817147, 28821548, 28222746, 14409276], 'label': '12130560.c.6240.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.k2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.R', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680674
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.L', '2080.B', '3120.D', '3120.H', '3120.S'], 'contains': ['12480.J', '18720.BC', '56160.Y'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1040, 'diagramx': None, 'generators': [23617626, 29227503, 24298787, 30882930, 29313514, 4514243, 27975829, 37911058], 'label': '12130560.c.6240.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '520.B', 'old_label': '6240.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.S', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680675
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2080.C', '3120.E', '3120.I', '3120.T'], 'contains': ['12480.K', '56160.Q', '56160.Y'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 520, 'diagramx': None, 'generators': [14409276, 28817147, 28821548, 28316667, 14497917, 28222746, 40621249, 19420862], 'label': '12130560.c.6240.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '520.A', 'old_label': '6240.l2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.T', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680676
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2080.B', '3120.A', '3120.L', '3120.M', '3120.O', '3120.U'], 'contains': ['18720.BC', '24960.O', '56160.Z'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 260, 'diagramx': None, 'generators': [14408529, 29166134, 28962689, 14790979, 2239764, 14410441, 18867497, 14819712], 'label': '12130560.c.6240.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '130.a1', 'old_label': '6240.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.U', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680677
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1560.J', '3120.J', '3120.Q', '3120.S'], 'contains': ['12480.J', '12480.O', '18720.BE', '56160.BB'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [10120304, 23617626, 29227503, 24298787, 30882930, 4514243, 31664856, 37911058], 'label': '12130560.c.6240.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.C', 'old_label': '6240.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.V', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680678
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6240.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.K', '3120.R', '3120.T'], 'contains': ['12480.K', '12480.P', '56160.BA', '56160.BB'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [9832222, 28316667, 14497917, 28817147, 14463520, 28821548, 28222746, 14409276], 'label': '12130560.c.6240.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1560.D', 'old_label': '6240.n2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6240.W', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680679
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '6318.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1'], 'contains': ['12636.a1', '31590.B', '37908.a1', '63180.L', '101088.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 6318, 'diagramx': None, 'generators': [21559533, 5951609, 16593017, 10921414, 21321187, 25470215], 'label': '12130560.c.6318.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6318.a1', 'old_label': '6318.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6318.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680680
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8320.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4160.A', '4160.B', '4160.D'], 'contains': ['16640.a1', '24960.B', '24960.D', '24960.E', '24960.F'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4160, 'diagramx': None, 'generators': [14409276, 35721160, 28817147, 28821548, 14497917, 28222746, 14850717], 'label': '12130560.c.8320.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2080.A', 'old_label': '8320.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8320.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680681
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8320.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4160.A', '4160.C', '4160.D'], 'contains': ['16640.a1', '24960.A', '24960.B', '24960.C', '24960.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4160, 'diagramx': None, 'generators': [14463600, 14497917, 28817147, 14850717, 28821548, 28222746, 14409276], 'label': '12130560.c.8320.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2080.A', 'old_label': '8320.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8320.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680682
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8320.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2080.B', '4160.A', '4160.E'], 'contains': ['16640.a1', '24960.L', '24960.N', '24960.O'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2080, 'diagramx': None, 'generators': [14409276, 28817147, 28821548, 14497917, 28222746, 14850717, 14463520], 'label': '12130560.c.8320.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2080.A', 'old_label': '8320.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8320.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680683
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '780.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['390.a1'], 'contains': ['1560.B', '1560.G', '1560.H', '2340.B', '3120.B', '63180.A'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [30888252, 6272156, 30987847, 40599884, 26838171, 29075747, 29691520, 14615915, 26325238, 17616772, 41950063], 'label': '12130560.c.780.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '780.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '780.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680684
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8320.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2080.C', '4160.B', '4160.C', '4160.E'], 'contains': ['16640.a1', '24960.K', '24960.M', '24960.P'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2080, 'diagramx': None, 'generators': [28316667, 14497917, 28817147, 14850717, 28821548, 28222746, 14409276], 'label': '12130560.c.8320.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2080.A', 'old_label': '8320.b2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8320.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680685
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8320.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4160.D', '4160.E'], 'contains': ['16640.a1', '24960.H', '24960.I', '24960.J', '24960.L', '24960.M'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2080, 'diagramx': None, 'generators': [14497917, 28817147, 14850717, 28821548, 28222746, 35666003, 14409276], 'label': '12130560.c.8320.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2080.A', 'old_label': '8320.b3', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8320.E', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680686
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8424.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['16848.A', '16848.B', '16848.E', '84240.H', '303264.E', '379080.K'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 8424, 'diagramx': None, 'generators': [5532418, 37851545, 2320358], 'label': '12130560.c.8424.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8424.A', 'old_label': '8424.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8424.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680687
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8424.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4212.A'], 'contains': ['16848.C', '84240.L', '303264.E', '379080.Z'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4212, 'diagramx': None, 'generators': [38682841, 35647396, 31719688], 'label': '12130560.c.8424.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4212.A', 'old_label': '8424.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8424.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680688
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8424.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3032640.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4212.A', '4212.B', '4212.C'], 'contains': ['16848.C', '50544.A', '84240.M', '126360.N'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2106, 'diagramx': None, 'generators': [1908526, 38682841, 5025723, 10043591], 'label': '12130560.c.8424.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2106.a1', 'old_label': '8424.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8424.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680689
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '8424.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1', '4212.C'], 'contains': ['16848.C', '16848.D', '50544.B', '50544.C', '84240.U', '126360.Q', '126360.U'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4212, 'diagramx': None, 'generators': [38682841, 11248870, 37550390], 'label': '12130560.c.8424.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4212.C', 'old_label': '8424.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8424.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680690
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.A', '4680.G', '4680.I'], 'contains': ['18720.A', '18720.C', '18720.K', '18720.S', '18720.X', '758160.A'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [29075747, 37809929, 41950063, 30987847, 6272156, 17616772, 26838171, 14615915], 'label': '12130560.c.9360.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680691
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.F', '4680.A', '4680.D', '4680.J'], 'contains': ['18720.C', '18720.Z', '18720.BB', '84240.B'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [18161601, 38119169, 15715498, 4514243, 31293946, 7265832, 40447218, 14611622], 'label': '12130560.c.9360.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680692
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.B', '4680.D', '4680.I'], 'contains': ['18720.C', '18720.BA', '18720.BB', '758160.C'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [29691520, 17396060, 29075747, 40599884, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680693
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.A', '3120.H', '4680.B', '4680.G', '4680.J'], 'contains': ['18720.C', '18720.X', '18720.BC', '84240.C'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1560, 'diagramx': None, 'generators': [40447218, 14611622, 31293946, 30801585, 7265832, 4514243, 27792121, 38119169], 'label': '12130560.c.9360.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '780.E', 'old_label': '9360.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680694
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '780.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['260.A', '390.a1'], 'contains': ['1560.B', '1560.I', '1560.L', '2340.D', '3120.D', '63180.B'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [22749994, 15477724, 30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 14218051, 41950063], 'label': '12130560.c.780.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '780.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '780.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680695
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.A', '4680.B', '4680.L'], 'contains': ['18720.C', '18720.D', '18720.Y', '18720.BD', '18720.BE', '758160.E'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [29691520, 4375630, 30757616, 29075747, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.E', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680696
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1040.A', '1040.B', '4680.K'], 'contains': ['18720.V', '28080.A', '28080.F', '37440.H', '84240.A'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 9360, 'diagramx': None, 'generators': [16856141, 14409276, 28817147, 28821548, 14408363, 21317906, 14850717, 19420862], 'label': '12130560.c.9360.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.K', 'old_label': '9360.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.F', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680697
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.C', '4680.D', '4680.E', '4680.F', '4680.G', '4680.H', '4680.L'], 'contains': ['18720.A', '18720.C', '18720.F', '18720.J', '18720.Y', '758160.F'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 29075747, 41950063, 30987847, 6272156, 17616772, 26838171, 14615915], 'label': '12130560.c.9360.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.G', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680698
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4680.L'], 'contains': ['18720.A', '18720.D', '18720.G', '18720.L', '18720.BD', '84240.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [4375630, 40218391, 29075747, 41950063, 30987847, 6272156, 17616772, 14615915], 'label': '12130560.c.9360.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.L', 'old_label': '9360.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.H', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680699
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.F', '4680.H', '4680.I'], 'contains': ['18720.F', '18720.S', '18720.BA', '758160.H'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 29075747, 41950063, 14222094, 30987847, 6272156, 17616772, 14615915], 'label': '12130560.c.9360.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.I', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680700
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1040.C', '1040.D', '4680.K'], 'contains': ['18720.V', '28080.D', '28080.G', '37440.E', '84240.E'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 9360, 'diagramx': None, 'generators': [14409276, 28220505, 28842987, 40620502, 35719719, 14847837, 14493516, 19420862], 'label': '12130560.c.9360.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.K', 'old_label': '9360.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.J', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680701
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.B', '4680.E', '4680.I', '4680.J'], 'contains': ['18720.F', '18720.X', '18720.BB', '84240.F'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [20767024, 40447218, 31293946, 30801585, 4514243, 33839636, 27971536, 38119169], 'label': '12130560.c.9360.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.K', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680702
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.D', '3120.L', '4680.F', '4680.J'], 'contains': ['18720.F', '18720.Z', '18720.BC', '84240.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [14408529, 29166134, 14790979, 2239764, 14410441, 14463253, 18867497, 14819712], 'label': '12130560.c.9360.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '9360.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.L', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680703
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1'], 'contains': ['18720.B', '18720.E', '18720.W', '28080.H', '37440.I', '252720.F'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 18720, 'diagramx': None, 'generators': [14409276, 12104840, 12043595, 28817147, 2595720, 28821548, 14408363, 21317906], 'label': '12130560.c.9360.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9360.M', 'old_label': '9360.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.M', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680704
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.J', '4680.I', '4680.J', '4680.L'], 'contains': ['18720.C', '18720.D', '18720.F', '18720.G', '18720.BE', '84240.I'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [14408529, 2240751, 14819712, 14410441, 14463520, 28817627, 29167121, 14790979], 'label': '12130560.c.9360.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.N', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680705
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '780.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['390.a1'], 'contains': ['1560.E', '1560.G', '1560.I', '2340.A', '3120.F', '63180.C'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [30888252, 6272156, 30987847, 40599884, 26838171, 12059806, 29075747, 29691520, 14615915, 26325238, 41950063], 'label': '12130560.c.780.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '780.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '780.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680706
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4680.M'], 'contains': ['18720.I', '18720.K', '84240.K', '84240.L'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [8345389, 40218391, 29075747, 24914595, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.M', 'old_label': '9360.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.O', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680707
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4680.C', '4680.M', '4680.N', '4680.S', '4680.Y'], 'contains': ['18720.I', '18720.J', '84240.M'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [29691520, 10464457, 29075747, 41950063, 30987847, 6272156, 42001605, 14615915], 'label': '12130560.c.9360.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.P', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680708
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.E', '4680.G', '4680.M', '4680.O', '4680.Q', '4680.T', '4680.W'], 'contains': ['18720.J', '18720.K', '18720.X', '18720.Y', '84240.N'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [6272156, 30987847, 26838171, 7701714, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.9360.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.Q', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680709
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.D', '4680.F', '4680.N', '4680.P', '4680.Q', '4680.U', '4680.W'], 'contains': ['18720.J', '18720.Z', '18720.BA', '84240.O'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 12059806, 29075747, 41950063, 30987847, 6272156, 26838171, 14615915], 'label': '12130560.c.9360.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.R', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680710
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.C', '4680.H', '4680.O', '4680.P', '4680.R', '4680.T', '4680.U'], 'contains': ['18720.J', '18720.BA', '758160.R'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [6272156, 30987847, 26838171, 11247527, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.9360.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.S', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680711
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.D', '4680.E', '4680.O', '4680.P', '4680.S', '4680.V', '4680.X'], 'contains': ['18720.J', '18720.BB', '758160.S'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 10464457, 6496812, 29075747, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.t1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.T', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680712
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4680.L', '4680.Q', '4680.R', '4680.V', '4680.Y'], 'contains': ['18720.J', '18720.L', '18720.BE', '84240.P'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [29691520, 10464457, 4375630, 29075747, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.u1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.U', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680713
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.A', '4680.F', '4680.W'], 'contains': ['18720.S', '18720.Y', '18720.Z', '84240.Q'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [29691520, 12059806, 29075747, 41950063, 14222094, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.v1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.V', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680714
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.H', '4680.T', '4680.W'], 'contains': ['18720.S', '18720.Y', '18720.BA', '84240.R'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [6272156, 30987847, 7701714, 14222094, 29075747, 29691520, 14615915, 41950063], 'label': '12130560.c.9360.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.D', 'old_label': '9360.w1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.W', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680715
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1', '3120.N'], 'contains': ['18720.N', '18720.Q', '18720.R', '28080.I', '37440.T', '252720.O'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 9360, 'diagramx': None, 'generators': [4375630, 40218391, 29075747, 12945967, 6272156, 3196208, 6040010, 6390353], 'label': '12130560.c.9360.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9360.X', 'old_label': '9360.x1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.X', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680716
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '780.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['260.A', '390.a1'], 'contains': ['1560.E', '1560.H', '1560.L', '2340.D', '3120.H', '63180.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 260, 'diagramx': None, 'generators': [22749994, 30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 14218051, 26325238, 41950063], 'label': '12130560.c.780.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '130.a1', 'old_label': '780.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '780.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680717
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.A', '4680.I', '4680.V'], 'contains': ['18720.S', '18720.BB', '18720.BE', '758160.BA'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [10464457, 4375630, 29075747, 37809929, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.y1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.Y', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680718
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.M', '4680.F', '4680.G', '4680.S', '4680.T', '4680.U', '4680.V', '4680.Z'], 'contains': ['18720.J', '18720.S', '18720.BC', '758160.BC'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [29691520, 14218051, 29075747, 41950063, 30987847, 6272156, 26838171, 14615915], 'label': '12130560.c.9360.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '9360.z1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.Z', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680719
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3120.N', '4680.Y'], 'contains': ['18720.I', '18720.L', '18720.O', '18720.P', '18720.T', '28080.I', '84240.T'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [4375630, 6272156, 30987847, 40218391, 14222094, 29075747, 14615915, 41950063], 'label': '12130560.c.9360.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.Y', 'old_label': '9360.ba1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BA', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680720
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4680.H', '4680.W', '4680.X', '4680.Y', '4680.Z'], 'contains': ['18720.J', '18720.S', '18720.T', '84240.V'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 1170, 'diagramx': None, 'generators': [29691520, 29075747, 41950063, 30987847, 6272156, 3196208, 26838171, 14615915], 'label': '12130560.c.9360.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.bb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BB', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680721
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.A', '4680.B', '4680.E'], 'contains': ['18720.X', '18720.Y', '18720.BB', '758160.BK'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [29691520, 30757616, 29075747, 40599884, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.bc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BC', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680722
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.O', '4680.B', '4680.F', '4680.T'], 'contains': ['18720.Y', '18720.BA', '18720.BC', '758160.BL'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 2340, 'diagramx': None, 'generators': [22749994, 30888252, 6272156, 30987847, 26838171, 29075747, 14615915, 41950063], 'label': '12130560.c.9360.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '1170.a1', 'old_label': '9360.bd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BD', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680723
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1', '1040.F'], 'contains': ['18720.U', '28080.J', '37440.T', '84240.BA'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 9360, 'diagramx': None, 'generators': [28313787, 38765815, 14497917, 14463520, 28221999, 40621942, 14849997, 14409276], 'label': '12130560.c.9360.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9360.BE', 'old_label': '9360.be1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BE', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680724
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.Q', '4680.A', '4680.J', '4680.Q'], 'contains': ['18720.X', '18720.Z', '18720.BE', '84240.W', '84240.Y'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [10120304, 40447218, 31293946, 28115878, 4514243, 33839636, 29516936, 38119169], 'label': '12130560.c.9360.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.bf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BF', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680725
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4680.B', '4680.I', '4680.Q'], 'contains': ['18720.X', '18720.BA', '18720.BE', '84240.Z'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [29691520, 4375630, 17396060, 29075747, 41950063, 30987847, 6272156, 14615915], 'label': '12130560.c.9360.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.bg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BG', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680726
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.P', '3120.S', '3120.U', '4680.B', '4680.J', '4680.V'], 'contains': ['18720.BB', '18720.BC', '18720.BE', '84240.X'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 4680, 'diagramx': None, 'generators': [10120304, 40447218, 31293946, 4514243, 33839636, 27792121, 17621843, 38119169], 'label': '12130560.c.9360.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2340.E', 'old_label': '9360.bh1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BH', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680727
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '780.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['390.a1'], 'contains': ['1560.A', '1560.B', '1560.E', '1560.F', '1560.J', '2340.E', '3120.J', '63180.F'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 780, 'diagramx': None, 'generators': [4375630, 30888252, 6272156, 30987847, 26838171, 29075747, 29691520, 14615915, 26325238, 17616772, 41950063], 'label': '12130560.c.780.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '390.a1', 'old_label': '780.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '780.E', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680728
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '9360.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1040.E', '1040.F', '4680.K'], 'contains': ['18720.V', '28080.K', '28080.M', '28080.N', '37440.V', '84240.BA'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 9360, 'diagramx': None, 'generators': [35723400, 19425929, 14409276, 40621942, 28220505, 14849997, 14493516, 14463520], 'label': '12130560.c.9360.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4680.K', 'old_label': '9360.bi1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9360.BI', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680729
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '10530.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['130.a1', '5265.a1'], 'contains': ['21060.A', '21060.D', '31590.A', '42120.B'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 5265, 'diagramx': None, 'generators': [4375630, 7050039, 6685919, 25141264, 37522917, 34385878, 9621433, 31315917, 17616772], 'label': '12130560.c.10530.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5265.a1', 'old_label': '10530.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10530.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680730
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '10530.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['21060.B', '21060.C', '21060.G', '94770.C', '168480.D'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 10530, 'diagramx': None, 'generators': [16197216, 13877844, 29347921, 19785297, 33545073, 11755711], 'label': '12130560.c.10530.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10530.B', 'old_label': '10530.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10530.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680731
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '10530.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5265.a1'], 'contains': ['21060.D', '94770.E', '168480.BJ'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 5265, 'diagramx': None, 'generators': [33191152, 22367179, 17111576, 33021920, 21875752, 23218198, 29347841, 35447982, 27255934], 'label': '12130560.c.10530.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5265.a1', 'old_label': '10530.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10530.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680732
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '10530.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6065280.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['234.a1', '5265.a1'], 'contains': ['21060.D', '21060.E', '31590.B', '168480.L'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 5265, 'diagramx': None, 'generators': [22367179, 17111576, 33021920, 21875752, 23218198, 29347841, 35447982, 27255934, 33204274], 'label': '12130560.c.10530.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5265.a1', 'old_label': '10530.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10530.D', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680733
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '11520.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.a1', '5760.a1'], 'contains': ['34560.a1', '149760.J', '311040.a1'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 11520, 'diagramx': None, 'generators': [38351050, 28817147, 28821548, 38471231, 14409276], 'label': '12130560.c.11520.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5760.a1', 'old_label': '11520.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11520.a1', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680734
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '12480.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3120.A', '4160.A', '6240.A', '6240.C', '6240.G'], 'contains': ['24960.B', '24960.O', '37440.B', '37440.G'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 6240, 'diagramx': None, 'generators': [14408363, 14497917, 14410441, 14463520, 28222666, 14849997, 14409276], 'label': '12130560.c.12480.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.J', 'old_label': '12480.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12480.A', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680735
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '12480.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4043520.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4160.C', '6240.B', '6240.D', '6240.H'], 'contains': ['24960.C', '24960.P', '37440.A', '37440.C'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 3120, 'diagramx': None, 'generators': [28316667, 14463600, 14497917, 28817147, 28821548, 28222746, 14409276], 'label': '12130560.c.12480.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3120.K', 'old_label': '12480.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12480.B', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680736
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '12480.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4160.D'], 'contains': ['24960.A', '24960.D', '24960.I', '37440.D', '37440.H', '37440.I'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 24960, 'diagramx': None, 'generators': [14463600, 14497917, 14410441, 14850717, 35721160, 28222746, 14409276], 'label': '12130560.c.12480.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12480.C', 'old_label': '12480.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12480.C', 'subgroup_fusion': None, 'weyl_group': None}
id: 262680737
{'ambient': '12130560.c', 'aut_centralizer_order': None, 'aut_label': '12480.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12130560.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4160.A', '4160.D', '6240.H'], 'contains': ['24960.C', '24960.E', '24960.L', '37440.B', '37440.E', '37440.H', '37440.J'], 'core': '12130560.a1', 'coset_action_label': None, 'count': 12480, 'diagramx': None, 'generators': [14409276, 28222666, 28817147, 28821548, 14497917, 14408363, 14463520], 'label': '12130560.c.12480.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6240.H', 'old_label': '12480.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12480.D', 'subgroup_fusion': None, 'weyl_group': None}

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.