LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [6, 8], 'aut_gens': [[3938632625685295871943746791959711692177342846391569385563424687439219660033259498372983731343195785497578337558334344355, 5512661209498819967020280990014347681011400779742950735797833264947559131608145782689824052719088350943896887434650941636], [4546827718076786023655309830207872385692149554473375856732050145234214376831883042529265429873627070660882339718929858121, 3559041876905299444537647595027790458300888637494333199111682568957611471079791330646624059617719462449592486946480376470], [179434987654430445210000456310829771807909831560978592961204264964477555123081012567433866574151657732098666864394037488, 1682514694102698159110427440087637326392034045189880765895422001826171333057070931378083979672399706102127499895234226879]], 'aut_group': '311040.j', 'aut_hash': 6830784901558741135, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 311040, 'aut_permdeg': 1080, 'aut_perms': [6858419221350180430375030102193455096682801002475324924473254081389271698476518494911021095886949578229979688584772875746522224312303006980231777792905035334960360929128284031501295516213482514643413940097548238563549120761507661386386603964257359834345552247528169831574490027219295379265634124800514244745427205372412177264766373267320177231614140546704215654425404530212243926397779106067695467779354726150731182610458338968006790804359852776235785325708614435601684085557936756293323302001158536011413148646876816568309614487904519340120531865056429574640906226394581024664573636029134920443172802829041476749778489634821246491818366443291841542214454613472057415539463603232214627170701756390685585518407602641752995192059991186232398263248180767269940509652481000266714916107850819571025500182173825130751389551503849517754042024492842010605320268631117425886909806750378679652828461135407551989796876706499898872550673026595336606275244479119335143701371110435229262760465341357477343646672525661930237841083722086186248761500610763399487399026436531379162404696263446922825906963647405711190834504547094053246810045418845120399066903497956471333333273067961458613393885497601483818293702873887698037054500975665981049664599406172133377199496946285791034376098128236032288883646798299521891525970594446445834701498182988711262510430759683878921041647059915123414561954391161770903605164910360818329632870935662071148642034093850082841393221664113077734558846552226955951856196315194277227211330654117867151152112858133397204131077688005926247400133128107168997688531753767905119257047048406453340887167270032165059228282876673676009920699746170555294119874023752824793690542282887168745004839009873748136248340583388088813966805092461013443189056764058091799224462882666329061163114658413166733111874998680296228996730411202176911764208728389187837801959808414948725011898073717123455395659694819011093912500432996491553035229103469249995520429893432409739693466060919926046190109887577558316891018001058753564478381608527905832544161885592000588959874105438891573073149062800649175973545963093582311949531914199932465993654913246707462204421260928127064343224019309941795968130178833731994988193191943339715929632304636979697599595043547314051627774472830878188110481175674611215896342576185873031423762917252052021797106642741639279511753386957549640562167098735246405171193233653170055315000132327564507615514655379344149789337780836929748949852685944537048201606519967713098457554467395113756048964000457563310464443508751549558904856695419112473490641660472832976631751468497147493744646839331449614160943867698365843367239160945918171601588701697830156604552027035943489071540935445124136441526411125869244108647695137399284672522792484276391434679754626770248432465286656495881463099323868809579, 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'aut_phi_ratio': 3.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [2, 90, 1, 1], [2, 1080, 1, 1], [3, 80, 1, 1], [3, 720, 1, 1], [3, 5760, 1, 1], [4, 540, 1, 1], [4, 1620, 1, 1], [4, 3240, 1, 1], [4, 4860, 1, 1], [4, 9720, 1, 1], [5, 31104, 1, 1], [6, 720, 1, 1], [6, 6480, 1, 1], [6, 8640, 1, 2], [6, 17280, 1, 1], [8, 1620, 1, 2], [8, 6480, 1, 2], [8, 9720, 1, 1], [8, 19440, 1, 1], [8, 38880, 1, 1], [10, 31104, 1, 1], [12, 4320, 1, 1], [12, 12960, 1, 1], [12, 25920, 1, 1], [24, 12960, 1, 4]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:S_3.C_2^4:S_5', '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': 120, 'autcentquo_group': '311040.j', 'autcentquo_hash': 6830784901558741135, 'autcentquo_nilpotent': False, 'autcentquo_order': 311040, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:S_3.C_2^4:S_5', 'cc_stats': [[1, 1, 1], [2, 81, 1], [2, 90, 1], [2, 1080, 1], [3, 80, 1], [3, 720, 1], [3, 5760, 1], [4, 540, 1], [4, 1620, 1], [4, 3240, 1], [4, 4860, 1], [4, 9720, 1], [5, 31104, 1], [6, 720, 1], [6, 6480, 1], [6, 8640, 2], [6, 17280, 1], [8, 1620, 2], [8, 6480, 2], [8, 9720, 1], [8, 19440, 1], [8, 38880, 1], [10, 31104, 1], [12, 4320, 1], [12, 12960, 1], [12, 25920, 1], [24, 12960, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '311040.j', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '60.5'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [2, 90, 1, 1], [2, 1080, 1, 1], [3, 80, 1, 1], [3, 720, 1, 1], [3, 5760, 1, 1], [4, 540, 1, 1], [4, 1620, 1, 1], [4, 3240, 1, 1], [4, 4860, 1, 1], [4, 9720, 1, 1], [5, 31104, 1, 1], [6, 720, 1, 1], [6, 6480, 1, 1], [6, 8640, 1, 2], [6, 17280, 1, 1], [8, 1620, 2, 1], [8, 6480, 2, 1], [8, 9720, 1, 1], [8, 19440, 1, 1], [8, 38880, 1, 1], [10, 31104, 1, 1], [12, 4320, 1, 1], [12, 12960, 1, 1], [12, 25920, 1, 1], [24, 12960, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 136800, 'exponent': 120, 'exponents_of_order': [8, 5, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[80, 1, 2], [160, 0, 2], [160, 1, 1], [240, 1, 2], [320, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '311040.j', 'hash': 6830784901558741135, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 120, 'inner_gen_orders': [6, 8], 'inner_gens': [[3938632625685295871943746791959711692177342846391569385563424687439219660033259498372983731343195785497578337558334344355, 1204688212998658619000334793945242109098409003317537044283164954829151548204437370340377386909595854753169830364257962917], [1369703252167805278818951658925534974015989240540526343408472167481828725179465657638062489175226389158015207098897864557, 5512661209498819967020280990014347681011400779742950735797833264947559131608145782689824052719088350943896887434650941636]], 'inner_hash': 6830784901558741135, 'inner_nilpotent': False, 'inner_order': 311040, 'inner_split': True, 'inner_tex': 'C_3^3:S_3.C_2^4:S_5', 'inner_used': [1, 2], 'irrC_degree': 80, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 80, 'irrep_stats': [[1, 2], [4, 4], [5, 4], [6, 1], [10, 5], [15, 2], [16, 2], [20, 4], [24, 1], [80, 2], [160, 3], [240, 2], [320, 1]], 'label': '311040.j', 'linC_count': 2, 'linC_degree': 80, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 80, 'linQ_degree_count': 2, 'linQ_dim': 80, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 80, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C3^3:S3.C2^4:S5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 33, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 33, 'number_divisions': 29, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 789, 'number_subgroup_classes': 789, 'number_subgroups': 1048248, 'old_label': None, 'order': 311040, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1251], [3, 6560], [4, 19980], [5, 31104], [6, 41760], [8, 84240], [10, 31104], [12, 43200], [24, 51840]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 81, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [5, 4], [6, 1], [8, 1], [10, 5], [15, 2], [20, 2], [24, 1], [32, 1], [40, 1], [80, 2], [160, 1], [240, 2], [320, 2]], 'representations': {'Perm': {'d': 81, 'gens': [3938632625685295871943746791959711692177342846391569385563424687439219660033259498372983731343195785497578337558334344355, 5512661209498819967020280990014347681011400779742950735797833264947559131608145782689824052719088350943896887434650941636]}}, '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': 'C_3^3:S_3.C_2^4:S_5', 'transitive_degree': 81, '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: 109705913
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 10, 'group_order': 311040, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 109705924
{'aut_label': '2A', 'centralizer': '81.a1.a1', 'counter': 2, 'group_counter': 10, 'group_order': 311040, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 72097542865538538962217160838673281972827977616579829606512882778592738790302059560351373746606977747018994389243278138, 'size': 81}
id: 109705935
{'aut_label': '2B', 'centralizer': '90.a1.a1', 'counter': 3, 'group_counter': 10, 'group_order': 311040, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 5775678086178319270018706841121549400597865880532689834515397344021776742752760895496622846828504689005999981828490416, 'size': 90}
id: 109705940
{'aut_label': '2C', 'centralizer': '1080.p1.a1', 'counter': 4, 'group_counter': 10, 'group_order': 311040, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 1628501491797908099940528110470249198709047439279578751555069164889603920114581516607541254172793100955567205951190580598, 'size': 1080}
id: 109705941
{'aut_label': '3A', 'centralizer': '80.s2.a1', 'counter': 5, 'group_counter': 10, 'group_order': 311040, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 5711485100285017638127433548403233505416679300438727842954738211427977521081717984664679066141204935057505624374295927660, 'size': 80}
id: 109705942
{'aut_label': '3B', 'centralizer': '720.f1.a1', 'counter': 6, 'group_counter': 10, 'group_order': 311040, 'label': '3B', 'order': 3, 'powers': [6, 1, 6], 'representative': 2654257678332834903927075894277902181808861181395748178172056415825166298346524337428061901242269349509059263164558947478, 'size': 720}
id: 109705943
{'aut_label': '3C', 'centralizer': '5760.f1.a1', 'counter': 7, 'group_counter': 10, 'group_order': 311040, 'label': '3C', 'order': 3, 'powers': [7, 1, 7], 'representative': 1832838254385236242806938849954268373513729855190705794816368464341865886405083895287291101784991932333505942741266655621, 'size': 5760}
id: 109705944
{'aut_label': '4A', 'centralizer': '540.f1.a1', 'counter': 8, 'group_counter': 10, 'group_order': 311040, 'label': '4A', 'order': 4, 'powers': [3, 8, 8], 'representative': 49591734020228763269098919453979083125334031700147040255364167321749706688955796567059219101127189925053446971107833147, 'size': 540}
id: 109705945
{'aut_label': '4B', 'centralizer': '1620.b1.a1', 'counter': 9, 'group_counter': 10, 'group_order': 311040, 'label': '4B', 'order': 4, 'powers': [2, 9, 9], 'representative': 5315886303384442636409826949215241803686714137454899300167038498974811564981709786636214125887591302550622690439260240728, 'size': 1620}
id: 109705914
{'aut_label': '4C', 'centralizer': '3240.n1.a1', 'counter': 10, 'group_counter': 10, 'group_order': 311040, 'label': '4C', 'order': 4, 'powers': [2, 10, 10], 'representative': 260934322450205509057102279555351754217445120092933669917341757806271555593851023300328250618851220895688688611043200618, 'size': 3240}
id: 109705915
{'aut_label': '4D', 'centralizer': '4860.j1.a1', 'counter': 11, 'group_counter': 10, 'group_order': 311040, 'label': '4D', 'order': 4, 'powers': [3, 11, 11], 'representative': 1324175273097538656177490263643041799367709716608579914932775968525124925870237483149694201541661005681420349981375378609, 'size': 4860}
id: 109705916
{'aut_label': '4E', 'centralizer': '9720.b1.a1', 'counter': 12, 'group_counter': 10, 'group_order': 311040, 'label': '4E', 'order': 4, 'powers': [2, 12, 12], 'representative': 1950340859286728541283548267700071294990890646070828408488562758570872172241319932382502676424871685487883664871389052963, 'size': 9720}
id: 109705917
{'aut_label': '5A', 'centralizer': '31104.a1.a1', 'counter': 13, 'group_counter': 10, 'group_order': 311040, 'label': '5A', 'order': 5, 'powers': [13, 13, 1], 'representative': 1080454360695056523057505076436660793903249435138812104256800601187890237487026943297507537735150709641252769592943214004, 'size': 31104}
id: 109705918
{'aut_label': '6A', 'centralizer': '720.r2.a1', 'counter': 14, 'group_counter': 10, 'group_order': 311040, 'label': '6A', 'order': 6, 'powers': [5, 3, 14], 'representative': 2058458018137558986435459819552790483875629939745277785049613888377258117401199855862609203314650558700566330527335302998, 'size': 720}
id: 109705919
{'aut_label': '6B', 'centralizer': '6480.e1.a1', 'counter': 15, 'group_counter': 10, 'group_order': 311040, 'label': '6B', 'order': 6, 'powers': [6, 2, 15], 'representative': 1888809482700779814671767851418855938641881679161029013680183798861710328001866557627092053435106798436672175863802168467, 'size': 6480}
id: 109705920
{'aut_label': '6C', 'centralizer': '8640.a1.a1', 'counter': 16, 'group_counter': 10, 'group_order': 311040, 'label': '6C', 'order': 6, 'powers': [6, 3, 16], 'representative': 1228420931930001613123340189942881641587987800781336025748467891632524285551722883590344302029367409937636203900191957290, 'size': 8640}
id: 109705921
{'aut_label': '6D', 'centralizer': '8640.p1.a1', 'counter': 17, 'group_counter': 10, 'group_order': 311040, 'label': '6D', 'order': 6, 'powers': [5, 4, 17], 'representative': 2255208224660141470139915162416178189235887160040543495059092137087719484188215222510419696463652992661833596715470171958, 'size': 8640}
id: 109705922
{'aut_label': '6E', 'centralizer': '17280.d1.a1', 'counter': 18, 'group_counter': 10, 'group_order': 311040, 'label': '6E', 'order': 6, 'powers': [7, 3, 18], 'representative': 2192506025827341977074096806023208954571332277168295186587587854631053018800236563791002151333064745880948901787233178765, 'size': 17280}
id: 109705923
{'aut_label': '8A1', 'centralizer': '1620.b1.a1', 'counter': 19, 'group_counter': 10, 'group_order': 311040, 'label': '8A1', 'order': 8, 'powers': [9, 19, 20], 'representative': 1262029242919231444837747136953932463694943101216600412321610267627012756432604460069626912991297009849181263126677626913, 'size': 1620}
id: 109705925
{'aut_label': '8A-1', 'centralizer': '1620.b1.a1', 'counter': 20, 'group_counter': 10, 'group_order': 311040, 'label': '8A-1', 'order': 8, 'powers': [9, 20, 19], 'representative': 3570289682204784861819660987147030673482593524860039655675951808373252275224252219272693662305100983897966102306941730937, 'size': 1620}
id: 109705926
{'aut_label': '8B1', 'centralizer': '6480.t1.a1', 'counter': 21, 'group_counter': 10, 'group_order': 311040, 'label': '8B1', 'order': 8, 'powers': [8, 21, 22], 'representative': 3907773184760321191190330627376132648269307043868622245732185267440082234638599034632338281550925486560952676961288661902, 'size': 6480}
id: 109705927
{'aut_label': '8B-1', 'centralizer': '6480.t1.a1', 'counter': 22, 'group_counter': 10, 'group_order': 311040, 'label': '8B-1', 'order': 8, 'powers': [8, 22, 21], 'representative': 3910020040876867316566518976468561697993751164036692393815698973629923955462063470982578169906978464239186599594421306034, 'size': 6480}
id: 109705928
{'aut_label': '8C', 'centralizer': '9720.o1.a1', 'counter': 23, 'group_counter': 10, 'group_order': 311040, 'label': '8C', 'order': 8, 'powers': [9, 23, 23], 'representative': 4998141902441428550546886133462910136328697904499575968037073738295526932935620400746384482077303504983563312070741014191, 'size': 9720}
id: 109705929
{'aut_label': '8D', 'centralizer': '19440.w1.a1', 'counter': 24, 'group_counter': 10, 'group_order': 311040, 'label': '8D', 'order': 8, 'powers': [9, 24, 24], 'representative': 3963921160341977175521391332606538965009858774073136098684928768313992571525034964566113807097240483605673230754244988024, 'size': 19440}
id: 109705930
{'aut_label': '8E', 'centralizer': '38880.r1.a1', 'counter': 25, 'group_counter': 10, 'group_order': 311040, 'label': '8E', 'order': 8, 'powers': [12, 25, 25], 'representative': 3177305056307682322937153345412606266560379770835086143114266931830153969508156235338633700167351014762019937870847819386, 'size': 38880}
id: 109705931
{'aut_label': '10A', 'centralizer': '31104.a1.a1', 'counter': 26, 'group_counter': 10, 'group_order': 311040, 'label': '10A', 'order': 10, 'powers': [13, 26, 2], 'representative': 336633159125138758543859346162358484351311273151128518803585153909782281192506344590199657323187302931187707975355937106, 'size': 31104}
id: 109705932
{'aut_label': '12A', 'centralizer': '4320.bb1.a1', 'counter': 27, 'group_counter': 10, 'group_order': 311040, 'label': '12A', 'order': 12, 'powers': [14, 8, 27], 'representative': 5722338234416121211331797706085955237708231560000162687934654346856693335204520060487043895203475778307470858286917239355, 'size': 4320}
id: 109705933
{'aut_label': '12B', 'centralizer': '12960.i1.a1', 'counter': 28, 'group_counter': 10, 'group_order': 311040, 'label': '12B', 'order': 12, 'powers': [15, 9, 28], 'representative': 5557684313862312695197900788073594325189276733000695345556568917246065288271572978848890921969019743042253429818443711927, 'size': 12960}
id: 109705934
{'aut_label': '12C', 'centralizer': '25920.d1.a1', 'counter': 29, 'group_counter': 10, 'group_order': 311040, 'label': '12C', 'order': 12, 'powers': [15, 10, 29], 'representative': 1031398058613289832910520192760340050450546291917560691525869163076404224134862479400268909123108705414097003550725067621, 'size': 25920}
id: 109705936
{'aut_label': '24A1', 'centralizer': '12960.i1.a1', 'counter': 30, 'group_counter': 10, 'group_order': 311040, 'label': '24A1', 'order': 24, 'powers': [28, 19, 31], 'representative': 4443165573990080738073981595088182123038167121577270365878341287039768655833166008384338556020130712050739754365256366390, 'size': 12960}
id: 109705937
{'aut_label': '24A-1', 'centralizer': '12960.i1.a1', 'counter': 31, 'group_counter': 10, 'group_order': 311040, 'label': '24A-1', 'order': 24, 'powers': [28, 20, 30], 'representative': 4424286908377489370150195494205186634262056397309904459428261764292078871188870282157986843886768354810574472832126755740, 'size': 12960}
id: 109705938
{'aut_label': '24B1', 'centralizer': '12960.t1.a1', 'counter': 32, 'group_counter': 10, 'group_order': 311040, 'label': '24B1', 'order': 24, 'powers': [27, 21, 33], 'representative': 5299826011141582701944916695067773120956067974106177826950853959594887754053805756086394271510899323751784029696986941561, 'size': 12960}
id: 109705939
{'aut_label': '24B-1', 'centralizer': '12960.t1.a1', 'counter': 33, 'group_counter': 10, 'group_order': 311040, 'label': '24B-1', 'order': 24, 'powers': [27, 22, 32], 'representative': 1025228265334594671753912583369482070707573833793684212564059165970153577718390669314572331026197795214263199668539315729, 'size': 12960}

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: 4371601
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4371612
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.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], 'schur_index': 1}
id: 4371623
{'cdim': 4, 'counter': 3, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.4a', 'multiplicity': 1, 'nt': [5, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 2, 4, 1, 1, 0, 4, 2, 0, 0, -1, 4, 1, 1, 2, 1, 2, 2, 0, 0, 2, 0, 0, -1, 0, 1, -1, -1, -1, 0, 0], 'schur_index': 1}
id: 4371624
{'cdim': 4, 'counter': 4, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.4b', 'multiplicity': 1, 'nt': [10, 12], 'qdim': 4, 'qvalues': [4, 4, 4, -2, 4, 1, 1, 0, 4, -2, 0, 0, -1, 4, 1, 1, -2, 1, -2, -2, 0, 0, -2, 0, 0, -1, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
id: 4371626
{'cdim': 5, 'counter': 6, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.5a', 'multiplicity': 1, 'nt': [6, 14], 'qdim': 5, 'qvalues': [5, 5, 5, -1, 5, -1, -1, 1, 5, -1, 1, 1, 0, 5, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 0, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
id: 4371627
{'cdim': 5, 'counter': 7, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.5b', 'multiplicity': 1, 'nt': [10, 13], 'qdim': 5, 'qvalues': [5, 5, 5, 1, 5, -1, -1, 1, 5, 1, 1, 1, 0, 5, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 0, 1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
id: 4371628
{'cdim': 5, 'counter': 8, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.5c', 'multiplicity': 1, 'nt': [10, 37], 'qdim': 5, 'qvalues': [5, 5, -3, -1, 5, 2, 2, 1, 1, 3, 1, 1, 0, -3, 2, 0, -1, 0, -3, -3, -1, -1, 1, -1, 1, 0, 1, -2, 0, 0, 0, -1, -1], 'schur_index': 1}
id: 4371629
{'cdim': 5, 'counter': 9, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.5d', 'multiplicity': 1, 'nt': [10, 38], 'qdim': 5, 'qvalues': [5, 5, -3, 1, 5, 2, 2, 1, 1, -3, 1, 1, 0, -3, 2, 0, 1, 0, 3, 3, 1, 1, -1, -1, -1, 0, 1, -2, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 4371602
{'cdim': 6, 'counter': 10, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.6a', 'multiplicity': 1, 'nt': [20, 30], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 6, 0, 0, -2, 6, 0, -2, -2, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371625
{'cdim': 4, 'counter': 5, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.4c', 'multiplicity': 2, 'nt': [240, 0], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, -4, -4, 4, 0, 0, -4, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371603
{'cdim': 10, 'counter': 11, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.10a', 'multiplicity': 1, 'nt': [16, 1328], 'qdim': 10, 'qvalues': [10, 10, 2, 0, 10, 1, 1, -2, -2, 4, -2, 2, 0, 2, 1, -1, 0, -1, 2, 2, 0, 0, -2, 0, 0, 0, -2, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
id: 4371604
{'cdim': 10, 'counter': 12, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.10b', 'multiplicity': 1, 'nt': [20, 218], 'qdim': 10, 'qvalues': [10, 10, 2, 2, 10, 1, 1, 2, -2, -2, 2, -2, 0, 2, 1, -1, 2, -1, -4, -4, 0, 0, 0, 0, 0, 0, 2, 1, 1, -1, -1, 0, 0], 'schur_index': 1}
id: 4371605
{'cdim': 10, 'counter': 13, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.10c', 'multiplicity': 1, 'nt': [20, 222], 'qdim': 10, 'qvalues': [10, 10, 2, 0, 10, 1, 1, -2, -2, -4, -2, 2, 0, 2, 1, -1, 0, -1, -2, -2, 0, 0, 2, 0, 0, 0, -2, 1, -1, 1, 1, 0, 0], 'schur_index': 1}
id: 4371606
{'cdim': 10, 'counter': 14, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.10d', 'multiplicity': 1, 'nt': [20, 223], 'qdim': 10, 'qvalues': [10, 10, 2, -2, 10, 1, 1, 2, -2, 2, 2, -2, 0, 2, 1, -1, -2, -1, 4, 4, 0, 0, 0, 0, 0, 0, 2, 1, -1, 1, 1, 0, 0], 'schur_index': 1}
id: 4371607
{'cdim': 10, 'counter': 15, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.10e', 'multiplicity': 1, 'nt': [30, 329], 'qdim': 10, 'qvalues': [10, 10, -6, 0, 10, -2, -2, 2, 2, 0, 2, 2, 0, -6, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371608
{'cdim': 15, 'counter': 16, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.15a', 'multiplicity': 1, 'nt': [30, 332], 'qdim': 15, 'qvalues': [15, 15, -9, 1, 15, 0, 0, -1, 3, -3, -1, -1, 0, -9, 0, 0, 1, 0, 3, 3, -1, -1, -1, 1, 1, 0, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
id: 4371609
{'cdim': 15, 'counter': 17, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.15b', 'multiplicity': 1, 'nt': [30, 333], 'qdim': 15, 'qvalues': [15, 15, -9, -1, 15, 0, 0, -1, 3, 3, -1, -1, 0, -9, 0, 0, -1, 0, -3, -3, 1, 1, 1, 1, -1, 0, -1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 4371611
{'cdim': 20, 'counter': 19, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.20a', 'multiplicity': 1, 'nt': [40, 1676], 'qdim': 20, 'qvalues': [20, 20, 4, 2, 20, -1, -1, 0, -4, 2, 0, 0, 0, 4, -1, 1, 2, 1, -2, -2, 0, 0, -2, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0], 'schur_index': 1}
id: 4371613
{'cdim': 20, 'counter': 20, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.20b', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 20, 'qvalues': [20, 20, 4, -2, 20, -1, -1, 0, -4, -2, 0, 0, 0, 4, -1, 1, -2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, -1, 1, -1, -1, 0, 0], 'schur_index': 1}
id: 4371615
{'cdim': 24, 'counter': 22, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.24a', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, 24, 0, 0, -4, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 4371610
{'cdim': 16, 'counter': 18, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.16a', 'multiplicity': 2, 'nt': [240, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 32, -4, -4, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371614
{'cdim': 20, 'counter': 21, 'faithful': False, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.20c', 'multiplicity': 2, 'nt': [80, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 40, 4, 4, 4, 0, 0, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371616
{'cdim': 80, 'counter': 23, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.80a', 'multiplicity': 1, 'nt': [81, 0], 'qdim': 80, 'qvalues': [80, 0, 8, 8, -1, 8, -1, 8, 0, 0, 0, 0, 0, -1, 0, 2, -1, -1, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
id: 4371617
{'cdim': 80, 'counter': 24, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.80b', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 80, 'qvalues': [80, 0, 8, -8, -1, 8, -1, 8, 0, 0, 0, 0, 0, -1, 0, 2, 1, -1, 0, 0, -2, -2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 4371618
{'cdim': 160, 'counter': 25, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.160a', 'multiplicity': 1, 'nt': [240, 0], 'qdim': 160, 'qvalues': [160, 0, 16, 0, -2, -8, 1, 16, 0, 0, 0, 0, 0, -2, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371620
{'cdim': 240, 'counter': 27, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.240a', 'multiplicity': 1, 'nt': [360, 0], 'qdim': 240, 'qvalues': [240, 0, 24, 8, -3, 0, 0, -8, 0, 0, 0, 0, 0, -3, 0, 0, -1, 0, 0, 0, -2, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
id: 4371621
{'cdim': 240, 'counter': 28, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.240b', 'multiplicity': 1, 'nt': [486, 0], 'qdim': 240, 'qvalues': [240, 0, 24, -8, -3, 0, 0, -8, 0, 0, 0, 0, 0, -3, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
id: 4371619
{'cdim': 160, 'counter': 26, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.160b', 'multiplicity': 2, 'nt': [1920, 0], 'qdim': 320, 'qvalues': [320, 0, -32, 0, -4, -16, 2, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4371622
{'cdim': 320, 'counter': 29, 'faithful': True, 'group': '311040.j', 'group_order': 311040, 'image': None, 'label': '311040.j.320a', 'multiplicity': 1, 'nt': [720, 0], 'qdim': 320, 'qvalues': [320, 0, -32, 0, -4, 8, -1, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 6613551
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 311040, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 311040, 'label': '311040.j.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 6613562
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 311040, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 155520, 'label': '311040.j.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]]]}
id: 6613573
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 2592, 'counter': 3, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 2592, 'label': '311040.j.4a', 'nt': [5, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613578
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 2592, 'counter': 4, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 2592, 'label': '311040.j.4b', 'nt': [10, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613579
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 5, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.4c1', 'nt': [240, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 6613580
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 6, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.4c2', 'nt': [240, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
id: 6613581
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 2592, 'counter': 7, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 2592, 'label': '311040.j.5a', 'nt': [6, 14], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 6613582
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 2592, 'counter': 8, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 2592, 'label': '311040.j.5b', 'nt': [10, 13], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6613583
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 9, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.5c', 'nt': [10, 37], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6613552
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 10, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.5d', 'nt': [10, 38], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[5, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
id: 6613553
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 2592, 'counter': 11, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 2592, 'label': '311040.j.6a', 'nt': [20, 30], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6613554
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 12, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.10a', 'nt': [16, 1328], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[0, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613555
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 13, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.10b', 'nt': [20, 218], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613556
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.10c', 'nt': [20, 222], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[0, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613557
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.10d', 'nt': [20, 223], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[2, 0]], [[-2, 0]], [[10, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613558
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 16, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.10e', 'nt': [30, 329], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-6, 0]], [[0, 0]], [[10, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6613559
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.15a', 'nt': [30, 332], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-9, 0]], [[1, 0]], [[15, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6613560
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 18, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.15b', 'nt': [30, 333], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-9, 0]], [[-1, 0]], [[15, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
id: 6613561
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 19, 'cyclotomic_n': 8, 'dim': 16, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.16a1', 'nt': [240, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, 3]], [[4, 1], [4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
id: 6613563
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 20, 'cyclotomic_n': 8, 'dim': 16, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.16a2', 'nt': [240, 2], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, 3]], [[-4, 1], [-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
id: 6613564
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 21, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.20a', 'nt': [40, 1676], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[4, 0]], [[2, 0]], [[20, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613565
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 22, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '1920.240996', 'image_order': 1920, 'indicator': 1, 'kernel': '1920.a1.a1', 'kernel_order': 162, 'label': '311040.j.20b', 'nt': [60, 0], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[4, 0]], [[-2, 0]], [[20, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
id: 6613566
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 23, 'cyclotomic_n': 8, 'dim': 20, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.20c1', 'nt': [80, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
id: 6613567
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 24, 'cyclotomic_n': 8, 'dim': 20, 'faithful': False, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': 0, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.20c2', 'nt': [80, 2], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[20, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 6613568
{'center': '1920.a1.a1', 'center_index': 1920, 'center_order': 162, 'counter': 25, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '3840.cb', 'image_order': 3840, 'indicator': -1, 'kernel': '3840.a1.a1', 'kernel_order': 81, 'label': '311040.j.24a', 'nt': [240, 0], 'q_character': None, 'values': [[[24, 0]], [[-24, 0]], [[0, 0]], [[0, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 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]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6613569
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 1, 'dim': 80, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.80a', 'nt': [81, 0], 'q_character': None, 'values': [[[80, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6613570
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 1, 'dim': 80, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.80b', 'nt': [162, 0], 'q_character': None, 'values': [[[80, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
id: 6613571
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 1, 'dim': 160, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.160a', 'nt': [240, 0], 'q_character': None, 'values': [[[160, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6613572
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 8, 'dim': 160, 'faithful': True, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 0, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.160b1', 'nt': [1920, 0], 'q_character': None, 'values': [[[160, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[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]]]}
id: 6613574
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 8, 'dim': 160, 'faithful': True, 'field': [2, 0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 0, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.160b2', 'nt': [1920, 2], 'q_character': None, 'values': [[[160, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[-2, 0]], [[-8, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[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]]]}
id: 6613575
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 31, 'cyclotomic_n': 1, 'dim': 240, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.240a', 'nt': [360, 0], 'q_character': None, 'values': [[[240, 0]], [[0, 0]], [[24, 0]], [[8, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
id: 6613576
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 32, 'cyclotomic_n': 1, 'dim': 240, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.240b', 'nt': [486, 0], 'q_character': None, 'values': [[[240, 0]], [[0, 0]], [[24, 0]], [[-8, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6613577
{'center': '311040.a1.a1', 'center_index': 311040, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 1, 'dim': 320, 'faithful': True, 'field': [0, 1], 'group': '311040.j', 'group_counter': 10, 'group_order': 311040, 'image': None, 'image_isoclass': '311040.j', 'image_order': 311040, 'indicator': 1, 'kernel': '311040.a1.a1', 'kernel_order': 1, 'label': '311040.j.320a', 'nt': [720, 0], 'q_character': None, 'values': [[[320, 0]], [[0, 0]], [[-32, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[-2, 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]]]}

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 789 matching records in this table.

id: 65252676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 311040, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '311040.j.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '311040.j', 'subgroup_hash': 6830784901558741135, 'subgroup_order': 311040, 'subgroup_tex': 'C_3^3:S_3.C_2^4:S_5', 'supersolvable': False, 'sylow': 0}
id: 65252787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 155520, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '311040.j.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': ['D', 'PC', 'L1', 'D1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2020582726259263130, 'subgroup_order': 155520, 'subgroup_tex': 'C_3^4.(C_4.C_2^3).A_5', 'supersolvable': False, 'sylow': 0}
id: 65252898
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '311040.j.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, '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': '62208.f', 'subgroup_hash': 7593492863576649709, 'subgroup_order': 62208, 'subgroup_tex': 'C_3^4:(Q_8^2:D_6)', 'supersolvable': False, 'sylow': 0}
id: 65253009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': 5768392878796609176, 'subgroup_order': 51840, 'subgroup_tex': 'C_3^4.(C_4.C_2^3).F_5', 'supersolvable': False, 'sylow': 0}
id: 65253120
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, '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': '31104.n', 'subgroup_hash': 3411689032478881447, 'subgroup_order': 31104, 'subgroup_tex': 'C_3^4:(Q_8^2:S_3)', 'supersolvable': False, 'sylow': 0}
id: 65253231
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id: 65253342
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id: 65253443
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id: 65253454
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id: 65252677
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id: 65252688
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id: 65252699
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id: 65252710
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id: 65252721
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id: 65252732
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id: 65252743
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id: 65252754
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id: 65252765
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id: 65252776
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id: 65252788
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id: 65252799
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id: 65252810
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id: 65252821
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id: 65252832
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id: 65252843
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id: 65252854
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id: 65252865
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id: 65252876
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id: 65252887
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.bg', 'subgroup_hash': 6759567540276202112, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65252899
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id: 65252910
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': 4623004179282330871, 'subgroup_order': 7776, 'subgroup_tex': 'C_3:S_3.C_6^2.D_6', 'supersolvable': False, 'sylow': 0}
id: 65252921
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id: 65252932
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.cw', 'subgroup_hash': 8212187940285761847, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:(S_3\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
id: 65252943
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.iq', 'subgroup_hash': 5457175150437015127, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\SL(2,3):C_2^2', 'supersolvable': False, 'sylow': 0}
id: 65252954
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.bf', 'subgroup_hash': 995969709981747757, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65252965
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.bi', 'subgroup_hash': 6351236678012487182, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\GL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65252976
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.ir', 'subgroup_hash': 8366434118354596016, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:\\Unitary(2,3)', 'supersolvable': False, 'sylow': 0}
id: 65252987
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.40.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, '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': '7776.jj', 'subgroup_hash': 8357839951792829016, 'subgroup_order': 7776, 'subgroup_tex': 'C_3^4:C_4.S_4', 'supersolvable': False, 'sylow': 0}
id: 65252998
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id: 65253010
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id: 65253021
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id: 65253032
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id: 65253043
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id: 65253054
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id: 65253065
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id: 65253076
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id: 65253087
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id: 65253098
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id: 65253109
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id: 65253121
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id: 65253132
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id: 65253143
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id: 65253154
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id: 65253165
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id: 65253176
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id: 65253187
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id: 65253198
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id: 65253209
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id: 65253220
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id: 65253232
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id: 65253243
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id: 65253254
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id: 65253265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.bu', 'subgroup_hash': 1539483115116172293, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
id: 65253276
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.el', 'subgroup_hash': 401516246772182357, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
id: 65253287
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id: 65253298
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.bw', 'subgroup_hash': 1308481736150857399, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65253309
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id: 65253320
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id: 65253331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.bw', 'subgroup_hash': 1308481736150857399, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65253343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.ec', 'subgroup_hash': 5418293035830087959, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:F_9:C_2', 'supersolvable': False, 'sylow': 0}
id: 65253354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.eo', 'subgroup_hash': 8859155090492874013, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2:F_9:S_3', 'supersolvable': False, 'sylow': 0}
id: 65253365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.jn', 'subgroup_hash': 1482963743422120308, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 65253376
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id: 65253387
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id: 65253398
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id: 65253409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.cc', 'subgroup_hash': 2999605190666228990, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:S_3.S_4', 'supersolvable': False, 'sylow': 0}
id: 65253420
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': '3888.cc', 'subgroup_hash': 2999605190666228990, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^3:S_3.S_4', 'supersolvable': False, 'sylow': 0}
id: 65253431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': 1052391586852888505, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2.Q_8:\\He_3.C_2', 'supersolvable': False, 'sylow': 0}
id: 65253442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.80.s2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.s2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, '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': 3916766963851188757, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^2.Q_8:\\He_3.C_2', 'supersolvable': False, 'sylow': 0}
id: 65253444
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.81.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '3840.cb', 'subgroup_hash': 7674287725982229969, 'subgroup_order': 3840, 'subgroup_tex': 'C_2.C_2^4:S_5', 'supersolvable': False, 'sylow': 0}
id: 65253445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, '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': 3988179859117302679, 'subgroup_order': 3456, 'subgroup_tex': 'C_3^2.Q_8^2.S_3', 'supersolvable': False, 'sylow': 0}
id: 65253446
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '3240.cf', 'subgroup_hash': 6807394357865232183, 'subgroup_order': 3240, 'subgroup_tex': 'C_3^4:C_5:C_8', 'supersolvable': False, 'sylow': 0}
id: 65253447
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '311040.j.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_5', 'simple': False, 'solvable': True, 'special_labels': ['R', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2592.cp', 'subgroup_hash': 863601208845687898, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:C_4.C_2^3', 'supersolvable': False, 'sylow': 0}
id: 65253448
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.fv', 'subgroup_hash': 9019849488891309561, 'subgroup_order': 2592, 'subgroup_tex': 'S_3\\times C_3^2:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 65253449
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cn', 'subgroup_hash': 6670355472127088951, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:C_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
id: 65253450
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cn', 'subgroup_hash': 6670355472127088951, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:C_4\\wr C_2', 'supersolvable': False, 'sylow': 0}
id: 65253451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cq', 'subgroup_hash': 8124813633988370158, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:\\OD_{16}:C_2', 'supersolvable': False, 'sylow': 0}
id: 65253452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cs', 'subgroup_hash': 5065227438088372863, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:Q_{16}:C_2', 'supersolvable': False, 'sylow': 0}
id: 65253453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cs', 'subgroup_hash': 5065227438088372863, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:Q_{16}:C_2', 'supersolvable': False, 'sylow': 0}
id: 65253455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.fq', 'subgroup_hash': 7732151897918737925, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2\\wr C_2.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 65253456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.ns', 'subgroup_hash': 1535737588287428553, 'subgroup_order': 2592, 'subgroup_tex': '\\PSU(3,2):S_3^2', 'supersolvable': False, 'sylow': 0}
id: 65253457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cp', 'subgroup_hash': 863601208845687898, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:C_4.C_2^3', 'supersolvable': False, 'sylow': 0}
id: 65253458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cv', 'subgroup_hash': 4088988131338656119, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_2\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
id: 65253459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.ck', 'subgroup_hash': 6340444901333315260, 'subgroup_order': 2592, 'subgroup_tex': 'C_3:S_3^3.C_4', 'supersolvable': False, 'sylow': 0}
id: 65253460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cv', 'subgroup_hash': 4088988131338656119, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_2\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
id: 65253461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.cj', 'subgroup_hash': 8800710472352522369, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:D_8:C_2', 'supersolvable': False, 'sylow': 0}
id: 65253462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.fr', 'subgroup_hash': 1117479816133821807, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_{12}:D_4', 'supersolvable': False, 'sylow': 0}
id: 65253463
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.lu', 'subgroup_hash': 273629761795729703, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_{12}:Q_8', 'supersolvable': False, 'sylow': 0}
id: 65253464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.ls', 'subgroup_hash': 2088917612038948738, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:(C_4\\times F_9)', 'supersolvable': False, 'sylow': 0}
id: 65252678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '311040.j', 'ambient_counter': 10, 'ambient_order': 311040, 'ambient_tex': 'C_3^3:S_3.C_2^4:S_5', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '311040.j.120.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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': '2592.pq', 'subgroup_hash': 6407552563315781201, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_{12}:C_8', '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 789 matching records in this table.

id: 65252676
{'ambient': '311040.j', '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': '311040.a1.a1', 'complements': ['311040.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '5.a1.a1', '6.a1.a1', '10.c1.a1', '16.a1.a1', '81.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3907, 5000, 1971, 5000, 1742, 5000, 248, 5000], 'generators': [457204064046573758978307144795219438090255661314408443180818087904292671781693752127328358647603419136569127435979989166, 4525871052914747761477529078798215834733845073975705251855087619796350294004697793370991725617733783533003610569486180195, 4563710714067491935264040177344169864551888572486591018600540525227151423335270770090012696578125793858508085145946273883, 4453752627959210896268661356034751969683795924800247672385480920630022105181639772599094186028181943665383257070115413981, 138832821307901968538686045597890228099867779856476519372912037646622083920531191694221948067982037953438729008707563, 76763658324156454045092776097743485226218055028682002632583964373530937842801897744159533810650098861407410314244963755, 4267809874053090789173650941523105288504419552233050415207957857879871696529096902822973175993406565388670805063628677409, 380700750079148879985321921519382354618791497329509622890147549746944857262659130896859586151519290582783737749633619240, 385935624875196838324085483851290277077168972194299422411085558576842311464152131756432172596584002899647699875185661962, 3345632128488307175833646681330089979655620178094775783321283107311837734822864928974997135331429168616622712467023387249, 77005995094495210252915858836731895070683090599749365730144605840758782931379232043737280156581675410091129478750605913], 'label': '311040.j.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '311040.j', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '311040.j'}
id: 65252677
{'ambient': '311040.j', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '311040.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1', '30.d1.a1', '30.e1.a1', '30.f1.a1', '30.g1.a1', '1215.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4558, -1, 5339, -1, 4647, -1, 4866, -1], 'generators': [457204064046573758978307144795219438090255661314408443180818087904292671781693752127328358647603419136569127435979989166, 4525871052914747761477529078798215834733845073975705251855087619796350294004697793370991725617733783533003610569486180195, 4563710714067491935264040177344169864551888572486591018600540525227151423335270770090012696578125793858508085145946273883, 138832821307901968538686045597890228099867779856476519372912037646622083920531191694221948067982037953438729008707563, 76763658324156454045092776097743485226218055028682002632583964373530937842801897744159533810650098861407410314244963755, 380700750079148879985321921519382354618791497329509622890147549746944857262659130896859586151519290582783737749633619240, 385935624875196838324085483851290277077168972194299422411085558576842311464152131756432172596584002899647699875185661962, 3345632128488307175833646681330089979655620178094775783321283107311837734822864928974997135331429168616622712467023387249, 77005995094495210252915858836731895070683090599749365730144605840758782931379232043737280156581675410091129478750605913, 3938632625685295871943746791959711692177342846391569385563424687439219660033259498372983731343195785497578337558334344355, 4204002836084325080553129261059894504266222770854523212313615648789848662890055221195717304787508514263057181912613813929, 361760627958261830353491108314339306446660436953218592414836237115730605993059212866059899489118613872536397215997042557], 'label': '311040.j.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '311040.j', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20736.w'}
id: 65252678
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id: 65252679
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id: 65252683
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id: 65252694
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id: 65252707
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id: 65252710
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id: 65252716
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id: 65252732
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id: 65252738
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id: 65252740
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id: 65252746
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id: 65252757
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id: 65252758
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id: 65252767
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id: 65252768
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id: 65252769
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id: 65252770
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id: 65252771
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id: 65252772
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id: 65252773
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id: 65252774
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id: 65252775
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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.