LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-25T09:30:16.700644

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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [6, 6, 18], 'aut_gens': [[3336181506444678334155174518, 6272981209169154803824879519], [2018939252634495532081951075, 8806515351680068134891129233], [1676530368706133686451914481, 5419989369896662762687531746], [885487926739832979960703699, 5437313590683861949016582199]], 'aut_group': None, 'aut_hash': 6899009085423557347, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 629856, 'aut_permdeg': 486, 'aut_perms': [3806408647337005064442766711118553261363647034126303932260628882134492675712684695902859122605678448493497782254473208289761202424083641500358173694060619927540589457744086770710890278062302849159469020530430495760740877515861237489692179545486450783919696008982658260236133712829420392588360809654266506481553353322881654365226583569460077826204246221450101898601953892811067855787602256212969564932633081491796362544090613557053573980247818163509405255832030797191382324034182416992492747440812127798133462972209838714074257890999104721425836880079558298353497885555526229257074027437710704344923909508152563380432266594389492542620723294860979851835202085913752441681190578943115790073042919509041313478166084265177566060082263551824160676871393554565533628589297351846992872313228523109788410691214948325690179671396099886578370284275144981900480841349275305699236201938693130990331028365514136180453906745902182290274551927889943932919543632657005925506935966871739220410794291176316163509102589234576691198151758514968011304626445563319883466898336652842140178071211352777560359932588211528, 16453284770636247448208535448891464818383929971809370996437503715257516602562396172582047004008903913374199706988468382313530592574642343143693214494405198964419390204253220303294319506502681895590941862713286984984454481353605366643784918533898826192523183550255931234841422539185053275860185080406853607602271254678191317031956169757280369144572069279266303126088652253023267879158954240484161710878122403015919827688405487679191093555439442818773356556543003031060794413483507355036838813277411812983836468818371190130429528303369748126691661683966966772015501718316212641681172737730147405588488562671010028851168075742498001710357497770748742822707095244009703223518165940507286612761396313207376245794548077732570094771087791643143968934233405307222686045267769871972867472619875225697145984293930111140639551800339376787869847531175866215103009194323367540683992234077907411185373793853657376383993802936703316838899689694735617242543504899929416285507872237518633633776950155167576116574310798278098948820059893734104915502981080039951421825730449072063336493316356086201040811247534449001, 3353229361417793645894473478644625271795409871223614439837255847967853072340240244482991904079054656262057986061139723784858243996076550708942765338379920865638726482224618844478346090882810387491175660192495948347446676288704651154102403028529549535988212459302786088529093296436344521838536774448344216660701996927813892147998634878304978383204599471750116159940032944644703690487807410766052219117276499165925974663711556061355526174661716198942256057786433580248711174221686284276206861451592349034355821536924599566992509551069231632011509304659368880373237790997539548821329078436988967551456440007563713236716032614796552498202894536290830306088357866769046463918000132135580796687169145527046677214711065044351651567184910224301022211972002529304268228242610352709707010209932205331745564832550047067269735580067049583372767418602409604782336370871870425923339580694982983702812309492447694543984858737862587319436173231626519639460050414743318366892293332781458330803322453413799105780207080699996883243955561889945605089976537684382422942572656900696185056238027182989866040419823066263], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 324, 1, 1], [2, 729, 1, 1], [3, 8, 1, 1], [3, 24, 1, 1], [3, 24, 3, 1], [3, 48, 1, 1], [3, 81, 2, 1], [3, 144, 1, 1], [3, 144, 3, 1], [3, 216, 1, 1], [3, 432, 1, 1], [3, 648, 2, 1], [3, 1296, 1, 1], [3, 1296, 3, 1], [4, 4374, 1, 1], [6, 648, 1, 1], [6, 729, 2, 1], [6, 1944, 1, 1], [6, 1944, 3, 1], [6, 2916, 2, 1], [6, 5832, 1, 1], [6, 5832, 2, 1], [8, 4374, 1, 2], [9, 648, 2, 1], [9, 1296, 2, 1], [9, 3888, 2, 1], [12, 4374, 2, 1], [18, 5832, 2, 1], [24, 4374, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.Q_8.C_3^3.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': None, 'autcentquo_hash': 6899009085423557347, 'autcentquo_nilpotent': False, 'autcentquo_order': 629856, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.Q_8.C_3^3.C_2^2', 'cc_stats': [[1, 1, 1], [2, 324, 1], [2, 729, 1], [3, 8, 1], [3, 24, 4], [3, 48, 1], [3, 81, 2], [3, 144, 4], [3, 216, 1], [3, 432, 1], [3, 648, 2], [3, 1296, 4], [4, 4374, 1], [6, 648, 1], [6, 729, 2], [6, 1944, 4], [6, 2916, 2], [6, 5832, 3], [8, 4374, 2], [9, 648, 2], [9, 1296, 2], [9, 3888, 2], [12, 4374, 2], [18, 5832, 2], [24, 4374, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '104976.cf', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 58, 'cyclic': False, 'derived_length': 5, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 324, 1, 1], [2, 729, 1, 1], [3, 8, 1, 1], [3, 24, 1, 4], [3, 48, 1, 1], [3, 81, 2, 1], [3, 144, 1, 4], [3, 216, 1, 1], [3, 432, 1, 1], [3, 648, 2, 1], [3, 1296, 1, 4], [4, 4374, 1, 1], [6, 648, 1, 1], [6, 729, 2, 1], [6, 1944, 1, 4], [6, 2916, 2, 1], [6, 5832, 1, 1], [6, 5832, 2, 1], [8, 4374, 2, 1], [9, 648, 2, 1], [9, 1296, 2, 1], [9, 3888, 2, 1], [12, 4374, 2, 1], [18, 5832, 2, 1], [24, 4374, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 5184, 'exponent': 72, 'exponents_of_order': [8, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 6], [48, 1, 3], [144, 1, 4]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '1296.3487', 'hash': 5926719532156794013, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [8, 18], 'inner_gens': [[3336181506444678334155174518, 6678183520191003949302224517], [2033911968893236405600890672, 6272981209169154803824879519]], 'inner_hash': 5926719532156794013, 'inner_nilpotent': False, 'inner_order': 104976, 'inner_split': True, 'inner_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 6], [2, 9], [3, 6], [4, 3], [8, 6], [16, 3], [24, 8], [48, 7], [144, 4]], 'label': '104976.cf', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6:(C3*GL(2,3))', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 52, 'number_divisions': 38, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 1412, 'number_subgroup_classes': 3784, 'number_subgroups': 2817116, 'old_label': None, 'order': 104976, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1053], [3, 8018], [4, 4374], [6, 33210], [8, 8748], [9, 11664], [12, 8748], [18, 11664], [24, 17496]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[1321608028342221393819450709, 7660595488142620810432092676]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [3, 2], [4, 3], [6, 2], [8, 4], [16, 3], [24, 8], [32, 1], [48, 5], [96, 1], [144, 4]], 'representations': {'PC': {'code': '7366701399442137380298728970576133736831127137286164629280243764951631719791125942356423141334979804313136822502024774602071394703841023327999886535842686858966527719571363910612259193343723508286990357365079607842181587745533591518556992139100151250372298050329145191080872651109951', 'gens': [1, 3, 4, 5, 7, 8, 9, 10, 11, 12], 'pres': [12, -2, -3, -3, -2, 2, -2, -3, 3, 3, 3, 3, 3, 24, 751693, 748226, 241178, 1393635, 1942719, 762363, 252135, 2439724, 3063976, 952408, 10960, 172, 2493509, 997937, 1143101, 381065, 2866758, 4003794, 48414, 8106, 4422, 402, 5280775, 3974419, 1520671, 504619, 254647, 1219, 3468104, 684308, 873536, 297260, 144344, 3956, 103689, 5901141, 552045, 209337, 13029, 9713098, 1321078, 342178, 51790, 147370, 42838, 13250315, 590999, 2160035, 436655, 278843, 140039]}, 'Perm': {'d': 27, 'gens': [3336181506444678334155174518, 6272981209169154803824879519]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6:(C_3\\times \\GL(2,3))', 'transitive_degree': 27, '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: 145007237
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 58, 'group_order': 104976, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 145007248
{'aut_label': '2A', 'centralizer': '324.l1', 'counter': 2, 'group_counter': 58, 'group_order': 104976, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2439039020644289071064867419, 'size': 324}
id: 145007259
{'aut_label': '2B', 'centralizer': '729.a1', 'counter': 3, 'group_counter': 58, 'group_order': 104976, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 853245917204823557876833615, 'size': 729}
id: 145007270
{'aut_label': '3A', 'centralizer': '8.a2', 'counter': 4, 'group_counter': 58, 'group_order': 104976, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 1258350440041370121233495490, 'size': 8}
id: 145007281
{'aut_label': '3B', 'centralizer': '24.g2', 'counter': 5, 'group_counter': 58, 'group_order': 104976, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 840788568358445655731059200, 'size': 24}
id: 145007285
{'aut_label': '3B', 'centralizer': '24.g2', 'counter': 6, 'group_counter': 58, 'group_order': 104976, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 3228220166063390033219386121, 'size': 24}
id: 145007286
{'aut_label': '3D', 'centralizer': '24.g2', 'counter': 7, 'group_counter': 58, 'group_order': 104976, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 1646776838392686240813619200, 'size': 24}
id: 145007287
{'aut_label': '3B', 'centralizer': '24.g2', 'counter': 8, 'group_counter': 58, 'group_order': 104976, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 2267507354112000, 'size': 24}
id: 145007288
{'aut_label': '3F', 'centralizer': '48.g1', 'counter': 9, 'group_counter': 58, 'group_order': 104976, 'label': '3F', 'order': 3, 'powers': [9, 1], 'representative': 3228220166064769884902033962, 'size': 48}
id: 145007238
{'aut_label': '3G1', 'centralizer': '81.a1', 'counter': 10, 'group_counter': 58, 'group_order': 104976, 'label': '3G1', 'order': 3, 'powers': [11, 1], 'representative': 5033401783213396734550751652, 'size': 81}
id: 145007239
{'aut_label': '3G1', 'centralizer': '81.a1', 'counter': 11, 'group_counter': 58, 'group_order': 104976, 'label': '3G-1', 'order': 3, 'powers': [10, 1], 'representative': 9196879524731576149216068885, 'size': 81}
id: 145007240
{'aut_label': '3H', 'centralizer': '144.a1', 'counter': 12, 'group_counter': 58, 'group_order': 104976, 'label': '3H', 'order': 3, 'powers': [12, 1], 'representative': 504943931211562, 'size': 144}
id: 145007241
{'aut_label': '3I', 'centralizer': '144.a1', 'counter': 13, 'group_counter': 58, 'group_order': 104976, 'label': '3I', 'order': 3, 'powers': [13, 1], 'representative': 513163763437432968023883562, 'size': 144}
id: 145007242
{'aut_label': '3H', 'centralizer': '144.a1', 'counter': 14, 'group_counter': 58, 'group_order': 104976, 'label': '3J', 'order': 3, 'powers': [14, 1], 'representative': 513163763437688063675389890, 'size': 144}
id: 145007243
{'aut_label': '3H', 'centralizer': '144.a1', 'counter': 15, 'group_counter': 58, 'group_order': 104976, 'label': '3K', 'order': 3, 'powers': [15, 1], 'representative': 513163763437688063675558744, 'size': 144}
id: 145007244
{'aut_label': '3L', 'centralizer': '216.bn1', 'counter': 16, 'group_counter': 58, 'group_order': 104976, 'label': '3L', 'order': 3, 'powers': [16, 1], 'representative': 646402603203369380794452, 'size': 216}
id: 145007245
{'aut_label': '3M', 'centralizer': '432.g1', 'counter': 17, 'group_counter': 58, 'group_order': 104976, 'label': '3M', 'order': 3, 'powers': [17, 1], 'representative': 1290043842459814726936884475, 'size': 432}
id: 145007246
{'aut_label': '3N1', 'centralizer': '648.cn1', 'counter': 18, 'group_counter': 58, 'group_order': 104976, 'label': '3N1', 'order': 3, 'powers': [19, 1], 'representative': 9629304118859240690935228970, 'size': 648}
id: 145007247
{'aut_label': '3N1', 'centralizer': '648.cn1', 'counter': 19, 'group_counter': 58, 'group_order': 104976, 'label': '3N-1', 'order': 3, 'powers': [18, 1], 'representative': 4226195040556565651728177345, 'size': 648}
id: 145007249
{'aut_label': '3O', 'centralizer': '1296.y1', 'counter': 20, 'group_counter': 58, 'group_order': 104976, 'label': '3O', 'order': 3, 'powers': [20, 1], 'representative': 840194069289275138269129296, 'size': 1296}
id: 145007250
{'aut_label': '3P', 'centralizer': '1296.z1', 'counter': 21, 'group_counter': 58, 'group_order': 104976, 'label': '3P', 'order': 3, 'powers': [21, 1], 'representative': 2483037980354963572576622006, 'size': 1296}
id: 145007251
{'aut_label': '3P', 'centralizer': '1296.z1', 'counter': 22, 'group_counter': 58, 'group_order': 104976, 'label': '3Q', 'order': 3, 'powers': [22, 1], 'representative': 3290886576084527014103654586, 'size': 1296}
id: 145007252
{'aut_label': '3P', 'centralizer': '1296.z1', 'counter': 23, 'group_counter': 58, 'group_order': 104976, 'label': '3R', 'order': 3, 'powers': [23, 1], 'representative': 3337395376140862758073921733, 'size': 1296}
id: 145007253
{'aut_label': '4A', 'centralizer': '4374.b1', 'counter': 24, 'group_counter': 58, 'group_order': 104976, 'label': '4A', 'order': 4, 'powers': [3, 24], 'representative': 2871437555839538876451679061, 'size': 4374}
id: 145007254
{'aut_label': '6A', 'centralizer': '648.a1', 'counter': 25, 'group_counter': 58, 'group_order': 104976, 'label': '6A', 'order': 6, 'powers': [4, 2], 'representative': 1256412665341224455891408226, 'size': 648}
id: 145007255
{'aut_label': '6B1', 'centralizer': '729.a1', 'counter': 26, 'group_counter': 58, 'group_order': 104976, 'label': '6B1', 'order': 6, 'powers': [10, 3], 'representative': 8403348603543330754538557492, 'size': 729}
id: 145007256
{'aut_label': '6B1', 'centralizer': '729.a1', 'counter': 27, 'group_counter': 58, 'group_order': 104976, 'label': '6B-1', 'order': 6, 'powers': [11, 3], 'representative': 5438499416316508898881864695, 'size': 729}
id: 145007257
{'aut_label': '6C', 'centralizer': '1944.a1', 'counter': 28, 'group_counter': 58, 'group_order': 104976, 'label': '6C', 'order': 6, 'powers': [5, 2], 'representative': 1677719507952271940087517019, 'size': 1944}
id: 145007258
{'aut_label': '6C', 'centralizer': '1944.a1', 'counter': 29, 'group_counter': 58, 'group_order': 104976, 'label': '6D', 'order': 6, 'powers': [6, 2], 'representative': 841328139922457244738431633, 'size': 1944}
id: 145007260
{'aut_label': '6E', 'centralizer': '1944.a1', 'counter': 30, 'group_counter': 58, 'group_order': 104976, 'label': '6E', 'order': 6, 'powers': [7, 2], 'representative': 1288106113864133693641982568, 'size': 1944}
id: 145007261
{'aut_label': '6C', 'centralizer': '1944.a1', 'counter': 31, 'group_counter': 58, 'group_order': 104976, 'label': '6F', 'order': 6, 'powers': [8, 2], 'representative': 3243110876615030474099730527, 'size': 1944}
id: 145007262
{'aut_label': '6G1', 'centralizer': '2916.a1', 'counter': 32, 'group_counter': 58, 'group_order': 104976, 'label': '6G1', 'order': 6, 'powers': [11, 2], 'representative': 5485062216939720201691528956, 'size': 2916}
id: 145007263
{'aut_label': '6G1', 'centralizer': '2916.a1', 'counter': 33, 'group_counter': 58, 'group_order': 104976, 'label': '6G-1', 'order': 6, 'powers': [10, 2], 'representative': 9971816208926772546419687314, 'size': 2916}
id: 145007264
{'aut_label': '6H', 'centralizer': '5832.bm1', 'counter': 34, 'group_counter': 58, 'group_order': 104976, 'label': '6H', 'order': 6, 'powers': [16, 3], 'representative': 3245699401633481811120787671, 'size': 5832}
id: 145007265
{'aut_label': '6I1', 'centralizer': '5832.bm1', 'counter': 35, 'group_counter': 58, 'group_order': 104976, 'label': '6I1', 'order': 6, 'powers': [18, 3], 'representative': 4985030263487411732125064188, 'size': 5832}
id: 145007266
{'aut_label': '6I1', 'centralizer': '5832.bm1', 'counter': 36, 'group_counter': 58, 'group_order': 104976, 'label': '6I-1', 'order': 6, 'powers': [19, 3], 'representative': 7970767933762440214433875089, 'size': 5832}
id: 145007267
{'aut_label': '8A1', 'centralizer': '4374.b1', 'counter': 37, 'group_counter': 58, 'group_order': 104976, 'label': '8A1', 'order': 8, 'powers': [24, 37], 'representative': 1690751118744283325952610989, 'size': 4374}
id: 145007268
{'aut_label': '8A-1', 'centralizer': '4374.b1', 'counter': 38, 'group_counter': 58, 'group_order': 104976, 'label': '8A-1', 'order': 8, 'powers': [24, 38], 'representative': 869946317463653882015891242, 'size': 4374}
id: 145007269
{'aut_label': '9A1', 'centralizer': '648.bn1', 'counter': 39, 'group_counter': 58, 'group_order': 104976, 'label': '9A1', 'order': 9, 'powers': [40, 4], 'representative': 3775051343174540500329888682, 'size': 648}
id: 145007271
{'aut_label': '9A1', 'centralizer': '648.bn1', 'counter': 40, 'group_counter': 58, 'group_order': 104976, 'label': '9A-1', 'order': 9, 'powers': [39, 4], 'representative': 10450703513968156865986734793, 'size': 648}
id: 145007272
{'aut_label': '9B1', 'centralizer': '1296.cd1', 'counter': 41, 'group_counter': 58, 'group_order': 104976, 'label': '9B1', 'order': 9, 'powers': [42, 4], 'representative': 9569793742188782076147737000, 'size': 1296}
id: 145007273
{'aut_label': '9B1', 'centralizer': '1296.cd1', 'counter': 42, 'group_counter': 58, 'group_order': 104976, 'label': '9B-1', 'order': 9, 'powers': [41, 4], 'representative': 4242951495000984397266536140, 'size': 1296}
id: 145007274
{'aut_label': '9C1', 'centralizer': '3888.bo1', 'counter': 43, 'group_counter': 58, 'group_order': 104976, 'label': '9C1', 'order': 9, 'powers': [44, 9], 'representative': 8018002838165397708423634743, 'size': 3888}
id: 145007275
{'aut_label': '9C1', 'centralizer': '3888.bo1', 'counter': 44, 'group_counter': 58, 'group_order': 104976, 'label': '9C-1', 'order': 9, 'powers': [43, 9], 'representative': 6212795517414292322737916569, 'size': 3888}
id: 145007276
{'aut_label': '12A1', 'centralizer': '4374.b1', 'counter': 45, 'group_counter': 58, 'group_order': 104976, 'label': '12A1', 'order': 12, 'powers': [26, 24], 'representative': 6210365379179953046897141249, 'size': 4374}
id: 145007277
{'aut_label': '12A1', 'centralizer': '4374.b1', 'counter': 46, 'group_counter': 58, 'group_order': 104976, 'label': '12A-1', 'order': 12, 'powers': [27, 24], 'representative': 10888218500596835522968189582, 'size': 4374}
id: 145007278
{'aut_label': '18A1', 'centralizer': '5832.d1', 'counter': 47, 'group_counter': 58, 'group_order': 104976, 'label': '18A1', 'order': 18, 'powers': [39, 25], 'representative': 8065803265895314958445023633, 'size': 5832}
id: 145007279
{'aut_label': '18A1', 'centralizer': '5832.d1', 'counter': 48, 'group_counter': 58, 'group_order': 104976, 'label': '18A-1', 'order': 18, 'powers': [40, 25], 'representative': 4616379483092772211816839953, 'size': 5832}
id: 145007280
{'aut_label': '24A1', 'centralizer': '4374.b1', 'counter': 49, 'group_counter': 58, 'group_order': 104976, 'label': '24A1', 'order': 24, 'powers': [45, 37], 'representative': 7631486117171988228666692271, 'size': 4374}
id: 145007282
{'aut_label': '24A-1', 'centralizer': '4374.b1', 'counter': 50, 'group_counter': 58, 'group_order': 104976, 'label': '24A-1', 'order': 24, 'powers': [46, 38], 'representative': 3870113807030951383608975829, 'size': 4374}
id: 145007283
{'aut_label': '24A-1', 'centralizer': '4374.b1', 'counter': 51, 'group_counter': 58, 'group_order': 104976, 'label': '24A7', 'order': 24, 'powers': [45, 38], 'representative': 8016062864123284595673480133, 'size': 4374}
id: 145007284
{'aut_label': '24A1', 'centralizer': '4374.b1', 'counter': 52, 'group_counter': 58, 'group_order': 104976, 'label': '24A-7', 'order': 24, 'powers': [46, 37], 'representative': 7079692321029843549717340252, 'size': 4374}

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: 14213203
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 14213214
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 14213225
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 14213235
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, -2, -1, -1, -2, -2, -2, -2, 1, 1, 2, -1, -1, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 14213236
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213240
{'cdim': 3, 'counter': 9, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0, 0, -1, -1, 3, 3, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 14213204
{'cdim': 3, 'counter': 10, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 3, 3, -1, -1, -1, -1, -1, -1, 0, 0, 0, 1, 1, 3, 3, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 14213237
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.2b', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 4, 4, 4, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, 1, 1, -2, -2, -2, -2, 4, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213238
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.2c', 'multiplicity': 2, 'nt': [24, 22], 'qdim': 4, 'qvalues': [4, 0, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213207
{'cdim': 4, 'counter': 13, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.4a', 'multiplicity': 1, 'nt': [8, 23], 'qdim': 4, 'qvalues': [4, 0, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 4, 4, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213205
{'cdim': 3, 'counter': 11, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.3c', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, 2, 6, 6, 6, 6, 6, 6, 6, -3, -3, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -3, -3, 2, 2, 2, 2, -1, -1, 0, 0, 0, -2, -2, -3, -3, 0, 0, 0, 0, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 14213206
{'cdim': 3, 'counter': 12, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.3d', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, -2, 6, 6, 6, 6, 6, 6, 6, -3, -3, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -3, -3, -2, -2, -2, -2, 1, 1, 0, 0, 0, 2, 2, -3, -3, 0, 0, 0, 0, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 14213239
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.2d', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 0, -8, 8, 8, 8, 8, 8, 8, -4, -4, 8, 8, 8, 8, -4, -4, 2, 2, -4, -4, -4, -4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213208
{'cdim': 4, 'counter': 14, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.4b', 'multiplicity': 2, 'nt': [24, 253], 'qdim': 8, 'qvalues': [8, 0, -8, 8, 8, 8, 8, 8, 8, -4, -4, 8, 8, 8, 8, 2, 2, -1, -1, 2, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, -4, -4, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213209
{'cdim': 8, 'counter': 15, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.8a', 'multiplicity': 1, 'nt': [9, 26], 'qdim': 8, 'qvalues': [8, 2, 0, 8, -1, -1, 8, -1, 8, 8, 8, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 0, 0, -1, -1, 2, -1, 2, 2, 0, 0, 0, 0, 0, -1, -1, 2, 2, -1, -1, 0, 0, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
id: 14213210
{'cdim': 8, 'counter': 16, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.8b', 'multiplicity': 1, 'nt': [18, 157], 'qdim': 8, 'qvalues': [8, -2, 0, 8, -1, -1, 8, -1, 8, 8, 8, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, 0, -2, 0, 0, 1, 1, -2, 1, -2, -2, 0, 0, 0, 0, 0, -1, -1, 2, 2, -1, -1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
id: 14213211
{'cdim': 8, 'counter': 17, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.8c', 'multiplicity': 2, 'nt': [24, 2917], 'qdim': 16, 'qvalues': [16, 4, 0, 16, -2, -2, 16, -2, 16, -8, -8, -2, -2, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, 0, 4, 0, 0, -2, -2, 4, -2, -2, -2, 0, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
id: 14213212
{'cdim': 8, 'counter': 18, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.8d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -4, 0, 16, -2, -2, 16, -2, 16, -8, -8, -2, -2, -2, -2, 4, 4, -2, -2, 4, -2, -2, -2, 0, -4, 0, 0, 2, 2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
id: 14213213
{'cdim': 16, 'counter': 19, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.16a', 'multiplicity': 1, 'nt': [24, 1334], 'qdim': 16, 'qvalues': [16, 0, 0, 16, -2, -2, 16, -2, 16, 16, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213216
{'cdim': 24, 'counter': 21, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24a', 'multiplicity': 1, 'nt': [27, 812], 'qdim': 24, 'qvalues': [24, 6, 0, 24, 6, 6, -3, 6, -3, 0, 0, -3, 6, -3, -3, 6, 6, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213217
{'cdim': 24, 'counter': 22, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24b', 'multiplicity': 1, 'nt': [27, 1303], 'qdim': 24, 'qvalues': [24, 6, 0, -3, -3, 15, 6, 6, -3, 0, 0, -3, -3, -3, 6, 6, -3, 0, 0, 0, 0, 3, -3, 0, -3, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213218
{'cdim': 24, 'counter': 23, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24c', 'multiplicity': 1, 'nt': [27, 1303], 'qdim': 24, 'qvalues': [24, 6, 0, -3, 6, -3, 6, 15, -3, 0, 0, 6, -3, -3, -3, 6, -3, 0, 0, 0, 3, -3, 0, 0, -3, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213219
{'cdim': 24, 'counter': 24, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24d', 'multiplicity': 1, 'nt': [27, 1303], 'qdim': 24, 'qvalues': [24, 6, 0, -3, 15, 6, 6, -3, -3, 0, 0, -3, -3, 6, -3, 6, -3, 0, 0, 0, -3, 0, 3, 0, -3, 0, 0, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213220
{'cdim': 24, 'counter': 25, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24e', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -6, 0, -3, -3, 15, 6, 6, -3, 0, 0, -3, -3, -3, 6, 6, -3, 0, 0, 0, 0, 3, -3, 0, 3, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213221
{'cdim': 24, 'counter': 26, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24f', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -6, 0, -3, 6, -3, 6, 15, -3, 0, 0, 6, -3, -3, -3, 6, -3, 0, 0, 0, 3, -3, 0, 0, 3, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213222
{'cdim': 24, 'counter': 27, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24g', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -6, 0, -3, 15, 6, 6, -3, -3, 0, 0, -3, -3, 6, -3, 6, -3, 0, 0, 0, -3, 0, 3, 0, 3, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213223
{'cdim': 24, 'counter': 28, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.24h', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -6, 0, 24, 6, 6, -3, 6, -3, 0, 0, -3, 6, -3, -3, 6, 6, 0, 0, -3, 0, 0, 0, 0, -6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213215
{'cdim': 16, 'counter': 20, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.16b', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 0, 32, -4, -4, 32, -4, 32, -16, -16, -4, -4, -4, -4, -4, -4, 2, 2, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213224
{'cdim': 48, 'counter': 29, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48a', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, -6, 30, 12, 12, -6, 0, 0, -6, -6, -6, 12, -6, 3, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213226
{'cdim': 48, 'counter': 30, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, 12, -6, 12, 30, -6, 0, 0, 12, -6, -6, -6, -6, 3, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213227
{'cdim': 48, 'counter': 31, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48c', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, 30, 12, 12, -6, -6, 0, 0, -6, -6, 12, -6, -6, 3, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213228
{'cdim': 48, 'counter': 32, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48d', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 48, -6, -6, -6, -6, -6, 0, 0, 3, -6, 3, 3, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213229
{'cdim': 48, 'counter': 33, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48e', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 48, 12, 12, -6, 12, -6, 0, 0, -6, 12, -6, -6, -6, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213230
{'cdim': 48, 'counter': 34, 'faithful': False, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.48f', 'multiplicity': 2, 'nt': [144, 0], 'qdim': 96, 'qvalues': [96, 0, 0, 96, -12, -12, -12, -12, -12, 0, 0, 6, -12, 6, 6, 0, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213231
{'cdim': 144, 'counter': 35, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.144a', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 144, 'qvalues': [144, 0, 0, -18, -18, -18, -18, 36, 9, 0, 0, -9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213232
{'cdim': 144, 'counter': 36, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.144b', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 144, 'qvalues': [144, 0, 0, -18, -18, -18, 36, -18, -18, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213233
{'cdim': 144, 'counter': 37, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.144c', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 144, 'qvalues': [144, 0, 0, -18, -18, 36, -18, -18, 9, 0, 0, 9, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14213234
{'cdim': 144, 'counter': 38, 'faithful': True, 'group': '104976.cf', 'group_order': 104976, 'image': None, 'label': '104976.cf.144d', 'multiplicity': 1, 'nt': [162, 0], 'qdim': 144, 'qvalues': [144, 0, 0, -18, 36, -18, -18, -18, 9, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 33667597
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 104976, 'label': '104976.cf.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 33667608
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 52488, 'label': '104976.cf.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 33667619
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 34992, 'label': '104976.cf.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
id: 33667630
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 34992, 'label': '104976.cf.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
id: 33667641
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 17496, 'label': '104976.cf.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
id: 33667645
{'center': '1.a1', 'center_index': 1, 'center_order': 104976, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 17496, 'label': '104976.cf.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
id: 33667646
{'center': '6.a1', 'center_index': 6, 'center_order': 17496, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 17496, 'label': '104976.cf.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667647
{'center': '6.a1', 'center_index': 6, 'center_order': 17496, 'counter': 8, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 5832, 'label': '104976.cf.2b1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667648
{'center': '6.a1', 'center_index': 6, 'center_order': 17496, 'counter': 9, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 5832, 'label': '104976.cf.2b2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667598
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 10, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '48.29', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1', 'kernel_order': 2187, 'label': '104976.cf.2c1', 'nt': [24, 22], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 33667599
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id: 33667600
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id: 33667601
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id: 33667602
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 14, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '144.122', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 729, 'label': '104976.cf.2d3', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 8]], [[1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 4]], [[1, 8]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[-2, 4]], [[2, 8]], [[-1, 8]], [[1, 4]], [[-1, 8]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 5], [1, 7]], [[-1, 1], [1, 7]], [[1, 3], [1, 5], [-1, 7]], [[1, 1], [-1, 7]]]}
id: 33667603
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 15, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '144.122', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 729, 'label': '104976.cf.2d4', 'nt': [48, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 8]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 8]], [[-1, 4]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[2, 8]], [[-2, 4]], [[1, 4]], [[-1, 8]], [[1, 4]], [[-1, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 7]], [[-1, 3], [-1, 5], [1, 7]], [[1, 1], [-1, 7]], [[1, 3], [1, 5], [-1, 7]]]}
id: 33667604
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 4374, 'label': '104976.cf.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 33667605
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 4374, 'label': '104976.cf.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 33667606
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 18, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 1458, 'label': '104976.cf.3c1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
id: 33667607
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 19, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 1458, 'label': '104976.cf.3c2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
id: 33667609
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 20, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 1458, 'label': '104976.cf.3d1', 'nt': [18, 30], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
id: 33667610
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 21, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 1458, 'label': '104976.cf.3d2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
id: 33667611
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 22, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '48.29', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1', 'kernel_order': 2187, 'label': '104976.cf.4a', 'nt': [8, 23], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667612
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 23, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '144.122', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 729, 'label': '104976.cf.4b1', 'nt': [24, 253], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, -1]], [[4, 1]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667613
{'center': '24.a1', 'center_index': 24, 'center_order': 4374, 'counter': 24, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '144.122', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 729, 'label': '104976.cf.4b2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 1]], [[4, -1]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667614
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 25, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '432.734', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1', 'kernel_order': 243, 'label': '104976.cf.8a', 'nt': [9, 26], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667615
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 26, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '432.734', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1', 'kernel_order': 243, 'label': '104976.cf.8b', 'nt': [18, 157], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667616
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 27, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.8c1', 'nt': [24, 2917], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, -1]], [[8, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667617
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 28, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, 1]], [[8, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667618
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 29, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.8d1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, -1]], [[8, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667620
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 30, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.8d2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[8, 1]], [[8, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667621
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 31, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '432.734', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1', 'kernel_order': 243, 'label': '104976.cf.16a', 'nt': [24, 1334], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[16, 0]], [[16, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667622
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 32, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.16b1', 'nt': [48, 0], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[16, 0]], [[16, -1]], [[16, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667623
{'center': '432.a1', 'center_index': 432, 'center_order': 243, 'counter': 33, 'cyclotomic_n': 3, 'dim': 16, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '1296.3487', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1', 'kernel_order': 81, 'label': '104976.cf.16b2', 'nt': [48, 2], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[16, 0]], [[-2, 0]], [[16, 0]], [[16, 1]], [[16, -1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667624
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 34, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 1, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.24a', 'nt': [27, 812], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[24, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667625
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24b', 'nt': [27, 1303], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667626
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24c', 'nt': [27, 1303], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667627
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24d', 'nt': [27, 1303], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667628
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24e', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667629
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24f', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[15, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667631
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.24g', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[15, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667632
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 1, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.24h', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[24, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667633
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.48a', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[30, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667634
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.48b', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[30, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667635
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.48c', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[30, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667636
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 1, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.48d', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667637
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 1, 'dim': 48, 'faithful': False, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 1, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.48e', 'nt': [72, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[48, 0]], [[12, 0]], [[12, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[12, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667638
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 3, 'dim': 48, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 0, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.48f1', 'nt': [144, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667639
{'center': '11664.a1', 'center_index': 11664, 'center_order': 9, 'counter': 48, 'cyclotomic_n': 3, 'dim': 48, 'faithful': False, 'field': [1, -1, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '11664.en', 'image_order': 11664, 'indicator': 0, 'kernel': '11664.a1', 'kernel_order': 9, 'label': '104976.cf.48f2', 'nt': [144, 2], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[48, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667640
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 49, 'cyclotomic_n': 1, 'dim': 144, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.144a', 'nt': [162, 0], 'q_character': None, 'values': [[[144, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[36, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667642
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 50, 'cyclotomic_n': 1, 'dim': 144, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.144b', 'nt': [162, 0], 'q_character': None, 'values': [[[144, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667643
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 51, 'cyclotomic_n': 1, 'dim': 144, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.144c', 'nt': [162, 0], 'q_character': None, 'values': [[[144, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33667644
{'center': '104976.a1', 'center_index': 104976, 'center_order': 1, 'counter': 52, 'cyclotomic_n': 1, 'dim': 144, 'faithful': True, 'field': [0, 1], 'group': '104976.cf', 'group_counter': 58, 'group_order': 104976, 'image': None, 'image_isoclass': '104976.cf', 'image_order': 104976, 'indicator': 1, 'kernel': '104976.a1', 'kernel_order': 1, 'label': '104976.cf.144d', 'nt': [162, 0], 'q_character': None, 'values': [[[144, 0]], [[0, 0]], [[0, 0]], [[-18, 0]], [[36, 0]], [[-18, 0]], [[-18, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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 1412 matching records in this table.

id: 124220807
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 104976, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '104976.cf.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104976.cf', 'subgroup_hash': 5926719532156794013, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'supersolvable': False, 'sylow': 0}
id: 124221331
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 52488, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '52488.cm', 'subgroup_hash': 3679697070905903602, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6:(C_3\\times \\SL(2,3))', 'supersolvable': False, 'sylow': 0}
id: 124221442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 34992, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2039641228390938043, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.Q_8.S_3', 'supersolvable': False, 'sylow': 0}
id: 124221553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 17496, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, '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': '34992.cs', 'subgroup_hash': 5151894112034611147, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(C_3\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
id: 124221664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4374, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.4.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, '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': '26244.em', 'subgroup_hash': 4523322583819533599, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6:(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 124221775
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ec', 'subgroup_hash': 973806794745079939, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^2\\wr C_3:Q_8', 'supersolvable': False, 'sylow': 0}
id: 124221886
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2', 'D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4447593647272623146, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^6.Q_8.C_3', 'supersolvable': False, 'sylow': 0}
id: 124221997
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id: 124222108
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id: 124220808
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id: 124220919
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id: 124221030
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id: 124221141
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id: 124221252
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, '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': '11664.en', 'subgroup_hash': 6180211205283515442, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^4:(C_3\\times \\GL(2,3))', 'supersolvable': False, 'sylow': 0}
id: 124221276
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 5832, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, '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': 3894362541543532166, 'subgroup_order': 11664, 'subgroup_tex': 'C_3^6.\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 124221287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 4374, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, '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': '8748.el', 'subgroup_hash': 7978454207897953251, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^2\\wr C_3:C_2^2', 'supersolvable': True, 'sylow': 0}
id: 124221298
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id: 124221309
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id: 124221320
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id: 124221332
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 2187, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '104976.cf.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, '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': '6561.225997', 'subgroup_hash': 6245178457529305503, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^6:C_3^2', 'supersolvable': True, 'sylow': 3}
id: 124221343
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id: 124221354
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id: 124221365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, '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': '5832.el', 'subgroup_hash': 3686938360739699673, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^4:(C_3\\times \\SL(2,3))', 'supersolvable': False, 'sylow': 0}
id: 124221376
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id: 124221387
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id: 124221398
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id: 124221409
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id: 124221420
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id: 124221431
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id: 124221443
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id: 124221454
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id: 124221465
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id: 124221476
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id: 124221487
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id: 124221498
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id: 124221509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, '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: 124221520
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id: 124221531
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id: 124221542
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id: 124221554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': '2916.dz', 'subgroup_hash': 7413141006862451953, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^5:(C_2\\times C_6)', 'supersolvable': True, 'sylow': 0}
id: 124221565
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id: 124221576
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id: 124221587
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id: 124221598
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id: 124221609
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id: 124221620
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': 7640976462238486466, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4.S_3^2', 'supersolvable': True, 'sylow': 0}
id: 124221631
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1458, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, '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': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
id: 124221642
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 2187, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\GL(2,3)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2187.2052', 'subgroup_hash': 6501777776849519009, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\wr C_3', 'supersolvable': True, 'sylow': 0}
id: 124221653
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.8516', 'subgroup_hash': 8795916686994291310, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^5:C_3^2', 'supersolvable': True, 'sylow': 0}
id: 124221665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.5022', 'subgroup_hash': 6492705017912641258, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 124221676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.5576', 'subgroup_hash': 7125665540591642229, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 124221687
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.5022', 'subgroup_hash': 6492705017912641258, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^4.C_3^3', 'supersolvable': True, 'sylow': 0}
id: 124221698
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 729, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.6477', 'subgroup_hash': 2003116083424246206, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^6.C_3', 'supersolvable': True, 'sylow': 0}
id: 124221709
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 729, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.48.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, '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': '2187.2052', 'subgroup_hash': 6501777776849519009, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\wr C_3', 'supersolvable': True, 'sylow': 0}
id: 124221720
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.2314', 'subgroup_hash': 2314, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
id: 124221731
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.3875', 'subgroup_hash': 3875, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 124221742
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.2298', 'subgroup_hash': 2298, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_{24}', 'supersolvable': False, 'sylow': 0}
id: 124221753
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 124221764
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.3875', 'subgroup_hash': 3875, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 124221776
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.2295', 'subgroup_hash': 2295, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 124221787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, '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': '1944.3875', 'subgroup_hash': 3875, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 124221798
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1458, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '104976.cf.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C4', 'D3', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1795', 'subgroup_hash': 1795, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221809
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1717', 'subgroup_hash': 1717, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 124221820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1205', 'subgroup_hash': 1205, 'subgroup_order': 1458, 'subgroup_tex': '(C_3^2\\times \\He_3):C_6', 'supersolvable': True, 'sylow': 0}
id: 124221831
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1107', 'subgroup_hash': 1107, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124221842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221864
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1108', 'subgroup_hash': 1108, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124221875
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221887
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221898
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1242', 'subgroup_hash': 1242, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5.C_6', 'supersolvable': True, 'sylow': 0}
id: 124221909
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221920
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1472', 'subgroup_hash': 1472, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124221931
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 729, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1798', 'subgroup_hash': 1798, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 124221942
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1183', 'subgroup_hash': 1183, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 124221953
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id: 124221964
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id: 124221975
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1193', 'subgroup_hash': 1193, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4.(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 124221986
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.576', 'subgroup_hash': 576, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4.(C_3\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 124221998
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1469', 'subgroup_hash': 1469, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124222009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1718', 'subgroup_hash': 1718, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
id: 124222020
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.621', 'subgroup_hash': 621, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:C_{18}', 'supersolvable': True, 'sylow': 0}
id: 124222031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1469', 'subgroup_hash': 1469, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124222042
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1469', 'subgroup_hash': 1469, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
id: 124222053
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id: 124222064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1182', 'subgroup_hash': 1182, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
id: 124222075
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1182', 'subgroup_hash': 1182, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^4:(C_3\\times C_6)', 'supersolvable': True, 'sylow': 0}
id: 124222086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222097
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1109', 'subgroup_hash': 1109, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222109
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1109', 'subgroup_hash': 1109, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222120
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222131
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1109', 'subgroup_hash': 1109, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222142
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.72.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, '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': '1458.1465', 'subgroup_hash': 1465, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
id: 124222153
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '1296.3487', 'subgroup_hash': 3487, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^3:\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 124222164
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '1296.3521', 'subgroup_hash': 3521, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 124222175
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '1296.3521', 'subgroup_hash': 3521, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 124222186
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.81.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, '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': '1296.3521', 'subgroup_hash': 3521, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 124222197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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': '972.427', 'subgroup_hash': 427, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 124222208
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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': '972.438', 'subgroup_hash': 438, 'subgroup_order': 972, 'subgroup_tex': '\\He_3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 124220809
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '104976.cf', 'ambient_counter': 58, 'ambient_order': 104976, 'ambient_tex': 'C_3^6:(C_3\\times \\GL(2,3))', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '104976.cf.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, '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': '972.802', 'subgroup_hash': 802, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, '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 1412 matching records in this table.

id: 124220807
{'ambient': '104976.cf', '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': '104976.a1', 'complements': ['104976.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '3.a1', '3.b1', '4.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2614, 1755, 2540, 1685], 'generators': [62667541564046866724616799, 840788568358445655731153962, 2267507354250690, 94762, 47231787976478806878222835, 3274210748016625531744563624, 3228220166065734606622251285, 497111853088237529361662180, 10778322852403986737323065600, 77321, 2917428344709336821008036634, 2849517333811721], 'label': '104976.cf.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '104976.cf'}
id: 124220808
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '104976.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['18.a1', '24.j1', '54.f1'], 'core': '18.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2583, -1, 2540, -1], 'generators': [3228220166065734606622251285, 3274210748016625531744563624, 2917428344709336821008036634, 94762, 840788568358445655731153962, 77321, 2267507354250690, 8871114994296129823979828933, 497111853088237529361662180, 2849517333811721], 'label': '104976.cf.6.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.e1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '52488.cm'}
id: 124220809
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '104976.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.d1'], 'contains': ['216.p1', '216.bd1', '216.bp1', '324.a1', '324.b1', '324.m1', '324.t1'], 'core': '11664.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7790, -1, 8543, -1], 'generators': [3228220166065734606622251285, 2917428344707247345216660815, 840788568358445655731153962, 9644865852858096763616590080, 62667541564046866724345510, 47231787976478806878222835, 760039582886744], 'label': '104976.cf.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '108.c1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '972.802'}
id: 124220810
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bj2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.by1', '1296.ca1', '1296.ce1', '1296.cr1', '1944.cp2'], 'contains': ['11664.f1', '11664.l1', '11664.bq1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [6255, -1, 7682, -1], 'generators': [840788568358445655731153962, 8375329513280704852408628933, 3228220166065152596642478793], 'label': '104976.cf.3888.bj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.x1', 'old_label': '3888.bj2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bj2', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 124220811
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.i1', '1296.bz1', '1296.ce1', '1296.cf1', '1296.cs1'], 'contains': ['11664.f1', '11664.m1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [7989, -1, 8636, -1], 'generators': [840788568358445655731153962, 3228220166065152596642478793, 62667541566146119976511494], 'label': '104976.cf.3888.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.e1', 'old_label': '3888.bk1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bk1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 124220812
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.j1', '1296.j2', '1296.ct1'], 'contains': ['11664.f1', '11664.n1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [8549, -1, 7652, -1], 'generators': [62667541564046866724616799, 840788568358445655731153962, 3228220166065152596642478793], 'label': '104976.cf.3888.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ba1', 'old_label': '3888.bl1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bl1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220813
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.ch1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bx1', '1296.cd1', '1296.ce1', '1296.cf1', '1296.cu1'], 'contains': ['11664.f1', '11664.o1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [7857, -1, 8869, -1], 'generators': [3228220166064769884902033962, 10778322852403986737323065600, 840788568360535133482442532], 'label': '104976.cf.3888.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.r1', 'old_label': '3888.bm1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bm1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 124220814
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bn1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bc1', '1296.cd1', '1296.ce1', '1296.cf1', '1296.cv1'], 'contains': ['11664.f1', '11664.p1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [7851, -1, 8852, -1], 'generators': [10004728076669665220887651370, 840788568358445655731153962, 3228220166064355282675956480], 'label': '104976.cf.3888.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.x1', 'old_label': '3888.bn1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bn1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 124220815
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bn2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bn2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bz1', '1296.cb1', '1296.cd1', '1296.cf1', '1296.cv1'], 'contains': ['11664.f1', '11664.p1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [7839, -1, 8831, -1], 'generators': [840788568358445655731153962, 3228220166065152596642478793, 9629304118860365476780576973], 'label': '104976.cf.3888.bn2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '144.r1', 'old_label': '3888.bn2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bn2', 'subgroup_fusion': None, 'weyl_group': '27.3'}
id: 124220816
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bo1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cc1', '1296.cc2', '1296.cw1'], 'contains': ['11664.f1', '11664.br1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3092, -1, 3898, -1], 'generators': [840788568358445655731153962, 3228220166065152596642478793, 8871114994296129823979828933], 'label': '104976.cf.3888.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bs1', 'old_label': '3888.bo1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bo1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220817
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bp1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.be1', '1296.by1', '1296.cx1', '1944.r1', '1944.bo2', '1944.ci1'], 'contains': ['11664.g1', '11664.j1', '11664.l1', '11664.bt1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7509, -1, 9115, -1], 'generators': [62667541564046866724276933, 840788568358445655731153962, 8390891254698787264183353600], 'label': '104976.cf.3888.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.c1', 'old_label': '3888.bp1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bp1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 124220818
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id: 124220819
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bq1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bg1', '1296.by1', '1296.cx1'], 'contains': ['11664.g1', '11664.k1', '11664.l1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [7582, -1, 9269, -1], 'generators': [482222266538081038568344487, 840788568358445655731153962, 8390891254698787264183353600], 'label': '104976.cf.3888.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bi1', 'old_label': '3888.bq1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bq1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220820
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '104976.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.c1', '36.e1'], 'contains': ['216.j1', '216.w1', '216.cm1', '324.c1', '324.d1', '324.d2', '324.i1', '324.j1', '324.j2', '324.k1', '324.n1', '324.o1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [7877, -1, 5112, -1], 'generators': [2917428344709336821008036634, 94762, 3228220166064769884902033962, 840788568358445655731153962, 513163763437432968024113685, 47231787976478806878222835, 760039582886744], 'label': '104976.cf.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1', 'old_label': '108.d1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '972.891'}
id: 124220821
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bq2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bq2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bg1', '1296.by1', '1296.cx1', '1944.s1'], 'contains': ['11664.g1', '11664.k1', '11664.l1', '11664.bu1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7380, -1, 9309, -1], 'generators': [840788568358445655731153962, 10450703513970751317359981144, 3337395376140862758074261599], 'label': '104976.cf.3888.bq2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.p1', 'old_label': '3888.bq2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bq2', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 124220822
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.b1', '1296.b2', '1296.b3', '1296.d1', '1296.p2', '1296.ch1', '1944.dx1'], 'contains': ['11664.h1', '11664.i1', '11664.bw1', '11664.bw2', '11664.bw3'], 'core': '104976.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4919, -1, 3311, -1], 'generators': [3228220166065734606622251285, 2849517333873090, 2900600827632244120698141732], 'label': '104976.cf.3888.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.br1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.br1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220823
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.b1', '1296.b2', '1296.b3', '1296.e1', '1296.g2', '1296.g3', '1296.o1', '1296.o2', '1296.da1', '1944.dy1'], 'contains': ['11664.h1', '11664.h2', '11664.bx1', '11664.bx2', '11664.bx3', '11664.bx4', '11664.bx5'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2955, -1, 2187, -1], 'generators': [3228220166065734606622251285, 840788568359155809536196132, 2900600827630783704654796800], 'label': '104976.cf.3888.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.bs1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bs1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220824
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bs2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1296.b1', '1296.b2', '1296.e1', '1296.g1', '1296.g3', '1296.o1', '1296.o2', '1296.da1', '1944.dy2'], 'contains': ['11664.h1', '11664.h2', '11664.bx1', '11664.bx2', '11664.bx3', '11664.bx6'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [2943, -1, 2172, -1], 'generators': [3228220166065734606622251285, 840788568360280067521670921, 840788568359155809536196132], 'label': '104976.cf.3888.bs2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.bs2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bs2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220825
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.h1', '1296.bl1', '1296.ci1', '1944.cq1'], 'contains': ['11664.i1', '11664.j1', '11664.k1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [8231, -1, 7989, -1], 'generators': [840788568358445655731153962, 482222266537325402011862869, 3228220166065734606622101193], 'label': '104976.cf.3888.bt1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.bx1', 'old_label': '3888.bt1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bt1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 124220826
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.i1', '1296.bn1', '1296.cj1'], 'contains': ['11664.i1', '11664.m1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [8824, -1, 8033, -1], 'generators': [62667541565180870396858573, 840788568358445655731153962, 3228220166065734606622101193], 'label': '104976.cf.3888.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.z1', 'old_label': '3888.bu1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bu1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220827
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.j1', '1296.j2', '1296.bo1', '1296.ck2'], 'contains': ['11664.i1', '11664.n1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [8861, -1, 7639, -1], 'generators': [840788568358445655731153962, 3228220166065734606622101193, 3337395376139729254515677893], 'label': '104976.cf.3888.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ba1', 'old_label': '3888.bv1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bv1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220828
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.j2', '1296.bo1', '1296.ck1'], 'contains': ['11664.i1', '11664.n1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [8894, -1, 7625, -1], 'generators': [482222266537325402011816133, 840788568358445655731153962, 3228220166065734606622101193], 'label': '104976.cf.3888.bv2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.ba1', 'old_label': '3888.bv2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bv2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220829
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bw1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bq1', '1296.cd1', '1296.db1'], 'contains': ['11664.j1', '11664.o1', '11664.p1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [9779, -1, 9714, -1], 'generators': [840788568358445655731153962, 62667541564700804455344170, 7550102686341101648035181144], 'label': '104976.cf.3888.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bu1', 'old_label': '3888.bw1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bw1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220830
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bw2', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.bq1', '1296.cd1', '1296.db1', '1944.t1'], 'contains': ['11664.j1', '11664.o1', '11664.p1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [9770, -1, 9735, -1], 'generators': [62667541564046866724276933, 840788568358445655731153962, 10450703513970751317359673600], 'label': '104976.cf.3888.bw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1', 'old_label': '3888.bw2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bw2', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 124220831
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '104976.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.c1', '36.f1'], 'contains': ['216.n1', '216.z1', '216.co1', '324.c1', '324.e1', '324.h1', '324.n1', '324.p1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8042, -1, 5977, -1], 'generators': [138690, 3228220166065734606622251285, 2917428344709336821008036634, 840788568358445655731153962, 47231787976478806878222835, 2267507354250690, 2849517333811721], 'label': '104976.cf.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '108.e1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '2916.dz'}
id: 124220832
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bx1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1296.bs1', '1296.cd1', '1296.db1'], 'contains': ['11664.k1', '11664.o1', '11664.p1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [9787, -1, 9756, -1], 'generators': [840788568358445655731153962, 8390891254698787264183448362, 3337395376139293617808788173], 'label': '104976.cf.3888.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.bu1', 'old_label': '3888.bx1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.bx1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220833
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id: 124220834
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id: 124220835
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id: 124220836
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id: 124220837
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cg1', '1296.ch1', '1296.cl1', '1296.cp1', '1296.cz1', '1296.da1', '1944.eb1'], 'contains': ['11664.a1', '11664.h1', '11664.h2'], 'core': '11664.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7071, -1, 4088, -1], 'generators': [3228220166065734606622251285, 2267507354286793, 840788568358445655731153962], 'label': '104976.cf.3888.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.j1', 'old_label': '3888.cb1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cb1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 124220838
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id: 124220839
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.bg1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1296.cr1', '1296.cx1', '1296.cz1', '1296.dc1', '1944.ct1'], 'contains': ['11664.a1', '11664.l1'], 'core': '11664.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7299, -1, 8938, -1], 'generators': [3228220166065734606622251285, 840788568358445655731153962, 8375329513280704852408628933], 'label': '104976.cf.3888.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.x1', 'old_label': '3888.cd1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cd1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 124220840
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id: 124220841
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id: 124220842
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id: 124220843
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id: 124220844
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id: 124220845
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id: 124220846
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id: 124220847
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id: 124220848
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id: 124220849
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id: 124220850
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id: 124220851
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id: 124220852
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id: 124220853
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id: 124220854
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id: 124220855
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id: 124220856
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id: 124220857
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id: 124220858
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id: 124220859
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id: 124220860
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id: 124220861
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id: 124220862
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id: 124220863
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id: 124220864
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id: 124220865
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id: 124220866
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id: 124220867
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id: 124220868
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id: 124220869
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id: 124220870
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id: 124220871
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id: 124220872
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id: 124220873
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id: 124220874
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id: 124220875
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id: 124220876
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id: 124220877
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id: 124220878
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id: 124220879
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id: 124220880
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id: 124220881
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id: 124220882
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id: 124220883
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id: 124220884
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id: 124220885
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id: 124220886
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id: 124220887
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cr2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1296.m1', '1296.dl2', '1296.dw1'], 'contains': ['11664.u4', '11664.y1', '11664.z4'], 'core': '104976.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [8810, -1, 6650, -1], 'generators': [2094763166518129150911761685, 62667541565180870396824487, 840788568358445655731366744], 'label': '104976.cf.3888.cr2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.o1', 'old_label': '3888.cr2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cr2', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220888
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cr3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.m2', '1296.dl3', '1296.dl4', '1296.dw4'], 'contains': ['11664.u4', '11664.y2', '11664.z5', '11664.z6'], 'core': '104976.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [9129, -1, 6527, -1], 'generators': [482222266539414877919679494, 94762, 2900600827630409708907456521], 'label': '104976.cf.3888.cr3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.o2', 'old_label': '3888.cr3', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cr3', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220889
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id: 124220890
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cr5', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3888.r1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.m2', '1296.dl4', '1296.dl5', '1296.dw3'], 'contains': ['11664.u3', '11664.y2', '11664.z5', '11664.z6'], 'core': '104976.a1', 'coset_action_label': None, 'count': 2592, 'diagramx': [9120, -1, 6540, -1], 'generators': [840788568358445655731366744, 513163763438812819706593993, 3337395376139729254515677893], 'label': '104976.cf.3888.cr5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '432.o2', 'old_label': '3888.cr5', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cr5', 'subgroup_fusion': None, 'weyl_group': '9.2'}
id: 124220891
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id: 124220892
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id: 124220893
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id: 124220894
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id: 124220895
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id: 124220896
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cv2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1296.d1', '1296.n2', '1296.t2', '1296.de3', '1296.di1', '1296.ds2', '1296.ds3', '1296.dx1', '1944.ej2'], 'contains': ['11664.q2', '11664.t1', '11664.t3', '11664.bb1', '11664.bf2', '11664.bh1', '11664.bv3', '11664.bw1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [6530, -1, 3555, -1], 'generators': [3228220166063390033219308800, 840788568358445655731366744, 840788568358819651478571562], 'label': '104976.cf.3888.cv2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cv2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cv2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220897
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '104976.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.f1'], 'contains': ['216.d1', '216.bk1', '216.bs1', '324.n1', '324.r1', '324.u1', '324.w1'], 'core': '104976.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8154, -1, 5701, -1], 'generators': [2499866465849389267238693391, 62667541564046866724276933, 94762, 3228220166064769884902033962, 840788568358445655731153962, 47231787976478806878222835, 760039582886744], 'label': '104976.cf.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.k1', 'old_label': '108.k1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '972.816'}
id: 124220898
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.b1', '1296.e1', '1296.o2', '1296.de1', '1296.di2', '1296.ds1', '1296.ds2', '1296.dx1', '1296.dy1', '1296.dy2', '1944.ek1'], 'contains': ['11664.q1', '11664.t2', '11664.t3', '11664.u1', '11664.u2', '11664.ba1', '11664.bf2', '11664.bg2', '11664.bw1', '11664.bx2', '11664.bx3', '11664.bx4'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5775, -1, 3204, -1], 'generators': [2900600827631917176678989321, 3228220166063390033219308800, 2900600827630154613256011562], 'label': '104976.cf.3888.cw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cw1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cw1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220899
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cw2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.b2', '1296.e1', '1296.o1', '1296.o2', '1296.de1', '1296.di1', '1296.di3', '1296.ds2', '1296.ds3', '1296.dx1', '1296.dy2', '1944.ek2'], 'contains': ['11664.q1', '11664.q2', '11664.t1', '11664.u1', '11664.u2', '11664.ba1', '11664.bf1', '11664.bg2', '11664.bw3', '11664.bx1', '11664.bx2'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5803, -1, 3220, -1], 'generators': [3228220166063390033219308800, 2900600827632244120697913600, 840788568357685616148708132], 'label': '104976.cf.3888.cw2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cw2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cw2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220900
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cw3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.b3', '1296.e1', '1296.o1', '1296.o2', '1296.de4', '1296.di1', '1296.di3', '1296.ds1', '1296.ds3', '1296.dx1', '1296.dy1', '1296.dy2', '1944.ek3'], 'contains': ['11664.q1', '11664.q2', '11664.t2', '11664.t3', '11664.u1', '11664.u2', '11664.ba2', '11664.bf1', '11664.bg2', '11664.bw2', '11664.bx1', '11664.bx2', '11664.bx4'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5791, -1, 3250, -1], 'generators': [3228220166063390033219308800, 2900600827632244120697913600, 840788568360535133482490880], 'label': '104976.cf.3888.cw3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cw3', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cw3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220901
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.n1', '1296.n2', '1296.p1', '1296.t1', '1296.de3', '1296.di1', '1296.di2', '1296.dr1', '1296.dr4', '1296.ds1', '1296.ds3', '1296.dt4', '1944.el1'], 'contains': ['11664.r1', '11664.s1', '11664.t2', '11664.t3', '11664.u1', '11664.u3', '11664.bb1', '11664.bo2', '11664.bo3', '11664.bv1', '11664.bv3', '11664.bv4'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5205, -1, 3006, -1], 'generators': [513163763437432968024113685, 3228220166065734606622101193, 1646776838391935480529963562], 'label': '104976.cf.3888.cx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx1', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220902
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.n1', '1296.n2', '1296.p1', '1296.t1', '1296.de3', '1296.di1', '1296.di3', '1296.dr1', '1296.dr3', '1296.dr4', '1296.ds1', '1296.ds2', '1296.dt3', '1944.el2'], 'contains': ['11664.r1', '11664.s1', '11664.t1', '11664.t2', '11664.u2', '11664.u3', '11664.bb1', '11664.bo1', '11664.bo3', '11664.bv1', '11664.bv2', '11664.bv3', '11664.bv4'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5104, -1, 2991, -1], 'generators': [3228220166065734606622101193, 1646776838391935480529963562, 3228220166065734606621926400], 'label': '104976.cf.3888.cx2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx2', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220903
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.n1', '1296.n2', '1296.p2', '1296.t1', '1296.de1', '1296.di2', '1296.di3', '1296.dr4', '1296.ds2', '1296.ds3', '1296.dt2', '1944.el3'], 'contains': ['11664.r1', '11664.s1', '11664.t1', '11664.t3', '11664.v1', '11664.ba1', '11664.bo1', '11664.bo3', '11664.bv4', '11664.bw2', '11664.bw3'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4877, -1, 3128, -1], 'generators': [504943931116800, 3228220166065734606622101193, 1646776838391935480529963562], 'label': '104976.cf.3888.cx3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx3', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220904
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1296.n1', '1296.n2', '1296.p2', '1296.t1', '1296.de4', '1296.di1', '1296.di3', '1296.dr2', '1296.dr4', '1296.ds2', '1296.ds3', '1296.dt1', '1944.el4'], 'contains': ['11664.r1', '11664.s1', '11664.t1', '11664.t2', '11664.v1', '11664.ba2', '11664.bo2', '11664.bo3', '11664.bv3', '11664.bw2', '11664.bw3'], 'core': '104976.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5097, -1, 3037, -1], 'generators': [3228220166062885089288516885, 3228220166065734606622101193, 1646776838391935480529963562], 'label': '104976.cf.3888.cx4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx4', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220905
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx5', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1296.n1', '1296.p1', '1296.t2', '1296.de2', '1296.di2', '1296.dr1', '1296.dr2', '1296.ds3', '1296.dt3', '1944.el5'], 'contains': ['11664.r2', '11664.s1', '11664.t3', '11664.u2', '11664.u4', '11664.bb1', '11664.bo2', '11664.bv1', '11664.bv3'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [5159, -1, 3021, -1], 'generators': [3228220166063390033219403562, 513163763437432968024113685, 1646776838391935480529963562], 'label': '104976.cf.3888.cx5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx5', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx5', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 124220906
{'ambient': '104976.cf', 'aut_centralizer_order': None, 'aut_label': '3888.cx6', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1296.n1', '1296.p1', '1296.t2', '1296.de2', '1296.di3', '1296.dr2', '1296.dr3', '1296.ds2', '1296.dt4', '1944.el6'], 'contains': ['11664.r2', '11664.s1', '11664.t1', '11664.u1', '11664.u4', '11664.bb1', '11664.bo1', '11664.bv2', '11664.bv3'], 'core': '104976.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [5379, -1, 3189, -1], 'generators': [3228220166063390033219403562, 77321, 1646776838391935480529963562], 'label': '104976.cf.3888.cx6', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1', 'old_label': '3888.cx6', 'projective_image': '104976.cf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.cx6', 'subgroup_fusion': None, 'weyl_group': '2.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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