LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-09-23T04:47:58.232069

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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 128, 'aut_gen_orders': [128, 32, 16, 16], 'aut_gens': [[1, 2], [211, 18], [209, 202], [137, 110], [55, 158]], 'aut_group': None, 'aut_hash': 1312969192172081052, 'aut_nilpotency_class': 7, 'aut_nilpotent': True, 'aut_order': 8192, 'aut_permdeg': 128, 'aut_perms': [275115721551631810792547138779931186819003096118118568124239482384756895780617236954670838475589823750270589523902792597412996834095899227061297572255946981469125689702541221377023287965880105366211119835164604552125, 14475204506687777329505562405524745899439479713396571710343838490781746584468087363370350231675241849499551903107943565720417036228694194654188206831078671519119932082034576401091101938134175135620589080299571882009, 7544274880928614416210163682490784594310190131059006789142587496481904748413690718533898212426528874476199945605768505344058126619356874555391795007358052007237188922896813981565309689104683419917585014562590255635, 125142573214468452141406217526353103328089946763977375189324255027605928631409039834246958668101729261036641332402937930968596185714951439694100030914375813488263320309864537083999100055510874500644090108347811552692], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 64, 2, 1], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1], [64, 2, 16, 1], [128, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{64}.C_{32}.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 64, 'autcentquo_group': '2048.ctr', 'autcentquo_hash': 5971394143399402126, 'autcentquo_nilpotent': True, 'autcentquo_order': 2048, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{64}:C_{16}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [4, 2, 1], [4, 64, 2], [8, 2, 2], [16, 2, 4], [32, 2, 8], [64, 2, 16], [128, 2, 32]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.161', 'commutator_count': 1, 'commutator_label': '64.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 541, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 2, 1, 1], [4, 64, 1, 2], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1], [64, 2, 16, 1], [128, 2, 32, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 128, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[2, -1, 32]], 'familial': True, 'frattini_label': '64.1', 'frattini_quotient': '4.2', 'hash': 541, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 64, 'inner_gen_orders': [2, 64], 'inner_gens': [[1, 254], [5, 2]], 'inner_hash': 161, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'D_{64}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 64, 'irrQ_dim': 128, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 63]], 'label': '256.541', 'linC_count': 32, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 64, 'linQ_degree_count': 1, 'linQ_dim': 128, 'linQ_dim_count': 1, 'linR_count': 32, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'Q256', 'ngens': 2, 'nilpotency_class': 7, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 67, 'number_divisions': 10, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 21, 'number_subgroups': 135, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 1], [4, 130], [8, 4], [16, 8], [32, 16], [64, 32], [128, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 32, 'outer_gen_orders': [2, 32], 'outer_gen_pows': [2, 0], 'outer_gens': [[3, 2], [1, 10]], 'outer_group': '64.50', 'outer_hash': 50, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 34, 'outer_perms': [8683317618811886495518194401280000000, 9594892858980471636264762118745970], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{32}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 256, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 1], [8, 1], [16, 1], [32, 1], [64, 1]], 'representations': {'PC': {'code': 2754453629584150573251214897832863473663, 'gens': [1, 2], 'pres': [8, -2, 2, -2, -2, -2, -2, -2, -2, 1024, 4065, 41, 6050, 66, 7939, 91, 9604, 116, 10757, 141, 10758, 166]}, 'Lie': [{'d': 2, 'q': 127, 'gens': [258117805, 258096384, 2495930, 99791683], 'family': 'CSOMinus'}], 'GLFp': {'d': 2, 'p': 127, 'gens': [59639806, 169454150]}, 'Perm': {'d': 256, 'gens': [433948434038085987162794147752658741368261713177308988242701445352284156151212856997754724040919481329638616521643367417407783039686461830495609977104933199397032245820257006282921602096264075232009388138170785155012213129296275299468936527466258860346201717750037540371876064626157518686766315821326063095145681717337562876202821312769020852403214320610590886541111872488180948562039701361740628992529549166564867481195193142258353617276449487739873955856164115053793740062720000000000000000000000000000000, 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20184207146113838373983466293884177291501146987831737786662237237143510365928561634205669417574729672461492498325195982930210613486732259167617455715079005596093929147695514851771938539253615062271736287111050226946363448909989127830779377549980315551528543466199909012555027498060074362232811468962207323796644357522876916649213533683897328513667223137967420531543955055115097743341980550785788812428309666150495169900331520216094483527354372781011532603168396129551467295730853539223530257550353982780856, 10078833239082355431497060352913373620207642413213184923888708759746132673602743795708042005653580362409343313138949533082064327243361834124405567639679209173025106806212793835194426946454190208298539837604884572591995343252462730201403838652536923421632065672323135265558898590250801540789582907201769706445851039464201794112785436716778915673090331019609233149295042243793255039767009308542050885549696714846268856561666748775450907991676164067298663971638700874603127471963849716741182782161508801942982, 3350902420354365371564525298448371370505108668544300291100163913264232846212281477037719064972917928856214257057673157334077993889285203243784519416297312690252930501076691681544236055260414001434389036569172503587027573119555266614535384674679063296535037642598843301212140611573899968563398563573705534745984971443794284627828064672867038164029313764066669561929851842598468362553761789151702761749666523672190192739643808874374065560200588309080006450788729187610131268709401146867497898583379392681647]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_{256}', 'transitive_degree': 256, '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: 109462494
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 541, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
id: 109462505
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 541, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
id: 109462516
{'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 3, 'group_counter': 541, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 64, 'size': 2}
id: 109462527
{'aut_label': '4B', 'centralizer': '64.b1.a1', 'counter': 4, 'group_counter': 541, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [2], 'representative': 135, 'size': 64}
id: 109462538
{'aut_label': '4B', 'centralizer': '64.b1.b1', 'counter': 5, 'group_counter': 541, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [2], 'representative': 17, 'size': 64}
id: 109462549
{'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 6, 'group_counter': 541, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [3], 'representative': 32, 'size': 2}
id: 109462558
{'aut_label': '8A1', 'centralizer': '2.b1.a1', 'counter': 7, 'group_counter': 541, 'group_order': 256, 'label': '8A3', 'order': 8, 'powers': [3], 'representative': 96, 'size': 2}
id: 109462559
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 541, 'group_order': 256, 'label': '16A1', 'order': 16, 'powers': [6], 'representative': 16, 'size': 2}
id: 109462560
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 9, 'group_counter': 541, 'group_order': 256, 'label': '16A3', 'order': 16, 'powers': [7], 'representative': 48, 'size': 2}
id: 109462495
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 10, 'group_counter': 541, 'group_order': 256, 'label': '16A5', 'order': 16, 'powers': [7], 'representative': 80, 'size': 2}
id: 109462496
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 11, 'group_counter': 541, 'group_order': 256, 'label': '16A7', 'order': 16, 'powers': [6], 'representative': 112, 'size': 2}
id: 109462497
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 541, 'group_order': 256, 'label': '32A1', 'order': 32, 'powers': [8], 'representative': 8, 'size': 2}
id: 109462498
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 13, 'group_counter': 541, 'group_order': 256, 'label': '32A3', 'order': 32, 'powers': [9], 'representative': 24, 'size': 2}
id: 109462499
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 541, 'group_order': 256, 'label': '32A5', 'order': 32, 'powers': [10], 'representative': 40, 'size': 2}
id: 109462500
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 541, 'group_order': 256, 'label': '32A7', 'order': 32, 'powers': [11], 'representative': 56, 'size': 2}
id: 109462501
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 541, 'group_order': 256, 'label': '32A9', 'order': 32, 'powers': [11], 'representative': 72, 'size': 2}
id: 109462502
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 17, 'group_counter': 541, 'group_order': 256, 'label': '32A11', 'order': 32, 'powers': [10], 'representative': 88, 'size': 2}
id: 109462503
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 541, 'group_order': 256, 'label': '32A13', 'order': 32, 'powers': [9], 'representative': 104, 'size': 2}
id: 109462504
{'aut_label': '32A1', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 541, 'group_order': 256, 'label': '32A15', 'order': 32, 'powers': [8], 'representative': 120, 'size': 2}
id: 109462506
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 541, 'group_order': 256, 'label': '64A1', 'order': 64, 'powers': [12], 'representative': 4, 'size': 2}
id: 109462507
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 21, 'group_counter': 541, 'group_order': 256, 'label': '64A3', 'order': 64, 'powers': [13], 'representative': 12, 'size': 2}
id: 109462508
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 22, 'group_counter': 541, 'group_order': 256, 'label': '64A5', 'order': 64, 'powers': [14], 'representative': 20, 'size': 2}
id: 109462509
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 23, 'group_counter': 541, 'group_order': 256, 'label': '64A7', 'order': 64, 'powers': [15], 'representative': 28, 'size': 2}
id: 109462510
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 24, 'group_counter': 541, 'group_order': 256, 'label': '64A9', 'order': 64, 'powers': [16], 'representative': 36, 'size': 2}
id: 109462511
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 25, 'group_counter': 541, 'group_order': 256, 'label': '64A11', 'order': 64, 'powers': [17], 'representative': 44, 'size': 2}
id: 109462512
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 26, 'group_counter': 541, 'group_order': 256, 'label': '64A13', 'order': 64, 'powers': [18], 'representative': 52, 'size': 2}
id: 109462513
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 27, 'group_counter': 541, 'group_order': 256, 'label': '64A15', 'order': 64, 'powers': [19], 'representative': 60, 'size': 2}
id: 109462514
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 28, 'group_counter': 541, 'group_order': 256, 'label': '64A17', 'order': 64, 'powers': [19], 'representative': 68, 'size': 2}
id: 109462515
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 541, 'group_order': 256, 'label': '64A19', 'order': 64, 'powers': [18], 'representative': 76, 'size': 2}
id: 109462517
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 541, 'group_order': 256, 'label': '64A21', 'order': 64, 'powers': [17], 'representative': 84, 'size': 2}
id: 109462518
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 31, 'group_counter': 541, 'group_order': 256, 'label': '64A23', 'order': 64, 'powers': [16], 'representative': 92, 'size': 2}
id: 109462519
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 541, 'group_order': 256, 'label': '64A25', 'order': 64, 'powers': [15], 'representative': 100, 'size': 2}
id: 109462520
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 541, 'group_order': 256, 'label': '64A27', 'order': 64, 'powers': [14], 'representative': 108, 'size': 2}
id: 109462521
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 541, 'group_order': 256, 'label': '64A29', 'order': 64, 'powers': [13], 'representative': 116, 'size': 2}
id: 109462522
{'aut_label': '64A1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 541, 'group_order': 256, 'label': '64A31', 'order': 64, 'powers': [12], 'representative': 124, 'size': 2}
id: 109462523
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 541, 'group_order': 256, 'label': '128A1', 'order': 128, 'powers': [20], 'representative': 2, 'size': 2}
id: 109462524
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 37, 'group_counter': 541, 'group_order': 256, 'label': '128A3', 'order': 128, 'powers': [21], 'representative': 6, 'size': 2}
id: 109462525
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 541, 'group_order': 256, 'label': '128A5', 'order': 128, 'powers': [22], 'representative': 10, 'size': 2}
id: 109462526
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 541, 'group_order': 256, 'label': '128A7', 'order': 128, 'powers': [23], 'representative': 14, 'size': 2}
id: 109462528
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 541, 'group_order': 256, 'label': '128A9', 'order': 128, 'powers': [24], 'representative': 18, 'size': 2}
id: 109462529
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 541, 'group_order': 256, 'label': '128A11', 'order': 128, 'powers': [25], 'representative': 22, 'size': 2}
id: 109462530
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 42, 'group_counter': 541, 'group_order': 256, 'label': '128A13', 'order': 128, 'powers': [26], 'representative': 26, 'size': 2}
id: 109462531
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 43, 'group_counter': 541, 'group_order': 256, 'label': '128A15', 'order': 128, 'powers': [27], 'representative': 226, 'size': 2}
id: 109462532
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 44, 'group_counter': 541, 'group_order': 256, 'label': '128A17', 'order': 128, 'powers': [28], 'representative': 34, 'size': 2}
id: 109462533
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 45, 'group_counter': 541, 'group_order': 256, 'label': '128A19', 'order': 128, 'powers': [29], 'representative': 38, 'size': 2}
id: 109462534
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 46, 'group_counter': 541, 'group_order': 256, 'label': '128A21', 'order': 128, 'powers': [30], 'representative': 42, 'size': 2}
id: 109462535
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 47, 'group_counter': 541, 'group_order': 256, 'label': '128A23', 'order': 128, 'powers': [31], 'representative': 210, 'size': 2}
id: 109462536
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 48, 'group_counter': 541, 'group_order': 256, 'label': '128A25', 'order': 128, 'powers': [32], 'representative': 50, 'size': 2}
id: 109462537
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 49, 'group_counter': 541, 'group_order': 256, 'label': '128A27', 'order': 128, 'powers': [33], 'representative': 202, 'size': 2}
id: 109462539
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 50, 'group_counter': 541, 'group_order': 256, 'label': '128A29', 'order': 128, 'powers': [34], 'representative': 58, 'size': 2}
id: 109462540
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 51, 'group_counter': 541, 'group_order': 256, 'label': '128A31', 'order': 128, 'powers': [35], 'representative': 194, 'size': 2}
id: 109462541
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 52, 'group_counter': 541, 'group_order': 256, 'label': '128A33', 'order': 128, 'powers': [35], 'representative': 66, 'size': 2}
id: 109462542
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 53, 'group_counter': 541, 'group_order': 256, 'label': '128A35', 'order': 128, 'powers': [34], 'representative': 70, 'size': 2}
id: 109462543
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 54, 'group_counter': 541, 'group_order': 256, 'label': '128A37', 'order': 128, 'powers': [33], 'representative': 74, 'size': 2}
id: 109462544
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 55, 'group_counter': 541, 'group_order': 256, 'label': '128A39', 'order': 128, 'powers': [32], 'representative': 178, 'size': 2}
id: 109462545
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 541, 'group_order': 256, 'label': '128A41', 'order': 128, 'powers': [31], 'representative': 82, 'size': 2}
id: 109462546
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 541, 'group_order': 256, 'label': '128A43', 'order': 128, 'powers': [30], 'representative': 170, 'size': 2}
id: 109462547
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 541, 'group_order': 256, 'label': '128A45', 'order': 128, 'powers': [29], 'representative': 90, 'size': 2}
id: 109462548
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 541, 'group_order': 256, 'label': '128A47', 'order': 128, 'powers': [28], 'representative': 162, 'size': 2}
id: 109462550
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 60, 'group_counter': 541, 'group_order': 256, 'label': '128A49', 'order': 128, 'powers': [27], 'representative': 98, 'size': 2}
id: 109462551
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 541, 'group_order': 256, 'label': '128A51', 'order': 128, 'powers': [26], 'representative': 154, 'size': 2}
id: 109462552
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 541, 'group_order': 256, 'label': '128A53', 'order': 128, 'powers': [25], 'representative': 106, 'size': 2}
id: 109462553
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 63, 'group_counter': 541, 'group_order': 256, 'label': '128A55', 'order': 128, 'powers': [24], 'representative': 146, 'size': 2}
id: 109462554
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 64, 'group_counter': 541, 'group_order': 256, 'label': '128A57', 'order': 128, 'powers': [23], 'representative': 114, 'size': 2}
id: 109462555
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 65, 'group_counter': 541, 'group_order': 256, 'label': '128A59', 'order': 128, 'powers': [22], 'representative': 138, 'size': 2}
id: 109462556
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 66, 'group_counter': 541, 'group_order': 256, 'label': '128A61', 'order': 128, 'powers': [21], 'representative': 134, 'size': 2}
id: 109462557
{'aut_label': '128A1', 'centralizer': '2.b1.a1', 'counter': 67, 'group_counter': 541, 'group_order': 256, 'label': '128A63', 'order': 128, 'powers': [20], 'representative': 130, 'size': 2}

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: 4285469
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4285471
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4285472
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4285473
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4285474
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4285475
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2b', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4285476
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2c', 'multiplicity': 4, 'nt': [16, 56], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 0, 8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 4285477
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2d', 'multiplicity': 8, 'nt': [32, 374], 'qdim': 16, 'qvalues': [16, 16, 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4285478
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2e', 'multiplicity': 16, 'nt': [64, 0], 'qdim': 32, 'qvalues': [32, 32, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 4285470
{'cdim': 2, 'counter': 10, 'faithful': True, 'group': '256.541', 'group_order': 256, 'image': None, 'label': '256.541.2f', 'multiplicity': 32, 'nt': [256, 0], 'qdim': 64, 'qvalues': [64, -64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}

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: 6370132
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.541.1a', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 6370143
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.541.1b', '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]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 6370154
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 128, 'label': '256.541.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6370165
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.541.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6370176
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 32, 'label': '256.541.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 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]], [[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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 6370187
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 6, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 16, 'label': '256.541.2b1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[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: 6370196
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 16, 'label': '256.541.2b2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-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: 6370197
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 8, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.541.2c1', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]]]}
id: 6370198
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 9, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.541.2c2', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]]]}
id: 6370133
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 10, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.541.2c3', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
id: 6370134
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 16, 'counter': 11, 'cyclotomic_n': 16, 'dim': 2, 'faithful': False, 'field': [2, 0, -4, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '32.18', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1.a1', 'kernel_order': 8, 'label': '256.541.2c4', 'nt': [16, 56], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
id: 6370135
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 12, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d1', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]]]}
id: 6370136
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 13, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d2', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]]]}
id: 6370137
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 14, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d3', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]]]}
id: 6370138
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 15, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d4', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]]]}
id: 6370139
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d5', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]]]}
id: 6370140
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d6', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]]]}
id: 6370141
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d7', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
id: 6370142
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [2, 0, -16, 0, 20, 0, -8, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '64.52', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 4, 'label': '256.541.2d8', 'nt': [32, 374], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
id: 6370144
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 20, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e1', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[-1, 14], [-1, -14]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[1, 14], [1, -14]], [[-1, 7], [-1, -7]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[-1, 15], [-1, -15]], [[1, 3], [1, -3]], [[-1, 11], [-1, -11]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[-1, 13], [-1, -13]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 5], [1, -5]], [[1, 15], [1, -15]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[1, 13], [1, -13]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 15], [-1, -15]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[1, 15], [1, -15]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 7], [-1, -7]]]}
id: 6370153
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 29, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e10', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[-1, 12], [-1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[-1, 14], [-1, -14]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 5], [1, -5]], [[1, 15], [1, -15]], [[-1, 15], [-1, -15]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 15], [-1, -15]], [[1, 11], [1, -11]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[1, 13], [1, -13]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[1, 15], [1, -15]], [[1, 5], [1, -5]]]}
id: 6370155
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id: 6370156
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id: 6370157
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id: 6370158
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e14', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[-1, 6], [-1, -6]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 14], [1, -14]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 14], [1, -14]], [[1, 6], [1, -6]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 11], [-1, -11]], [[1, 15], [1, -15]], [[-1, 9], [-1, -9]], [[-1, 13], [-1, -13]], [[-1, 13], [-1, -13]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 15], [-1, -15]], [[1, 13], [1, -13]], [[-1, 7], [-1, -7]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 7], [1, -7]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 11], [-1, -11]], [[1, 15], [1, -15]], [[-1, 15], [-1, -15]], [[-1, 1], [-1, -1]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[1, 13], [1, -13]], [[1, 9], [1, -9]], [[1, 3], [1, -3]]]}
id: 6370159
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e15', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 14], [1, -14]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 14], [-1, -14]], [[-1, 6], [-1, -6]], [[-1, 13], [-1, -13]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[1, 9], [1, -9]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[-1, 15], [-1, -15]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 5], [-1, -5]], [[1, 11], [1, -11]], [[1, 13], [1, -13]], [[-1, 9], [-1, -9]], [[-1, 9], [-1, -9]], [[1, 15], [1, -15]], [[1, 15], [1, -15]], [[-1, 11], [-1, -11]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 15], [-1, -15]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[-1, 13], [-1, -13]]]}
id: 6370160
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e16', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 12], [1, -12]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[1, 12], [1, -12]], [[-1, 12], [-1, -12]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 12], [-1, -12]], [[1, 6], [1, -6]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 14], [1, -14]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 14], [-1, -14]], [[-1, 6], [-1, -6]], [[1, 13], [1, -13]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[-1, 9], [-1, -9]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[1, 7], [1, -7]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[1, 15], [1, -15]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 5], [1, -5]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]], [[1, 9], [1, -9]], [[1, 9], [1, -9]], [[-1, 15], [-1, -15]], [[-1, 15], [-1, -15]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 15], [1, -15]], [[1, 5], [1, -5]], [[1, 11], [1, -11]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[1, 13], [1, -13]]]}
id: 6370145
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id: 6370146
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id: 6370147
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id: 6370148
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e5', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 14], [1, -14]], [[-1, 14], [-1, -14]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 13], [-1, -13]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 3], [1, -3]], [[-1, 15], [-1, -15]], [[-1, 15], [-1, -15]], [[1, 1], [1, -1]], [[-1, 11], [-1, -11]], [[1, 5], [1, -5]], [[1, 15], [1, -15]], [[-1, 13], [-1, -13]], [[1, 7], [1, -7]], [[1, 9], [1, -9]], [[1, 1], [1, -1]], [[1, 13], [1, -13]], [[1, 13], [1, -13]], [[1, 11], [1, -11]], [[1, 11], [1, -11]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 7], [-1, -7]], [[-1, 5], [-1, -5]], [[1, 5], [1, -5]], [[-1, 11], [-1, -11]], [[1, 7], [1, -7]], [[-1, 9], [-1, -9]], [[1, 15], [1, -15]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
id: 6370149
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e6', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 14], [-1, -14]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 10], [-1, -10]], [[-1, 2], [-1, -2]], [[1, 14], [1, -14]], [[-1, 14], [-1, -14]], [[1, 6], [1, -6]], [[-1, 10], [-1, -10]], [[1, 10], [1, -10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 13], [1, -13]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 3], [-1, -3]], [[1, 15], [1, -15]], [[1, 15], [1, -15]], [[-1, 1], [-1, -1]], [[1, 11], [1, -11]], [[-1, 5], [-1, -5]], [[-1, 15], [-1, -15]], [[1, 13], [1, -13]], [[-1, 7], [-1, -7]], [[-1, 9], [-1, -9]], [[-1, 1], [-1, -1]], [[-1, 13], [-1, -13]], [[-1, 13], [-1, -13]], [[-1, 11], [-1, -11]], [[-1, 11], [-1, -11]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 7], [1, -7]], [[1, 5], [1, -5]], [[-1, 5], [-1, -5]], [[1, 11], [1, -11]], [[-1, 7], [-1, -7]], [[1, 9], [1, -9]], [[-1, 15], [-1, -15]], [[1, 3], [1, -3]], [[1, 1], [1, -1]]]}
id: 6370150
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e7', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 14], [1, -14]], [[-1, 14], [-1, -14]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 14], [-1, -14]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 15], [-1, -15]], [[1, 13], [1, -13]], [[-1, 13], [-1, -13]], [[-1, 3], [-1, -3]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[-1, 13], [-1, -13]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 15], [1, -15]], [[1, 5], [1, -5]], [[1, 11], [1, -11]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 9], [-1, -9]], [[1, 7], [1, -7]], [[1, 15], [1, -15]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 7], [-1, -7]], [[1, 7], [1, -7]], [[1, 9], [1, -9]], [[-1, 11], [-1, -11]], [[1, 11], [1, -11]], [[1, 5], [1, -5]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 1], [-1, -1]], [[1, 13], [1, -13]], [[-1, 15], [-1, -15]]]}
id: 6370151
{'center': '64.a1.a1', 'center_index': 64, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 64, 'dim': 2, 'faithful': False, 'field': [2, 0, -64, 0, 336, 0, -672, 0, 660, 0, -352, 0, 104, 0, -16, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '128.161', 'image_order': 128, 'indicator': 1, 'kernel': '128.a1.a1', 'kernel_order': 2, 'label': '256.541.2e8', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 8], [-1, -8]], [[1, 8], [1, -8]], [[1, 8], [1, -8]], [[-1, 8], [-1, -8]], [[1, 4], [1, -4]], [[1, 12], [1, -12]], [[1, 12], [1, -12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 12], [-1, -12]], [[-1, 12], [-1, -12]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 10], [-1, -10]], [[1, 14], [1, -14]], [[-1, 14], [-1, -14]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 10], [1, -10]], [[1, 2], [1, -2]], [[-1, 14], [-1, -14]], [[1, 14], [1, -14]], [[-1, 6], [-1, -6]], [[1, 10], [1, -10]], [[-1, 10], [-1, -10]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[1, 15], [1, -15]], [[-1, 13], [-1, -13]], [[1, 13], [1, -13]], [[1, 3], [1, -3]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[1, 13], [1, -13]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 15], [-1, -15]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 9], [1, -9]], [[-1, 7], [-1, -7]], [[-1, 15], [-1, -15]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 7], [1, -7]], [[-1, 7], [-1, -7]], [[-1, 9], [-1, -9]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[-1, 5], [-1, -5]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[1, 1], [1, -1]], [[-1, 13], [-1, -13]], [[1, 15], [1, -15]]]}
id: 6370152
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id: 6370161
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id: 6370171
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id: 6370172
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id: 6370173
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id: 6370174
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id: 6370175
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id: 6370177
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id: 6370178
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id: 6370179
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id: 6370180
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id: 6370181
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id: 6370162
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id: 6370182
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id: 6370183
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id: 6370184
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id: 6370185
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id: 6370186
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id: 6370188
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id: 6370189
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id: 6370190
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id: 6370191
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id: 6370192
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id: 6370163
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id: 6370193
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id: 6370194
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id: 6370195
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id: 6370164
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id: 6370166
{'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 128, 'dim': 2, 'faithful': True, 'field': [2, 0, -256, 0, 5440, 0, -45696, 0, 201552, 0, -537472, 0, 940576, 0, -1136960, 0, 980628, 0, -615296, 0, 283360, 0, -95680, 0, 23400, 0, -4032, 0, 464, 0, -32, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '256.541', 'image_order': 256, 'indicator': -1, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.541.2f5', 'nt': [256, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[1, 16], [1, -16]], [[-1, 8], [-1, -8]], [[1, 24], [1, -24]], [[-1, 24], [-1, -24]], [[1, 8], [1, -8]], [[1, 20], [1, -20]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 20], [-1, -20]], [[1, 12], [1, -12]], [[-1, 28], [-1, -28]], [[1, 28], [1, -28]], [[-1, 12], [-1, -12]], [[-1, 22], [-1, -22]], [[1, 30], [1, -30]], [[1, 14], [1, -14]], [[-1, 26], [-1, -26]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 18], [1, -18]], [[1, 22], [1, -22]], [[1, 6], [1, -6]], [[1, 26], [1, -26]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 5], [-1, -5]], [[-1, 15], [-1, -15]], [[1, 17], [1, -17]], [[-1, 1], [-1, -1]], [[1, 29], [1, -29]], [[1, 25], [1, -25]], [[-1, 17], [-1, -17]], [[-1, 11], [-1, -11]], [[1, 11], [1, -11]], [[1, 27], [1, -27]], [[-1, 9], [-1, -9]], [[-1, 7], [-1, -7]], [[-1, 21], [-1, -21]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 13], [-1, -13]], [[-1, 27], [-1, -27]], [[-1, 31], [-1, -31]], [[1, 31], [1, -31]], [[-1, 23], [-1, -23]], [[1, 23], [1, -23]], [[-1, 19], [-1, -19]], [[1, 13], [1, -13]], [[-1, 29], [-1, -29]], [[-1, 25], [-1, -25]], [[1, 7], [1, -7]], [[1, 9], [1, -9]], [[1, 3], [1, -3]], [[1, 19], [1, -19]], [[1, 21], [1, -21]], [[1, 15], [1, -15]], [[1, 5], [1, -5]]]}
id: 6370167
{'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 128, 'dim': 2, 'faithful': True, 'field': [2, 0, -256, 0, 5440, 0, -45696, 0, 201552, 0, -537472, 0, 940576, 0, -1136960, 0, 980628, 0, -615296, 0, 283360, 0, -95680, 0, 23400, 0, -4032, 0, 464, 0, -32, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '256.541', 'image_order': 256, 'indicator': -1, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.541.2f6', 'nt': [256, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[1, 16], [1, -16]], [[-1, 8], [-1, -8]], [[1, 24], [1, -24]], [[-1, 24], [-1, -24]], [[1, 8], [1, -8]], [[1, 20], [1, -20]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 20], [-1, -20]], [[1, 12], [1, -12]], [[-1, 28], [-1, -28]], [[1, 28], [1, -28]], [[-1, 12], [-1, -12]], [[-1, 22], [-1, -22]], [[1, 30], [1, -30]], [[1, 14], [1, -14]], [[-1, 26], [-1, -26]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 18], [1, -18]], [[1, 22], [1, -22]], [[1, 6], [1, -6]], [[1, 26], [1, -26]], [[-1, 30], [-1, -30]], [[-1, 18], [-1, -18]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[1, 5], [1, -5]], [[1, 15], [1, -15]], [[-1, 17], [-1, -17]], [[1, 1], [1, -1]], [[-1, 29], [-1, -29]], [[-1, 25], [-1, -25]], [[1, 17], [1, -17]], [[1, 11], [1, -11]], [[-1, 11], [-1, -11]], [[-1, 27], [-1, -27]], [[1, 9], [1, -9]], [[1, 7], [1, -7]], [[1, 21], [1, -21]], [[-1, 1], [-1, -1]], [[1, 3], [1, -3]], [[1, 13], [1, -13]], [[1, 27], [1, -27]], [[1, 31], [1, -31]], [[-1, 31], [-1, -31]], [[1, 23], [1, -23]], [[-1, 23], [-1, -23]], [[1, 19], [1, -19]], [[-1, 13], [-1, -13]], [[1, 29], [1, -29]], [[1, 25], [1, -25]], [[-1, 7], [-1, -7]], [[-1, 9], [-1, -9]], [[-1, 3], [-1, -3]], [[-1, 19], [-1, -19]], [[-1, 21], [-1, -21]], [[-1, 15], [-1, -15]], [[-1, 5], [-1, -5]]]}
id: 6370168
{'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 128, 'dim': 2, 'faithful': True, 'field': [2, 0, -256, 0, 5440, 0, -45696, 0, 201552, 0, -537472, 0, 940576, 0, -1136960, 0, 980628, 0, -615296, 0, 283360, 0, -95680, 0, 23400, 0, -4032, 0, 464, 0, -32, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '256.541', 'image_order': 256, 'indicator': -1, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.541.2f7', 'nt': [256, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[1, 16], [1, -16]], [[-1, 8], [-1, -8]], [[1, 24], [1, -24]], [[-1, 24], [-1, -24]], [[1, 8], [1, -8]], [[1, 20], [1, -20]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 20], [-1, -20]], [[1, 12], [1, -12]], [[-1, 28], [-1, -28]], [[1, 28], [1, -28]], [[-1, 12], [-1, -12]], [[1, 22], [1, -22]], [[-1, 30], [-1, -30]], [[-1, 14], [-1, -14]], [[1, 26], [1, -26]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 18], [-1, -18]], [[-1, 22], [-1, -22]], [[-1, 6], [-1, -6]], [[-1, 26], [-1, -26]], [[1, 30], [1, -30]], [[1, 18], [1, -18]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[-1, 27], [-1, -27]], [[1, 17], [1, -17]], [[1, 15], [1, -15]], [[-1, 31], [-1, -31]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[-1, 15], [-1, -15]], [[1, 21], [1, -21]], [[-1, 21], [-1, -21]], [[-1, 5], [-1, -5]], [[-1, 23], [-1, -23]], [[1, 25], [1, -25]], [[-1, 11], [-1, -11]], [[1, 31], [1, -31]], [[1, 29], [1, -29]], [[-1, 19], [-1, -19]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[1, 13], [1, -13]], [[1, 19], [1, -19]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[-1, 25], [-1, -25]], [[1, 23], [1, -23]], [[-1, 29], [-1, -29]], [[-1, 13], [-1, -13]], [[1, 11], [1, -11]], [[-1, 17], [-1, -17]], [[1, 27], [1, -27]]]}
id: 6370169
{'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 128, 'dim': 2, 'faithful': True, 'field': [2, 0, -256, 0, 5440, 0, -45696, 0, 201552, 0, -537472, 0, 940576, 0, -1136960, 0, 980628, 0, -615296, 0, 283360, 0, -95680, 0, 23400, 0, -4032, 0, 464, 0, -32, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '256.541', 'image_order': 256, 'indicator': -1, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.541.2f8', 'nt': [256, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[1, 16], [1, -16]], [[-1, 8], [-1, -8]], [[1, 24], [1, -24]], [[-1, 24], [-1, -24]], [[1, 8], [1, -8]], [[1, 20], [1, -20]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[-1, 20], [-1, -20]], [[1, 12], [1, -12]], [[-1, 28], [-1, -28]], [[1, 28], [1, -28]], [[-1, 12], [-1, -12]], [[1, 22], [1, -22]], [[-1, 30], [-1, -30]], [[-1, 14], [-1, -14]], [[1, 26], [1, -26]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 10], [-1, -10]], [[-1, 18], [-1, -18]], [[-1, 22], [-1, -22]], [[-1, 6], [-1, -6]], [[-1, 26], [-1, -26]], [[1, 30], [1, -30]], [[1, 18], [1, -18]], [[1, 14], [1, -14]], [[1, 2], [1, -2]], [[1, 10], [1, -10]], [[1, 27], [1, -27]], [[-1, 17], [-1, -17]], [[-1, 15], [-1, -15]], [[1, 31], [1, -31]], [[-1, 3], [-1, -3]], [[-1, 7], [-1, -7]], [[1, 15], [1, -15]], [[-1, 21], [-1, -21]], [[1, 21], [1, -21]], [[1, 5], [1, -5]], [[1, 23], [1, -23]], [[-1, 25], [-1, -25]], [[1, 11], [1, -11]], [[-1, 31], [-1, -31]], [[-1, 29], [-1, -29]], [[1, 19], [1, -19]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 9], [-1, -9]], [[1, 9], [1, -9]], [[-1, 13], [-1, -13]], [[-1, 19], [-1, -19]], [[1, 3], [1, -3]], [[1, 7], [1, -7]], [[1, 25], [1, -25]], [[-1, 23], [-1, -23]], [[1, 29], [1, -29]], [[1, 13], [1, -13]], [[-1, 11], [-1, -11]], [[1, 17], [1, -17]], [[-1, 27], [-1, -27]]]}
id: 6370170
{'center': '128.a1.a1', 'center_index': 128, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 128, 'dim': 2, 'faithful': True, 'field': [2, 0, -256, 0, 5440, 0, -45696, 0, 201552, 0, -537472, 0, 940576, 0, -1136960, 0, 980628, 0, -615296, 0, 283360, 0, -95680, 0, 23400, 0, -4032, 0, 464, 0, -32, 0, 1], 'group': '256.541', 'group_counter': 541, 'group_order': 256, 'image': None, 'image_isoclass': '256.541', 'image_order': 256, 'indicator': -1, 'kernel': '256.a1.a1', 'kernel_order': 1, 'label': '256.541.2f9', 'nt': [256, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 16], [-1, -16]], [[1, 16], [1, -16]], [[1, 8], [1, -8]], [[-1, 24], [-1, -24]], [[1, 24], [1, -24]], [[-1, 8], [-1, -8]], [[-1, 12], [-1, -12]], [[-1, 28], [-1, -28]], [[1, 28], [1, -28]], [[1, 12], [1, -12]], [[1, 20], [1, -20]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[-1, 20], [-1, -20]], [[-1, 6], [-1, -6]], [[-1, 14], [-1, -14]], [[-1, 2], [-1, -2]], [[1, 22], [1, -22]], [[-1, 10], [-1, -10]], [[-1, 18], [-1, -18]], [[1, 26], [1, -26]], [[1, 30], [1, -30]], [[1, 6], [1, -6]], [[1, 10], [1, -10]], [[-1, 22], [-1, -22]], [[1, 14], [1, -14]], [[-1, 30], [-1, -30]], [[1, 2], [1, -2]], [[1, 18], [1, -18]], [[-1, 26], [-1, -26]], [[-1, 13], [-1, -13]], [[1, 25], [1, -25]], [[1, 7], [1, -7]], [[-1, 23], [-1, -23]], [[1, 27], [1, -27]], [[-1, 1], [-1, -1]], [[-1, 7], [-1, -7]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 19], [1, -19]], [[1, 15], [1, -15]], [[1, 31], [1, -31]], [[-1, 29], [-1, -29]], [[1, 23], [1, -23]], [[1, 5], [1, -5]], [[1, 21], [1, -21]], [[-1, 19], [-1, -19]], [[1, 9], [1, -9]], [[-1, 9], [-1, -9]], [[-1, 17], [-1, -17]], [[1, 17], [1, -17]], [[1, 11], [1, -11]], [[-1, 21], [-1, -21]], [[-1, 27], [-1, -27]], [[1, 1], [1, -1]], [[-1, 31], [-1, -31]], [[-1, 15], [-1, -15]], [[-1, 5], [-1, -5]], [[-1, 11], [-1, -11]], [[1, 29], [1, -29]], [[-1, 25], [-1, -25]], [[1, 13], [1, -13]]]}

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 64576512
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.541.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.541', 'subgroup_hash': 541, 'subgroup_order': 256, 'subgroup_tex': 'Q_{256}', 'supersolvable': True, 'sylow': 2}
id: 64576523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.541.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.163', 'subgroup_hash': 163, 'subgroup_order': 128, 'subgroup_tex': 'Q_{128}', 'supersolvable': True, 'sylow': 0}
id: 64576526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.541.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.163', 'subgroup_hash': 163, 'subgroup_order': 128, 'subgroup_tex': 'Q_{128}', 'supersolvable': True, 'sylow': 0}
id: 64576527
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.1', 'subgroup_hash': 1, 'subgroup_order': 128, 'subgroup_tex': 'C_{128}', 'supersolvable': True, 'sylow': 0}
id: 64576528
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 5, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'U1', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.1', 'subgroup_hash': 1, 'subgroup_order': 64, 'subgroup_tex': 'C_{64}', 'supersolvable': True, 'sylow': 0}
id: 64576529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.54', 'subgroup_hash': 54, 'subgroup_order': 64, 'subgroup_tex': 'Q_{64}', 'supersolvable': True, 'sylow': 0}
id: 64576530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.54', 'subgroup_hash': 54, 'subgroup_order': 64, 'subgroup_tex': 'Q_{64}', 'supersolvable': True, 'sylow': 0}
id: 64576531
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'L2', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.1', 'subgroup_hash': 1, 'subgroup_order': 32, 'subgroup_tex': 'C_{32}', 'supersolvable': True, 'sylow': 0}
id: 64576532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 64576513
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 64576514
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 11, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': ['U3', 'L3', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 64576515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 64576516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 64576517
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.18', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{16}', 'simple': False, 'solvable': True, 'special_labels': ['U4', 'L4', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 64576518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 64576519
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.541.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 64576520
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.52', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 52, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{32}', 'simple': False, 'solvable': True, 'special_labels': ['U5', 'L5', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 64576521
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.541.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 64576522
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.541.64.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 64576524
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.541.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.161', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{64}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'S', 'U6', 'L6', 'C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 64576525
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.541', 'ambient_counter': 541, 'ambient_order': 256, 'ambient_tex': 'Q_{256}', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 21, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.541.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.541', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 541, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{256}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U7', 'L7', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 64576512
{'ambient': '256.541', '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': '128.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5001, 5001, 5000, 5000, 4986, 4986, 5000, 4991], 'generators': [1, 2], 'label': '256.541.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '128.161'}
id: 64576513
{'ambient': '256.541', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.913', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.a1.a1', '16.b1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7768, -1, 8226, -1, 7746, -1, 8225, -1], 'generators': [1, 240], 'label': '256.541.8.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.b1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 64576514
{'ambient': '256.541', 'aut_centralizer_order': 1024, 'aut_label': '16.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 1024, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['32.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2740, 5001, 5000, 5000, 2732, 4986, 5000, 4991], 'generators': [240], 'label': '256.541.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576515
{'ambient': '256.541', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.43', 'aut_weyl_index': 256, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.a1.a1', '32.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7768, -1, 1775, -1, 7746, -1, 1775, -1], 'generators': [3, 32], 'label': '256.541.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 64576516
{'ambient': '256.541', 'aut_centralizer_order': 16, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '32.43', 'aut_weyl_index': 256, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1'], 'contains': ['32.a1.a1', '32.b1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7768, -1, 8226, -1, 7746, -1, 8225, -1], 'generators': [1, 32], 'label': '256.541.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 64576517
{'ambient': '256.541', 'aut_centralizer_order': 2048, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2048, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['64.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3701, 5001, 5000, 5000, 3690, 4986, 5000, 4991], 'generators': [32], 'label': '256.541.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.1', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576518
{'ambient': '256.541', 'aut_centralizer_order': 32, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1024, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1'], 'contains': ['64.a1.a1', '64.b1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7768, -1, 2391, -1, 7746, -1, 2391, -1], 'generators': [3, 192], 'label': '256.541.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.b1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 64576519
{'ambient': '256.541', 'aut_centralizer_order': 32, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '8.3', 'aut_weyl_index': 1024, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1'], 'contains': ['64.a1.a1', '64.b1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7768, -1, 7610, -1, 7746, -1, 7609, -1], 'generators': [1, 192], 'label': '256.541.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.b1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 64576520
{'ambient': '256.541', 'aut_centralizer_order': 4096, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4096, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'contains': ['128.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3701, 5001, 5000, 5000, 3690, 4986, 5000, 4991], 'generators': [192], 'label': '256.541.64.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.1', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576521
{'ambient': '256.541', 'aut_centralizer_order': 64, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4096, 'centralizer': '64.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [7768, -1, 2391, -1, 7746, -1, 2391, -1], 'generators': [3], 'label': '256.541.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.a1', 'old_label': '64.b1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576522
{'ambient': '256.541', 'aut_centralizer_order': 64, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 4096, 'centralizer': '64.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1'], 'contains': ['128.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [7768, -1, 7610, -1, 7746, -1, 7609, -1], 'generators': [1], 'label': '256.541.64.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.b1', 'old_label': '64.b1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576523
{'ambient': '256.541', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2048.ctr', 'aut_weyl_index': 4, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7768, 7768, 1449, 5000, 7746, 7746, 1449, 4991], 'generators': [3, 252], 'label': '256.541.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '128.161'}
id: 64576524
{'ambient': '256.541', 'aut_centralizer_order': 8192, 'aut_label': '128.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 8192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.b1.b1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5735, 5001, 5000, 5000, 5718, 4986, 5000, 4991], 'generators': [128], 'label': '256.541.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.161', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 64576525
{'ambient': '256.541', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5735, 5001, 5000, 5000, 5718, 4986, 5000, 4991], 'generators': [], 'label': '256.541.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.541', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 64576526
{'ambient': '256.541', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2048.ctr', 'aut_weyl_index': 4, 'centralizer': '128.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7768, 7768, 8551, 8564, 7746, 7746, 8551, 8548], 'generators': [1, 252], 'label': '256.541.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '128.161'}
id: 64576527
{'ambient': '256.541', 'aut_centralizer_order': 128, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.50', 'aut_weyl_index': 128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2232, 2232, 5000, 1436, 2225, 2225, 5000, 1434], 'generators': [2], 'label': '256.541.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576528
{'ambient': '256.541', 'aut_centralizer_order': 256, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '32.16', 'aut_weyl_index': 256, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2740, 5001, 5000, 5000, 2732, 4986, 5000, 4991], 'generators': [252], 'label': '256.541.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576529
{'ambient': '256.541', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.58302', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7768, -1, 1775, -1, 7746, -1, 1775, -1], 'generators': [3, 8], 'label': '256.541.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '64.52'}
id: 64576530
{'ambient': '256.541', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '512.58302', 'aut_weyl_index': 16, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '8.b1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7768, -1, 8226, -1, 7746, -1, 8225, -1], 'generators': [1, 8], 'label': '256.541.4.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.b1.b1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '64.52'}
id: 64576531
{'ambient': '256.541', 'aut_centralizer_order': 512, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.5', 'aut_weyl_index': 512, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2740, 5001, 5000, 5000, 2732, 4986, 5000, 4991], 'generators': [8], 'label': '256.541.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '128.161', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 64576532
{'ambient': '256.541', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '128.913', 'aut_weyl_index': 64, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '16.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7768, -1, 1775, -1, 7746, -1, 1775, -1], 'generators': [3, 240], 'label': '256.541.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '128.161', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}

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.