LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-10-25T18:27:26.631491

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': '14.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [6, 12, 6, 6], 'aut_gens': [[415592052, 801250460, 448893330, 772289600, 490366493], [294836845, 106189820, 458546950, 77228960, 497824801], [111840979, 405452040, 555083150, 381317990, 787352083], [437693192, 497161430, 342703510, 473027380, 642707898], [480480096, 106189820, 419932470, 77228960, 525646957]], 'aut_group': None, 'aut_hash': 3088507494921977175, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 26208, 'aut_permdeg': 164, 'aut_perms': [2004630720954118643507715643077900787989263106935190196340145424238025960803084726339798406807074263968727908911009093837885706471000189439805165407962534579848621812507902117052097987266081475168753509035569348768670717027795063471988813513765253586363734615065800372892324111293875017680287, 2004554339521578856567974883907603835253945464870345456422595388492217296351919875879479019910586693078559658157048251100475020293029445990964684418675092012055558088934383464825785067505430677142556218706682281667252472474335706291916433313144348553554990124643781603999967332901511240897641, 2004781111798000207273494004803026670746264360793540055080024420733044546785411988266377259914707740827331921443598256677115764957368809032996401400202868718884890354324744400104328458793004003656073414403365053076855045008290476853170790406336320337717078312278244695872201438325524267793084, 229144408816341723184968750709194632538046268481749525125381334763529433397622501256788183778954298430502683067123392447223972404112642572256210583531866779677380659503310092452154247644793421904634080183011958091347653937689555673599036174946166461434127340770702346943800741961158718234], 'aut_phi_ratio': 3.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 1, 3], [7, 156, 6, 3], [12, 182, 1, 2], [12, 182, 2, 1], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 1, 3], [14, 156, 6, 3], [14, 182, 6, 1], [21, 182, 6, 1], [26, 84, 2, 1], [28, 1, 12, 1], [28, 156, 2, 3], [28, 156, 12, 3], [28, 182, 6, 1], [42, 182, 6, 1], [42, 182, 12, 1], [52, 84, 4, 1], [84, 182, 6, 2], [84, 182, 12, 1], [91, 84, 12, 1], [182, 84, 12, 1], [364, 84, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6\\times \\PSL(2,13).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 182, 1], [3, 182, 1], [4, 1, 2], [4, 182, 1], [6, 182, 3], [7, 1, 6], [7, 156, 21], [12, 182, 4], [13, 84, 2], [14, 1, 6], [14, 156, 21], [14, 182, 6], [21, 182, 6], [26, 84, 2], [28, 1, 12], [28, 156, 42], [28, 182, 6], [42, 182, 18], [52, 84, 4], [84, 182, 24], [91, 84, 12], [182, 84, 12], [364, 84, 24]], 'center_label': '28.2', 'center_order': 28, 'central_product': True, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '2184.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '1092.25'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4368.c', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 3, 1], [7, 156, 6, 3], [12, 182, 2, 2], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 3, 1], [14, 156, 6, 3], [14, 182, 6, 1], [21, 182, 6, 1], [26, 84, 2, 1], [28, 1, 12, 1], [28, 156, 6, 1], [28, 156, 12, 3], [28, 182, 6, 1], [42, 182, 6, 1], [42, 182, 12, 1], [52, 84, 4, 1], [84, 182, 12, 2], [91, 84, 12, 1], [182, 84, 12, 1], [364, 84, 24, 1]], 'element_repr_type': 'GLFq', 'elementary': 1, 'eulerian_function': 23760, 'exponent': 1092, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[6, 0, 24], [12, 0, 36], [14, 0, 36]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 4812302980474511629, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [2, 1, 1, 1, 13], 'inner_gens': [[415592052, 801250460, 448893330, 772289600, 754050027], [415592052, 801250460, 448893330, 772289600, 490366493], [415592052, 801250460, 448893330, 772289600, 490366493], [415592052, 801250460, 448893330, 772289600, 490366493], [461168301, 801250460, 448893330, 772289600, 490366493]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [1, 5], 'irrC_degree': 6, 'irrQ_degree': 144, 'irrQ_dim': 144, 'irrR_degree': 12, 'irrep_stats': [[1, 14], [6, 28], [7, 28], [12, 84], [13, 14], [14, 70]], 'label': '30576.b', 'linC_count': 24, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 30, 'linQ_degree_count': 2, 'linQ_dim': 30, 'linQ_dim_count': 2, 'linR_count': 12, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,13):C14', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 46, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 238, 'number_divisions': 38, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 103, 'number_subgroup_classes': 125, 'number_subgroups': 9480, 'old_label': None, 'order': 30576, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 183], [3, 182], [4, 184], [6, 546], [7, 3282], [12, 728], [13, 168], [14, 4374], [21, 1092], [26, 168], [28, 7656], [42, 3276], [52, 336], [84, 4368], [91, 1008], [182, 1008], [364, 2016]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [4826810, 4826810, 384816314], 'outer_gens': [[681743844, 106189820, 419932470, 77228960, 693124739], [415592052, 801250460, 429586090, 772289600, 393341787], [446031988, 613004870, 608178060, 598524440, 529201394]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 63, 'pgroup': 0, 'primary_abelian_invariants': [2, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2], [13, 2], [14, 6], [24, 1], [28, 1], [36, 2], [56, 1], [72, 7], [78, 2], [84, 6], [144, 4], [168, 1], [336, 1]], 'representations': {'GLFq': {'d': 2, 'q': 169, 'gens': [415592052, 801250460, 448893330, 772289600, 490366493]}, 'Perm': {'d': 63, 'gens': [32002948941137034641416832985497490978007525106250773638624883403760055231942559171015, 64970972549750024706108539941705397670731766767467678709527345421353203852470876987148, 96998038569281425749773367228660699792763256836694904840270762937020750251723752764328, 1095, 128984611192195342033586122315690645346142148987522422933279218836973360577646295888087]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [14], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,13):C_{14}', 'transitive_degree': 392, '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
Showing the first 100 of 238 matching records in this table.

id: 109683452
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2, 'group_order': 30576, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 4826810, 'size': 1}
id: 109683563
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2, 'group_order': 30576, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 57921720, 'size': 1}
id: 109683613
{'aut_label': '2B', 'centralizer': '182.a1.a1', 'counter': 3, 'group_counter': 2, 'group_order': 30576, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 525468563, 'size': 182}
id: 109683624
{'aut_label': '3A', 'centralizer': '182.a1.a1', 'counter': 4, 'group_counter': 2, 'group_order': 30576, 'label': '3A', 'order': 3, 'powers': [4, 1, 4, 4], 'representative': 814501428, 'size': 182}
id: 109683635
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 2, 'group_order': 30576, 'label': '4A1', 'order': 4, 'powers': [2, 6, 6, 5], 'representative': 38614480, 'size': 1}
id: 109683646
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 2, 'group_order': 30576, 'label': '4A-1', 'order': 4, 'powers': [2, 5, 5, 6], 'representative': 24134050, 'size': 1}
id: 109683657
{'aut_label': '4B', 'centralizer': '182.a1.a1', 'counter': 7, 'group_counter': 2, 'group_order': 30576, 'label': '4B', 'order': 4, 'powers': [2, 7, 7, 7], 'representative': 395183786, 'size': 182}
id: 109683668
{'aut_label': '6A', 'centralizer': '182.a1.a1', 'counter': 8, 'group_counter': 2, 'group_order': 30576, 'label': '6A', 'order': 6, 'powers': [4, 2, 8, 8], 'representative': 756579721, 'size': 182}
id: 109683679
{'aut_label': '6B1', 'centralizer': '182.a1.a1', 'counter': 9, 'group_counter': 2, 'group_order': 30576, 'label': '6B1', 'order': 6, 'powers': [4, 3, 9, 9], 'representative': 603880159, 'size': 182}
id: 109683453
{'aut_label': '6B1', 'centralizer': '182.a1.a1', 'counter': 10, 'group_counter': 2, 'group_order': 30576, 'label': '6B-1', 'order': 6, 'powers': [4, 3, 10, 10], 'representative': 570092489, 'size': 182}
id: 109683464
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 2, 'group_order': 30576, 'label': '7A1', 'order': 7, 'powers': [13, 15, 1, 12], 'representative': 598524440, 'size': 1}
id: 109683475
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 2, 'group_order': 30576, 'label': '7A-1', 'order': 7, 'powers': [14, 16, 1, 11], 'representative': 265474550, 'size': 1}
id: 109683486
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 2, 'group_order': 30576, 'label': '7A2', 'order': 7, 'powers': [16, 12, 1, 14], 'representative': 772289600, 'size': 1}
id: 109683497
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 2, 'group_order': 30576, 'label': '7A-2', 'order': 7, 'powers': [15, 11, 1, 13], 'representative': 77228960, 'size': 1}
id: 109683508
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 2, 'group_order': 30576, 'label': '7A3', 'order': 7, 'powers': [12, 13, 1, 16], 'representative': 473027380, 'size': 1}
id: 109683519
{'aut_label': '7A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 2, 'group_order': 30576, 'label': '7A-3', 'order': 7, 'powers': [11, 14, 1, 15], 'representative': 381317990, 'size': 1}
id: 109683530
{'aut_label': '7B1', 'centralizer': '156.b1.a1', 'counter': 17, 'group_counter': 2, 'group_order': 30576, 'label': '7B1', 'order': 7, 'powers': [18, 19, 1, 17], 'representative': 15684050, 'size': 156}
id: 109683541
{'aut_label': '7B2', 'centralizer': '156.b1.a1', 'counter': 18, 'group_counter': 2, 'group_order': 30576, 'label': '7B2', 'order': 7, 'powers': [19, 17, 1, 18], 'representative': 52685750, 'size': 156}
id: 109683552
{'aut_label': '7B3', 'centralizer': '156.b1.a1', 'counter': 19, 'group_counter': 2, 'group_order': 30576, 'label': '7B3', 'order': 7, 'powers': [17, 18, 1, 19], 'representative': 60745537, 'size': 156}
id: 109683564
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 20, 'group_counter': 2, 'group_order': 30576, 'label': '7C1', 'order': 7, 'powers': [22, 24, 1, 21], 'representative': 610117392, 'size': 156}
id: 109683575
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 21, 'group_counter': 2, 'group_order': 30576, 'label': '7C-1', 'order': 7, 'powers': [23, 25, 1, 20], 'representative': 765195046, 'size': 156}
id: 109683586
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 22, 'group_counter': 2, 'group_order': 30576, 'label': '7C2', 'order': 7, 'powers': [25, 21, 1, 23], 'representative': 431033317, 'size': 156}
id: 109683597
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 23, 'group_counter': 2, 'group_order': 30576, 'label': '7C-2', 'order': 7, 'powers': [24, 20, 1, 22], 'representative': 827688, 'size': 156}
id: 109683607
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 24, 'group_counter': 2, 'group_order': 30576, 'label': '7C3', 'order': 7, 'powers': [21, 22, 1, 25], 'representative': 110075984, 'size': 156}
id: 109683608
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 25, 'group_counter': 2, 'group_order': 30576, 'label': '7C-3', 'order': 7, 'powers': [20, 23, 1, 24], 'representative': 724223809, 'size': 156}
id: 109683609
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 26, 'group_counter': 2, 'group_order': 30576, 'label': '7D1', 'order': 7, 'powers': [28, 30, 1, 27], 'representative': 449135862, 'size': 156}
id: 109683610
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 27, 'group_counter': 2, 'group_order': 30576, 'label': '7D-1', 'order': 7, 'powers': [29, 31, 1, 26], 'representative': 321740935, 'size': 156}
id: 109683611
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 28, 'group_counter': 2, 'group_order': 30576, 'label': '7D2', 'order': 7, 'powers': [31, 27, 1, 29], 'representative': 556551138, 'size': 156}
id: 109683612
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 29, 'group_counter': 2, 'group_order': 30576, 'label': '7D-2', 'order': 7, 'powers': [30, 26, 1, 28], 'representative': 4425674, 'size': 156}
id: 109683614
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 30, 'group_counter': 2, 'group_order': 30576, 'label': '7D3', 'order': 7, 'powers': [27, 28, 1, 31], 'representative': 499991256, 'size': 156}
id: 109683615
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 31, 'group_counter': 2, 'group_order': 30576, 'label': '7D-3', 'order': 7, 'powers': [26, 29, 1, 30], 'representative': 814793531, 'size': 156}
id: 109683616
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 32, 'group_counter': 2, 'group_order': 30576, 'label': '7E1', 'order': 7, 'powers': [34, 36, 1, 33], 'representative': 544831621, 'size': 156}
id: 109683617
{'aut_label': '7C2', 'centralizer': '156.b1.a1', 'counter': 33, 'group_counter': 2, 'group_order': 30576, 'label': '7E-1', 'order': 7, 'powers': [35, 37, 1, 32], 'representative': 275339262, 'size': 156}
id: 109683618
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 34, 'group_counter': 2, 'group_order': 30576, 'label': '7E2', 'order': 7, 'powers': [37, 33, 1, 35], 'representative': 83838365, 'size': 156}
id: 109683619
{'aut_label': '7C3', 'centralizer': '156.b1.a1', 'counter': 35, 'group_counter': 2, 'group_order': 30576, 'label': '7E-2', 'order': 7, 'powers': [36, 32, 1, 34], 'representative': 4206740, 'size': 156}
id: 109683620
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 36, 'group_counter': 2, 'group_order': 30576, 'label': '7E3', 'order': 7, 'powers': [33, 34, 1, 37], 'representative': 106655464, 'size': 156}
id: 109683621
{'aut_label': '7C1', 'centralizer': '156.b1.a1', 'counter': 37, 'group_counter': 2, 'group_order': 30576, 'label': '7E-3', 'order': 7, 'powers': [32, 35, 1, 36], 'representative': 556750217, 'size': 156}
id: 109683622
{'aut_label': '12A1', 'centralizer': '182.a1.a1', 'counter': 38, 'group_counter': 2, 'group_order': 30576, 'label': '12A1', 'order': 12, 'powers': [8, 7, 39, 38], 'representative': 241034359, 'size': 182}
id: 109683623
{'aut_label': '12A5', 'centralizer': '182.a1.a1', 'counter': 39, 'group_counter': 2, 'group_order': 30576, 'label': '12A5', 'order': 12, 'powers': [8, 7, 38, 39], 'representative': 221727119, 'size': 182}
id: 109683625
{'aut_label': '12B1', 'centralizer': '182.a1.a1', 'counter': 40, 'group_counter': 2, 'group_order': 30576, 'label': '12B1', 'order': 12, 'powers': [8, 6, 41, 40], 'representative': 545032342, 'size': 182}
id: 109683626
{'aut_label': '12B1', 'centralizer': '182.a1.a1', 'counter': 41, 'group_counter': 2, 'group_order': 30576, 'label': '12B-1', 'order': 12, 'powers': [8, 5, 40, 41], 'representative': 520898292, 'size': 182}
id: 109683627
{'aut_label': '13A1', 'centralizer': '84.b1.a1', 'counter': 42, 'group_counter': 2, 'group_order': 30576, 'label': '13A1', 'order': 13, 'powers': [43, 42, 43, 1], 'representative': 211434858, 'size': 84}
id: 109683628
{'aut_label': '13A1', 'centralizer': '84.b1.a1', 'counter': 43, 'group_counter': 2, 'group_order': 30576, 'label': '13A2', 'order': 13, 'powers': [42, 43, 42, 1], 'representative': 413185157, 'size': 84}
id: 109683629
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 44, 'group_counter': 2, 'group_order': 30576, 'label': '14A1', 'order': 14, 'powers': [11, 46, 2, 45], 'representative': 497161430, 'size': 1}
id: 109683630
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 45, 'group_counter': 2, 'group_order': 30576, 'label': '14A-1', 'order': 14, 'powers': [12, 47, 2, 44], 'representative': 405452040, 'size': 1}
id: 109683631
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 46, 'group_counter': 2, 'group_order': 30576, 'label': '14A3', 'order': 14, 'powers': [15, 49, 2, 47], 'representative': 801250460, 'size': 1}
id: 109683632
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 47, 'group_counter': 2, 'group_order': 30576, 'label': '14A-3', 'order': 14, 'powers': [16, 48, 2, 46], 'representative': 106189820, 'size': 1}
id: 109683633
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 48, 'group_counter': 2, 'group_order': 30576, 'label': '14A5', 'order': 14, 'powers': [14, 44, 2, 49], 'representative': 613004870, 'size': 1}
id: 109683634
{'aut_label': '14A1', 'centralizer': '1.a1.a1', 'counter': 49, 'group_counter': 2, 'group_order': 30576, 'label': '14A-5', 'order': 14, 'powers': [13, 45, 2, 48], 'representative': 279954980, 'size': 1}
id: 109683636
{'aut_label': '14B1', 'centralizer': '156.b1.a1', 'counter': 50, 'group_counter': 2, 'group_order': 30576, 'label': '14B1', 'order': 14, 'powers': [17, 51, 2, 50], 'representative': 26957867, 'size': 156}
id: 109683637
{'aut_label': '14B3', 'centralizer': '156.b1.a1', 'counter': 51, 'group_counter': 2, 'group_order': 30576, 'label': '14B3', 'order': 14, 'powers': [19, 52, 2, 51], 'representative': 4417663, 'size': 156}
id: 109683638
{'aut_label': '14B5', 'centralizer': '156.b1.a1', 'counter': 52, 'group_counter': 2, 'group_order': 30576, 'label': '14B5', 'order': 14, 'powers': [18, 50, 2, 52], 'representative': 39818100, 'size': 156}
id: 109683639
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 53, 'group_counter': 2, 'group_order': 30576, 'label': '14C1', 'order': 14, 'powers': [20, 55, 2, 54], 'representative': 154657662, 'size': 156}
id: 109683640
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 54, 'group_counter': 2, 'group_order': 30576, 'label': '14C-1', 'order': 14, 'powers': [21, 56, 2, 53], 'representative': 773603735, 'size': 156}
id: 109683641
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 55, 'group_counter': 2, 'group_order': 30576, 'label': '14C3', 'order': 14, 'powers': [24, 58, 2, 56], 'representative': 4401354, 'size': 156}
id: 109683642
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 56, 'group_counter': 2, 'group_order': 30576, 'label': '14C-3', 'order': 14, 'powers': [25, 57, 2, 55], 'representative': 452674781, 'size': 156}
id: 109683643
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 57, 'group_counter': 2, 'group_order': 30576, 'label': '14C5', 'order': 14, 'powers': [23, 53, 2, 58], 'representative': 118513234, 'size': 156}
id: 109683644
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 58, 'group_counter': 2, 'group_order': 30576, 'label': '14C-5', 'order': 14, 'powers': [22, 54, 2, 57], 'representative': 273590888, 'size': 156}
id: 109683645
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 59, 'group_counter': 2, 'group_order': 30576, 'label': '14D1', 'order': 14, 'powers': [26, 61, 2, 60], 'representative': 68914749, 'size': 156}
id: 109683647
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 60, 'group_counter': 2, 'group_order': 30576, 'label': '14D-1', 'order': 14, 'powers': [27, 62, 2, 59], 'representative': 383717024, 'size': 156}
id: 109683648
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 61, 'group_counter': 2, 'group_order': 30576, 'label': '14D3', 'order': 14, 'powers': [30, 64, 2, 62], 'representative': 803368, 'size': 156}
id: 109683649
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 62, 'group_counter': 2, 'group_order': 30576, 'label': '14D-3', 'order': 14, 'powers': [31, 63, 2, 61], 'representative': 327156960, 'size': 156}
id: 109683650
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 63, 'group_counter': 2, 'group_order': 30576, 'label': '14D5', 'order': 14, 'powers': [29, 59, 2, 64], 'representative': 561938784, 'size': 156}
id: 109683651
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 64, 'group_counter': 2, 'group_order': 30576, 'label': '14D-5', 'order': 14, 'powers': [28, 60, 2, 63], 'representative': 429745609, 'size': 156}
id: 109683652
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 65, 'group_counter': 2, 'group_order': 30576, 'label': '14E1', 'order': 14, 'powers': [32, 67, 2, 66], 'representative': 326958063, 'size': 156}
id: 109683653
{'aut_label': '14C5', 'centralizer': '156.b1.a1', 'counter': 66, 'group_counter': 2, 'group_order': 30576, 'label': '14E-1', 'order': 14, 'powers': [33, 68, 2, 65], 'representative': 777052816, 'size': 156}
id: 109683654
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 67, 'group_counter': 2, 'group_order': 30576, 'label': '14E3', 'order': 14, 'powers': [36, 70, 2, 68], 'representative': 1022302, 'size': 156}
id: 109683655
{'aut_label': '14C1', 'centralizer': '156.b1.a1', 'counter': 68, 'group_counter': 2, 'group_order': 30576, 'label': '14E-3', 'order': 14, 'powers': [37, 69, 2, 67], 'representative': 799869733, 'size': 156}
id: 109683656
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 69, 'group_counter': 2, 'group_order': 30576, 'label': '14E5', 'order': 14, 'powers': [35, 65, 2, 70], 'representative': 603542209, 'size': 156}
id: 109683658
{'aut_label': '14C3', 'centralizer': '156.b1.a1', 'counter': 70, 'group_counter': 2, 'group_order': 30576, 'label': '14E-5', 'order': 14, 'powers': [34, 66, 2, 69], 'representative': 338848098, 'size': 156}
id: 109683659
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 71, 'group_counter': 2, 'group_order': 30576, 'label': '14F1', 'order': 14, 'powers': [14, 73, 3, 72], 'representative': 443679327, 'size': 182}
id: 109683660
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 72, 'group_counter': 2, 'group_order': 30576, 'label': '14F-1', 'order': 14, 'powers': [13, 74, 3, 71], 'representative': 509941015, 'size': 182}
id: 109683661
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 73, 'group_counter': 2, 'group_order': 30576, 'label': '14F3', 'order': 14, 'powers': [11, 76, 3, 74], 'representative': 184942590, 'size': 182}
id: 109683662
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 74, 'group_counter': 2, 'group_order': 30576, 'label': '14F-3', 'order': 14, 'powers': [12, 75, 3, 73], 'representative': 663795372, 'size': 182}
id: 109683663
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 75, 'group_counter': 2, 'group_order': 30576, 'label': '14F5', 'order': 14, 'powers': [16, 71, 3, 76], 'representative': 469936188, 'size': 182}
id: 109683664
{'aut_label': '14F1', 'centralizer': '182.a1.a1', 'counter': 76, 'group_counter': 2, 'group_order': 30576, 'label': '14F-5', 'order': 14, 'powers': [15, 72, 3, 75], 'representative': 673919315, 'size': 182}
id: 109683665
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 77, 'group_counter': 2, 'group_order': 30576, 'label': '21A1', 'order': 21, 'powers': [79, 14, 4, 78], 'representative': 55815722, 'size': 182}
id: 109683666
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 78, 'group_counter': 2, 'group_order': 30576, 'label': '21A-1', 'order': 21, 'powers': [80, 13, 4, 77], 'representative': 120838790, 'size': 182}
id: 109683667
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 79, 'group_counter': 2, 'group_order': 30576, 'label': '21A2', 'order': 21, 'powers': [81, 15, 4, 80], 'representative': 228776676, 'size': 182}
id: 109683669
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 80, 'group_counter': 2, 'group_order': 30576, 'label': '21A-2', 'order': 21, 'powers': [82, 16, 4, 79], 'representative': 151239379, 'size': 182}
id: 109683670
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 81, 'group_counter': 2, 'group_order': 30576, 'label': '21A4', 'order': 21, 'powers': [77, 12, 4, 82], 'representative': 726573629, 'size': 182}
id: 109683671
{'aut_label': '21A1', 'centralizer': '182.a1.a1', 'counter': 82, 'group_counter': 2, 'group_order': 30576, 'label': '21A-4', 'order': 21, 'powers': [78, 11, 4, 81], 'representative': 307284535, 'size': 182}
id: 109683672
{'aut_label': '26A1', 'centralizer': '84.b1.a1', 'counter': 83, 'group_counter': 2, 'group_order': 30576, 'label': '26A1', 'order': 26, 'powers': [42, 83, 84, 2], 'representative': 336137900, 'size': 84}
id: 109683673
{'aut_label': '26A1', 'centralizer': '84.b1.a1', 'counter': 84, 'group_counter': 2, 'group_order': 30576, 'label': '26A5', 'order': 26, 'powers': [43, 84, 83, 2], 'representative': 806660842, 'size': 84}
id: 109683674
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 85, 'group_counter': 2, 'group_order': 30576, 'label': '28A1', 'order': 28, 'powers': [44, 87, 5, 95], 'representative': 535775910, 'size': 1}
id: 109683675
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 86, 'group_counter': 2, 'group_order': 30576, 'label': '28A-1', 'order': 28, 'powers': [45, 88, 6, 96], 'representative': 555083150, 'size': 1}
id: 109683676
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 87, 'group_counter': 2, 'group_order': 30576, 'label': '28A3', 'order': 28, 'powers': [46, 91, 6, 93], 'representative': 429586090, 'size': 1}
id: 109683677
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 88, 'group_counter': 2, 'group_order': 30576, 'label': '28A-3', 'order': 28, 'powers': [47, 92, 5, 94], 'representative': 419932470, 'size': 1}
id: 109683678
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 89, 'group_counter': 2, 'group_order': 30576, 'label': '28A5', 'order': 28, 'powers': [48, 96, 5, 91], 'representative': 608178060, 'size': 1}
id: 109683680
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 90, 'group_counter': 2, 'group_order': 30576, 'label': '28A-5', 'order': 28, 'powers': [49, 95, 6, 92], 'representative': 603351250, 'size': 1}
id: 109683681
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 91, 'group_counter': 2, 'group_order': 30576, 'label': '28A9', 'order': 28, 'powers': [49, 86, 5, 89], 'representative': 275128170, 'size': 1}
id: 109683682
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 92, 'group_counter': 2, 'group_order': 30576, 'label': '28A-9', 'order': 28, 'powers': [48, 85, 6, 90], 'representative': 270301360, 'size': 1}
id: 109683683
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 93, 'group_counter': 2, 'group_order': 30576, 'label': '28A11', 'order': 28, 'powers': [47, 89, 6, 87], 'representative': 458546950, 'size': 1}
id: 109683684
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 94, 'group_counter': 2, 'group_order': 30576, 'label': '28A-11', 'order': 28, 'powers': [46, 90, 5, 88], 'representative': 448893330, 'size': 1}
id: 109683685
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 95, 'group_counter': 2, 'group_order': 30576, 'label': '28A13', 'order': 28, 'powers': [45, 93, 5, 85], 'representative': 323396270, 'size': 1}
id: 109683686
{'aut_label': '28A1', 'centralizer': '1.a1.a1', 'counter': 96, 'group_counter': 2, 'group_order': 30576, 'label': '28A-13', 'order': 28, 'powers': [44, 94, 6, 86], 'representative': 342703510, 'size': 1}
id: 109683687
{'aut_label': '28B1', 'centralizer': '156.b1.a1', 'counter': 97, 'group_counter': 2, 'group_order': 30576, 'label': '28B1', 'order': 28, 'powers': [50, 99, 5, 97], 'representative': 54298517, 'size': 156}
id: 109683688
{'aut_label': '28B1', 'centralizer': '156.b1.a1', 'counter': 98, 'group_counter': 2, 'group_order': 30576, 'label': '28B-1', 'order': 28, 'powers': [50, 100, 6, 98], 'representative': 13678860, 'size': 156}
id: 109683689
{'aut_label': '28B3', 'centralizer': '156.b1.a1', 'counter': 99, 'group_counter': 2, 'group_order': 30576, 'label': '28B3', 'order': 28, 'powers': [51, 101, 6, 99], 'representative': 60211996, 'size': 156}
id: 109683454
{'aut_label': '28B3', 'centralizer': '156.b1.a1', 'counter': 100, 'group_counter': 2, 'group_order': 30576, 'label': '28B-3', 'order': 28, 'powers': [51, 102, 5, 100], 'representative': 9215232, 'size': 156}

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: 4365664
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '30576.b', 'group_order': 30576, 'image': None, 'label': '30576.b.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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 4365675
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '30576.b', 'group_order': 30576, 'image': None, 'label': '30576.b.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, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 4365686
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id: 4365700
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id: 4365683
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id: 4365684
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id: 4365685
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id: 4365687
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id: 4365688
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id: 4365666
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id: 4365667
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id: 4365689
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id: 4365668
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id: 4365669
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id: 4365670
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id: 4365671
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id: 4365672
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id: 4365673
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id: 4365674
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id: 4365681
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id: 4365682
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id: 4365701
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id: 4365665
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id: 4365690
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id: 4365691
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id: 4365692
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id: 4365693
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id: 4365698
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id: 4365676
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id: 4365677
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id: 4365678
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id: 4365694
{'cdim': 14, 'counter': 37, 'faithful': True, 'group': '30576.b', 'group_order': 30576, 'image': None, 'label': '30576.b.14k', 'multiplicity': 12, 'nt': [392, 0], 'qdim': 168, 'qvalues': [168, -168, 0, 24, 0, 0, 0, -24, 0, 0, -28, -28, -28, -28, -28, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 28, 28, 28, 28, 28, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
id: 4365695
{'cdim': 14, 'counter': 38, 'faithful': True, 'group': '30576.b', 'group_order': 30576, 'image': None, 'label': '30576.b.14l', 'multiplicity': 24, 'nt': [1176, 0], 'qdim': 336, 'qvalues': [336, -336, 0, -24, 0, 0, 0, 24, 0, 0, -56, -56, -56, -56, -56, -56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 24, 56, 56, 56, 56, 56, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -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], 'schur_index': 1}

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

gps_char • Show schema
Showing the first 100 of 238 matching records in this table.

id: 6591090
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 30576, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '30576.b', 'group_counter': 2, 'group_order': 30576, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 30576, 'label': '30576.b.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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 6591201
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 30576, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '30576.b', 'group_counter': 2, 'group_order': 30576, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 15288, 'label': '30576.b.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]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 6591251
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 30576, 'counter': 3, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '30576.b', 'group_counter': 2, 'group_order': 30576, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1.a1', 'kernel_order': 4368, 'label': '30576.b.1c1', 'nt': [7, 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, -3]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -3]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -3]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, 3]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 3]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
id: 6591262
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id: 6591273
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id: 6591284
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id: 6591295
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id: 6591306
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id: 6591317
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id: 6591091
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id: 6591102
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id: 6591113
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id: 6591124
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id: 6591135
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id: 6591146
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id: 6591157
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id: 6591168
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id: 6591179
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id: 6591190
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id: 6591249
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id: 6591250
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id: 6591252
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id: 6591253
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id: 6591254
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id: 6591255
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id: 6591256
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id: 6591257
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id: 6591258
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id: 6591259
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id: 6591202
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id: 6591260
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id: 6591261
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id: 6591263
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id: 6591264
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id: 6591265
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id: 6591213
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id: 6591224
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id: 6591235
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id: 6591245
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id: 6591246
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id: 6591247
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id: 6591248
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id: 6591266
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id: 6591267
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id: 6591268
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id: 6591269
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id: 6591270
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id: 6591280
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id: 6591281
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id: 6591282
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id: 6591271
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id: 6591272
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id: 6591274
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id: 6591275
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id: 6591276
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id: 6591277
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id: 6591278
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id: 6591279
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id: 6591283
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id: 6591293
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id: 6591294
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id: 6591285
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id: 6591286
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id: 6591287
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id: 6591288
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id: 6591289
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id: 6591290
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id: 6591291
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id: 6591292
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id: 6591297
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id: 6591298
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id: 6591299
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id: 6591300
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id: 6591301
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id: 6591302
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id: 6591303
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id: 6591304
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id: 6591305
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id: 6591307
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id: 6591308
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id: 6591309
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id: 6591310
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id: 6591311
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id: 6591312
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id: 6591313
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id: 6591314
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id: 6591315
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id: 6591316
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id: 6591318
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id: 6591319
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id: 6591320
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id: 6591321
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id: 6591322
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id: 6591323
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id: 6591324
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id: 6591325
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id: 6591326
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id: 6591327
{'center': '1092.a1.a1', 'center_index': 1092, 'center_order': 28, 'counter': 99, 'cyclotomic_n': 7, 'dim': 12, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '30576.b', 'group_counter': 2, 'group_order': 30576, 'image': None, 'image_isoclass': None, 'image_order': 7644, 'indicator': 0, 'kernel': '7644.a1.a1', 'kernel_order': 4, 'label': '30576.b.12f5', 'nt': [546, 0], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[12, -2]], [[12, 2]], [[12, -3]], [[12, 3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, 1], [-1, -2]], [[-1, -3], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, -3], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 3], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, -2], [-1, -1]], [[-1, 1], [-1, 2]], [[-1, 2], [-1, -3]], [[-1, 3], [-1, -2]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[12, 3]], [[12, -3]], [[12, 2]], [[12, -2]], [[12, 1]], [[12, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, 3]], [[-1, -3], [-1, -1]], [[-1, 2], [-1, 3]], [[-1, -3], [-1, -2]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, 3], [-1, -2]], [[-1, 2], [-1, -3]], [[-1, 1], [-1, 2]], [[-1, -2], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, 3], [-1, -1]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[12, -2]], [[12, 2]], [[12, 1]], [[12, -1]], [[12, -3]], [[12, 3]], [[12, 3]], [[12, -3]], [[12, -1]], [[12, 1]], [[12, 2]], [[12, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, -3], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, -3], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, -3], [-1, -1]], [[-1, 2], [-1, -1]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, -3], [-1, -2]], [[-1, -2], [-1, -1]], [[-1, 1], [-1, 2]], [[-1, 1], [-1, -3]], [[-1, 3], [-1, -1]], [[-1, 2], [-1, -3]], [[-1, 3], [-1, -2]], [[-1, 3], [-1, -2]], [[-1, 2], [-1, -3]], [[-1, 3], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, 1], [-1, 2]], [[-1, -2], [-1, -1]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 2]], [[-1, -2]], [[-1, 3]], [[-1, -3]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -3]], [[-1, 3]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -2]]]}
id: 6591092
{'center': '1092.a1.a1', 'center_index': 1092, 'center_order': 28, 'counter': 100, 'cyclotomic_n': 7, 'dim': 12, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '30576.b', 'group_counter': 2, 'group_order': 30576, 'image': None, 'image_isoclass': None, 'image_order': 7644, 'indicator': 0, 'kernel': '7644.a1.a1', 'kernel_order': 4, 'label': '30576.b.12f6', 'nt': [546, 6], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[12, 2]], [[12, -2]], [[12, 3]], [[12, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, 2], [-1, 3]], [[-1, -3], [-1, -2]], [[-1, 1], [-1, 3]], [[-1, -3], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, 3], [-1, -1]], [[-1, 1], [-1, 2]], [[-1, -2], [-1, -1]], [[-1, 3], [-1, -2]], [[-1, 2], [-1, -3]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[12, -3]], [[12, 3]], [[12, -2]], [[12, 2]], [[12, -1]], [[12, 1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, -3], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, -3], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, 2], [-1, -1]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, -3]], [[-1, 3], [-1, -2]], [[-1, -2], [-1, -1]], [[-1, 1], [-1, 2]], [[-1, 3], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[12, 2]], [[12, -2]], [[12, -1]], [[12, 1]], [[12, 3]], [[12, -3]], [[12, -3]], [[12, 3]], [[12, 1]], [[12, -1]], [[12, -2]], [[12, 2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, -3], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, 1], [-1, -2]], [[-1, 1], [-1, 3]], [[-1, -3], [-1, -1]], [[-1, -3], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -2]], [[-1, 2], [-1, -1]], [[-1, -3], [-1, -2]], [[-1, 2], [-1, 3]], [[-1, 1], [-1, 2]], [[-1, -2], [-1, -1]], [[-1, 3], [-1, -1]], [[-1, 1], [-1, -3]], [[-1, 3], [-1, -2]], [[-1, 2], [-1, -3]], [[-1, 2], [-1, -3]], [[-1, 3], [-1, -2]], [[-1, 1], [-1, -3]], [[-1, 3], [-1, -1]], [[-1, -2], [-1, -1]], [[-1, 1], [-1, 2]], [[-1, 0], [-1, -2]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, 3]], [[-1, 0], [-1, -3]], [[-1, 0], [-1, -1]], [[-1, 0], [-1, 1]], [[-1, 0], [-1, 2]], [[-1, 0], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, -2]], [[-1, 2]], [[-1, -3]], [[-1, 3]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 3]], [[-1, -3]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 2]]]}

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

gps_subgroup_search • Show schema
Showing the first 100 of 125 matching records in this table.

id: 65178952
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': True, 'core_order': 30576, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 546, 'label': '30576.b.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30576.b', 'subgroup_hash': 4812302980474511629, 'subgroup_order': 30576, 'subgroup_tex': '\\SL(2,13):C_{14}', 'supersolvable': False, 'sylow': 0}
id: 65178989
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 28, 'characteristic': True, 'core_order': 15288, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '30576.b.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': 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': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15288.a', 'subgroup_hash': 5491248784773491045, 'subgroup_order': 15288, 'subgroup_tex': 'C_7\\times \\SL(2,13)', 'supersolvable': False, 'sylow': 0}
id: 65179000
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 28, 'characteristic': True, 'core_order': 4368, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '30576.b.7.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4368.c', 'subgroup_hash': 3569960785506628826, 'subgroup_order': 4368, 'subgroup_tex': '\\SL(2,13):C_2', 'supersolvable': False, 'sylow': 0}
id: 65179011
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': True, 'centralizer_order': 28, 'characteristic': True, 'core_order': 2184, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '30576.b.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': False, 'special_labels': ['D', 'PC', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2184.a', 'subgroup_hash': 3261644830183217154, 'subgroup_order': 2184, 'subgroup_tex': '\\SL(2,13)', 'supersolvable': False, 'sylow': 0}
id: 65179022
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.14.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, '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': '2184.g', 'subgroup_hash': 8995000045596313501, 'subgroup_order': 2184, 'subgroup_tex': 'C_{364}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65179033
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '1092.38', 'subgroup_hash': 38, 'subgroup_order': 1092, 'subgroup_tex': 'C_{26}:C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65179044
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, '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': '1092.13', 'subgroup_hash': 13, 'subgroup_order': 1092, 'subgroup_tex': 'C_{13}:C_{84}', 'supersolvable': True, 'sylow': 0}
id: 65179055
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '1092.1', 'subgroup_hash': 1, 'subgroup_order': 1092, 'subgroup_tex': 'C_{13}:C_{84}', 'supersolvable': True, 'sylow': 0}
id: 65179066
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, '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': '728.15', 'subgroup_hash': 15, 'subgroup_order': 728, 'subgroup_tex': 'D_{13}\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178953
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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': '546.13', 'subgroup_hash': 13, 'subgroup_order': 546, 'subgroup_tex': 'C_{13}:C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65178964
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, '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': '546.1', 'subgroup_hash': 1, 'subgroup_order': 546, 'subgroup_tex': 'C_{13}:C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65178975
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.56.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, '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': '546.1', 'subgroup_hash': 1, 'subgroup_order': 546, 'subgroup_tex': 'C_{13}:C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65178982
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.78.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '78.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 78, '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': '392.24', 'subgroup_hash': 24, 'subgroup_order': 392, 'subgroup_tex': 'D_7\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178983
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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': '364.8', 'subgroup_hash': 8, 'subgroup_order': 364, 'subgroup_tex': 'C_7\\times D_{26}', 'supersolvable': True, 'sylow': 0}
id: 65178984
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 28, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, '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': '364.4', 'subgroup_hash': 4, 'subgroup_order': 364, 'subgroup_tex': 'C_{364}', 'supersolvable': True, 'sylow': 0}
id: 65178985
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, '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': '364.2', 'subgroup_hash': 2, 'subgroup_order': 364, 'subgroup_tex': 'C_{13}:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178986
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.91.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '91.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 91, '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': '336.170', 'subgroup_hash': 170, 'subgroup_order': 336, 'subgroup_tex': '\\SL(2,3):C_{14}', 'supersolvable': False, 'sylow': 0}
id: 65178987
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.91.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '91.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': 91, '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': '336.187', 'subgroup_hash': 187, 'subgroup_order': 336, 'subgroup_tex': 'D_{12}:C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65178988
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.98.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '98.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 98, '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': '312.9', 'subgroup_hash': 9, 'subgroup_order': 312, 'subgroup_tex': 'C_{52}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65178990
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, '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': '273.2', 'subgroup_hash': 2, 'subgroup_order': 273, 'subgroup_tex': 'C_{13}:C_{21}', 'supersolvable': True, 'sylow': 0}
id: 65178991
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.156.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '156.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 156, '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': '196.10', 'subgroup_hash': 10, 'subgroup_order': 196, 'subgroup_tex': 'C_7\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 65178992
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 28, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.156.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '156.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': 156, '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': '196.7', 'subgroup_hash': 7, 'subgroup_order': 196, 'subgroup_tex': 'C_7\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178993
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.156.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '156.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 156, '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': '196.5', 'subgroup_hash': 5, 'subgroup_order': 196, 'subgroup_tex': 'C_7:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178994
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 14, 'counter': 24, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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': '182.4', 'subgroup_hash': 4, 'subgroup_order': 182, 'subgroup_tex': 'C_{182}', 'supersolvable': True, 'sylow': 0}
id: 65178995
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, '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': '182.2', 'subgroup_hash': 2, 'subgroup_order': 182, 'subgroup_tex': 'C_7\\times D_{13}', 'supersolvable': True, 'sylow': 0}
id: 65178996
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.168.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, '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': '182.2', 'subgroup_hash': 2, 'subgroup_order': 182, 'subgroup_tex': 'C_7\\times D_{13}', 'supersolvable': True, 'sylow': 0}
id: 65178997
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '182.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
id: 65178998
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.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': 182, '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': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65178999
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179001
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.33', 'subgroup_hash': 33, 'subgroup_order': 168, 'subgroup_tex': 'D_6:C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179002
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.33', 'subgroup_hash': 33, 'subgroup_order': 168, 'subgroup_tex': 'D_6:C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179003
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.31', 'subgroup_hash': 31, 'subgroup_order': 168, 'subgroup_tex': 'C_7\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 65179004
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.29', 'subgroup_hash': 29, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 65179005
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.182.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '182.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 182, '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': '168.22', 'subgroup_hash': 22, 'subgroup_order': 168, 'subgroup_tex': 'C_7\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 65179006
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.196.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '196.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 196, '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': '156.8', 'subgroup_hash': 8, 'subgroup_order': 156, 'subgroup_tex': 'C_{26}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65179007
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.196.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '196.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': 196, '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': '156.2', 'subgroup_hash': 2, 'subgroup_order': 156, 'subgroup_tex': 'C_{13}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 65179008
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.196.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '196.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 196, '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': '156.1', 'subgroup_hash': 1, 'subgroup_order': 156, 'subgroup_tex': 'C_{13}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 65179009
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 28, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.273.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '273.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 273, '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': '112.40', 'subgroup_hash': 40, 'subgroup_order': 112, 'subgroup_tex': 'D_4:C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179010
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.294.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '294.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 294, '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': '104.5', 'subgroup_hash': 5, 'subgroup_order': 104, 'subgroup_tex': 'C_4\\times D_{13}', 'supersolvable': True, 'sylow': 0}
id: 65179012
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 14, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.312.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '312.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 312, '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': '98.5', 'subgroup_hash': 5, 'subgroup_order': 98, 'subgroup_tex': 'C_7\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179013
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.312.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '312.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': 312, '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': '98.3', 'subgroup_hash': 3, 'subgroup_order': 98, 'subgroup_tex': 'C_7\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 65179014
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.312.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '312.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 312, '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': '98.3', 'subgroup_hash': 3, 'subgroup_order': 98, 'subgroup_tex': 'C_7\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 65179015
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 7, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, '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': '91.1', 'subgroup_hash': 1, 'subgroup_order': 91, 'subgroup_tex': 'C_{91}', 'supersolvable': True, 'sylow': 0}
id: 65179016
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.364.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '364.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65179017
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.364.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '364.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': 364, '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': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179018
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.364.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '364.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179019
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.364.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '364.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
id: 65179020
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.364.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '364.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
id: 65179021
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.364.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '364.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179023
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.364.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '364.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 364, '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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179024
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.392.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '392.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 392, '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': '78.2', 'subgroup_hash': 2, 'subgroup_order': 78, 'subgroup_tex': 'C_{13}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65179025
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.392.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '392.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': 392, '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': '78.1', 'subgroup_hash': 1, 'subgroup_order': 78, 'subgroup_tex': 'C_{13}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65179026
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.392.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '392.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 392, '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': '78.1', 'subgroup_hash': 1, 'subgroup_order': 78, 'subgroup_tex': 'C_{13}:C_6', 'supersolvable': True, 'sylow': 0}
id: 65179027
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 28, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.546.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '546.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 546, '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': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179028
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.546.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '546.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': 546, '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': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 65179029
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.546.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '546.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 546, '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': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 65179030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 14, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.546.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '546.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 546, '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': '56.10', 'subgroup_hash': 10, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 65179031
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.588.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '588.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 588, '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': '52.4', 'subgroup_hash': 4, 'subgroup_order': 52, 'subgroup_tex': 'D_{26}', 'supersolvable': True, 'sylow': 0}
id: 65179032
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.588.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '588.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': 588, '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': '52.2', 'subgroup_hash': 2, 'subgroup_order': 52, 'subgroup_tex': 'C_{52}', 'supersolvable': True, 'sylow': 0}
id: 65179034
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.588.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '588.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 588, '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': '52.1', 'subgroup_hash': 1, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 65179035
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 7, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 7, 'label': '30576.b.624.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '624.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 624, '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': '49.2', 'subgroup_hash': 2, 'subgroup_order': 49, 'subgroup_tex': 'C_7^2', 'supersolvable': True, 'sylow': 7}
id: 65179036
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '30576.b.637.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '637.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 637, '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': '48.33', 'subgroup_hash': 33, 'subgroup_order': 48, 'subgroup_tex': '\\SL(2,3):C_2', 'supersolvable': False, 'sylow': 0}
id: 65179037
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '30576.b.637.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '637.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': 637, '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': '48.37', 'subgroup_hash': 37, 'subgroup_order': 48, 'subgroup_tex': 'D_{12}:C_2', 'supersolvable': True, 'sylow': 0}
id: 65179038
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '728.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 728, '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': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65179039
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 65, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.728.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '728.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': 728, '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': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
id: 65179040
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.728.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '728.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 728, '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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
id: 65179041
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 7, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.728.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '728.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 728, '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': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
id: 65179042
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 39, 'label': '30576.b.784.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '784.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 784, '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': '39.1', 'subgroup_hash': 1, 'subgroup_order': 39, 'subgroup_tex': 'C_{13}:C_3', 'supersolvable': True, 'sylow': 0}
id: 65179043
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 30576, 'characteristic': True, 'core_order': 28, 'counter': 69, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '30576.b.1092.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1092.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1092.25', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1092, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,13)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179045
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1092.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.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': 1092, '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': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179046
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1092.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1092.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1092, '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': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179047
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1092.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1092, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179048
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1092.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1092, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179049
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1092.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.e1.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': 1092, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179050
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1092.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.e1.c1', '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': 1092, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179051
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 14, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1092.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1092.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1092, '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': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 65179052
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1092.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1092.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1092, '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': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
id: 65179053
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1176, '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': '26.2', 'subgroup_hash': 2, 'subgroup_order': 26, 'subgroup_tex': 'C_{26}', 'supersolvable': True, 'sylow': 0}
id: 65179054
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1176.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': 1176, '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': '26.1', 'subgroup_hash': 1, 'subgroup_order': 26, 'subgroup_tex': 'D_{13}', 'supersolvable': True, 'sylow': 0}
id: 65179056
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1176.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1176.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1176, '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': '26.1', 'subgroup_hash': 1, 'subgroup_order': 26, 'subgroup_tex': 'D_{13}', 'supersolvable': True, 'sylow': 0}
id: 65179057
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1274.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 65179058
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.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': 1274, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 65179059
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 65179060
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 65179061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.c1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.c1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 65179062
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
id: 65179063
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 65179064
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.1274.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1274.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1274, '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': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 65179065
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 89, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.1456.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1456.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1456, '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': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
id: 65179067
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '30576.b.1911.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1911.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1911, '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': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 2}
id: 65179068
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': True, 'central_factor': False, 'centralizer_order': 30576, 'characteristic': True, 'core_order': 14, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '30576.b.2184.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2184.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2184.o', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7979629276488959051, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 2184, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\PSL(2,13)', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179069
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.2184.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2184.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': 2184, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179070
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.2184.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2184.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2184, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179071
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.2184.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2184.c1.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': 2184, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179072
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 196, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.2184.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2184.c1.c1', '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': 2184, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179073
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 7, 'counter': 96, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '30576.b.2184.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2184.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2184, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 65179074
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.2184.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2184.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2184, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 65179075
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.2184.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2184.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2184, '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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 65179076
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 364, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 13, 'label': '30576.b.2352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2352.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2352, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '13.1', 'subgroup_hash': 1, 'subgroup_order': 13, 'subgroup_tex': 'C_{13}', 'supersolvable': True, 'sylow': 13}
id: 65178954
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '30576.b', 'ambient_counter': 2, 'ambient_order': 30576, 'ambient_tex': '\\SL(2,13):C_{14}', 'central': False, 'central_factor': False, 'centralizer_order': 168, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '30576.b.2548.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2548.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2548, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}

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

gps_subgroup_data • Show schema
Showing the first 100 of 125 matching records in this table.

id: 65178952
{'ambient': '30576.b', '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': '1092.a1.a1', 'complements': ['30576.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '7.a1.a1', '14.b1.a1', '78.a1.a1', '91.a1.a1', '91.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7029, 4857, 5037, 5014, 7356, 5934, 2408, 5934], 'generators': [115345194, 466071127, 801250460, 448893330, 265474550], 'label': '30576.b.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '7.a1.a1', '1092.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1092.25', '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': '1092.25'}
id: 65178953
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '28.b1.a1', '28.c1.a1'], 'contains': ['112.a1.a1', '168.a1.a1', '392.a1.a1', '728.a1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1435, -1, 7072, -1, 1169, -1, 8226, -1], 'generators': [660312193, 483724728, 801250460, 265474550], 'label': '30576.b.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178954
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['196.a1.a1', '364.a1.a1', '1274.a1.a1', '1274.c1.a1', '1274.c1.a2'], 'contains': ['5096.a1.a1', '5096.b1.a1', '7644.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [2477, -1, 8446, -1, 4585, -1, 5379, -1], 'generators': [20176919, 57921720, 43393128], 'label': '30576.b.2548.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178955
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.b1.a1', '1274.b1.a1', '1274.c1.a2', '1274.d1.a1'], 'contains': ['5096.a1.a1', '5096.c1.a1', '7644.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [4043, -1, 8098, -1, 5254, -1, 4657, -1], 'generators': [436393243, 57921720, 785063325], 'label': '30576.b.2548.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178956
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.b1.a2', '1274.b1.a2', '1274.c1.a1', '1274.d1.a1'], 'contains': ['5096.a1.a1', '5096.c1.a2', '7644.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [4043, -1, 7422, -1, 5254, -1, 4511, -1], 'generators': [451549837, 436393243, 57921720], 'label': '30576.b.2548.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.b1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178957
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['196.b1.a1', '364.c1.a1', '637.a1.a1', '1274.a1.a1', '1274.b1.a1', '1274.b1.a2'], 'contains': ['5096.a1.a1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [5411, -1, 5295, -1, 5063, -1, 3363, -1], 'generators': [57921720, 31536929, 24134050], 'label': '30576.b.2548.c1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178958
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['196.c1.a1', '364.d1.a1', '1274.a1.a1', '1274.d1.a1', '1274.e1.a1'], 'contains': ['5096.a1.a1', '7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [6543, -1, 7165, -1, 6048, -1, 4349, -1], 'generators': [30249993, 7899068, 57921720], 'label': '30576.b.2548.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178959
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.e1.a1', '1274.b1.a1', '1274.c1.a1', '1274.e1.a1'], 'contains': ['5096.a1.a1', '7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [4266, -1, 6233, -1, 6263, -1, 3655, -1], 'generators': [436393243, 57921720, 361694077], 'label': '30576.b.2548.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178960
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2548.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.e1.a2', '1274.b1.a2', '1274.c1.a2', '1274.e1.a1'], 'contains': ['5096.a1.a1', '7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [4266, -1, 6433, -1, 6263, -1, 3842, -1], 'generators': [436393243, 57921720, 616633735], 'label': '30576.b.2548.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '2548.e1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2548.e1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178961
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '3822.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['294.a1.a1', '546.a1.a1', '546.c1.a1', '1274.a1.a1', '1274.b1.a1', '1274.b1.a2', '1911.a1.a1'], 'contains': ['7644.a1.a1', '7644.b1.a1', '7644.c1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [5733, -1, 3919, -1, 6536, -1, 2958, -1], 'generators': [30249993, 57921720, 24134050], 'label': '30576.b.3822.a1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '3822.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3822.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178962
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '3822.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['546.b1.a1', '1274.c1.a1', '1274.c1.a2', '1274.d1.a1', '1911.a1.a1'], 'contains': ['7644.b1.a1', '7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 273, 'diagramx': [5270, -1, 4815, -1, 7000, -1, 4186, -1], 'generators': [451549837, 57921720, 677577488], 'label': '30576.b.3822.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '273.a1.a1', 'old_label': '3822.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3822.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 65178963
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '3822.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['546.d1.a1', '1274.e1.a1', '1274.f1.a1', '1911.a1.a1'], 'contains': ['7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [7472, -1, 4218, -1, 7694, -1, 2747, -1], 'generators': [57921720, 677577488, 616633735], 'label': '30576.b.3822.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '3822.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3822.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65178964
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.a1.a1', '168.b1.a1', '392.b1.a1', '728.b1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [226, -1, 7622, -1, 210, -1, 9822, -1], 'generators': [483724728, 423170885, 746691038, 265474550], 'label': '30576.b.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.b1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178965
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '4368.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['336.a1.a1', '624.a1.a1', '1456.a1.a1', '2184.a1.a1', '2184.d1.a1'], 'contains': ['30576.a1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2798, 7851, 2110, 1239, 4898, 7576, 4606, 7576], 'generators': [265474550], 'label': '30576.b.4368.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '4368.a1.a1', 'normal_contained_in': ['2184.a1.a1'], 'normal_contains': ['30576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4368.a1.a1', 'projective_image': '4368.c', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4368.c', 'quotient_action_kernel_order': 4368, 'quotient_fusion': None, 'short_label': '4368.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65178966
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '4368.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['624.a1.a1', '2184.b1.a1', '2184.e1.a1', '2184.e1.a2'], 'contains': ['30576.a1.a1'], 'core': '30576.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8915, -1, 1149, -1, 8301, -1, 2248, -1], 'generators': [766871995], 'label': '30576.b.4368.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '4368.b1.a1', 'projective_image': '30576.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4368.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178967
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id: 65178968
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id: 65178969
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id: 65178970
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id: 65178971
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '5096.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['392.b1.a1', '392.b1.a2', '728.b1.a1', '2548.a1.a1'], 'contains': ['10192.a1.a1', '15288.b1.a1'], 'core': '30576.a1.a1', 'coset_action_label': None, 'count': 182, 'diagramx': [1456, -1, 9024, -1, 4238, -1, 7423, -1], 'generators': [20176919, 43393128], 'label': '30576.b.5096.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '182.a1.a1', 'old_label': '5096.b1.a1', 'projective_image': '30576.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5096.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65178972
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id: 65178973
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '5096.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['728.c1.a2', '2548.b1.a2'], 'contains': ['10192.a1.a1', '15288.b1.a1'], 'core': '30576.a1.a1', 'coset_action_label': None, 'count': 182, 'diagramx': [1847, -1, 8135, -1, 4620, -1, 5304, -1], 'generators': [451549837, 436393243], 'label': '30576.b.5096.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '182.b1.a2', 'old_label': '5096.c1.a2', 'projective_image': '30576.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5096.c1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 65178974
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id: 65178975
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id: 65178976
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '7644.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['588.a1.a1', '1092.b1.a1', '1092.c1.a1', '2548.a1.a1', '2548.b1.a1', '2548.b1.a2', '3822.a1.a1', '3822.b1.a1'], 'contains': ['15288.a1.a1', '15288.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [4266, -1, 4928, -1, 5388, -1, 4584, -1], 'generators': [20176919, 57921720], 'label': '30576.b.7644.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '7644.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7644.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178977
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id: 65178978
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '10192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['784.a1.a1', '1456.a1.a1', '5096.a1.a1', '5096.b1.a1', '5096.c1.a1', '5096.c1.a2'], 'contains': ['30576.a1.a1'], 'core': '30576.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [1721, -1, 8331, -1, 4448, -1, 5628, -1], 'generators': [36440461], 'label': '30576.b.10192.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '10192.a1.a1', 'projective_image': '30576.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178979
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id: 65178980
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id: 65178981
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id: 65178982
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id: 65178983
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id: 65178984
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1', '42.a1.a1'], 'contains': ['168.a1.a1', '588.b1.a1', '1092.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2521, -1, 6145, -1, 2470, -1, 6488, -1], 'generators': [801250460, 448893330, 642694551, 265474550], 'label': '30576.b.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 65178985
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1.a1', '42.a1.a1'], 'contains': ['168.a1.a1', '588.c1.a1', '1092.f1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5350, -1, 6451, -1, 3561, -1, 7508, -1], 'generators': [716814548, 483724728, 801250460, 265474550], 'label': '30576.b.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '84.c1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178986
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '91.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['182.f1.a1', '273.a1.a1', '364.c1.a1', '637.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [7660, -1, 6684, -1, 7256, -1, 2501, -1], 'generators': [801250460, 448893330, 120984722, 572990001, 724856504, 265474550], 'label': '30576.b.91.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '91.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '91.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65178987
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '91.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['182.a1.a1', '182.b1.a1', '182.b1.a2', '182.c1.a1', '182.c1.a2', '182.d1.a1', '182.e1.a1', '273.a1.a1', '637.b1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [5005, -1, 4675, -1, 6347, -1, 3657, -1], 'generators': [611803378, 801250460, 448893330, 739236111, 265474550, 177590821], 'label': '30576.b.91.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '91.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '91.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178988
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '98.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '14.b1.a1'], 'contains': ['196.a1.a1', '196.b1.a1', '196.c1.a1', '294.a1.a1', '1274.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5746, -1, 8600, -1, 2784, -1, 7145, -1], 'generators': [30249993, 57921720, 285962998, 43393128, 24134050], 'label': '30576.b.98.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '98.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '98.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178989
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': ['15288.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '28.c1.a1', '156.c1.a1', '182.e1.a1', '182.f1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6839, 4857, 5974, 5014, 8019, 5934, 2258, 5934], 'generators': [115345194, 466071127, 801250460, 265474550], 'label': '30576.b.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1', '2184.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1092.25'}
id: 65178990
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '56.b1.a1', '56.b1.a2'], 'contains': ['336.a1.a1', '784.a1.a1', '1456.a1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [421, -1, 7793, -1, 1267, -1, 8552, -1], 'generators': [388890067, 483724728, 265474550], 'label': '30576.b.112.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.a1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178991
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '156.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['78.a1.a1'], 'contains': ['312.a1.a1', '312.b1.a1', '312.b1.a2', '1092.b1.a1', '1092.c1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8801, -1, 2418, -1, 9435, -1, 480, -1], 'generators': [801250460, 724242170, 751430811, 265474550], 'label': '30576.b.156.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '156.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '156.a1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 65178992
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '156.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['78.a1.a1'], 'contains': ['312.a1.a1', '1092.a1.a1', '1092.d1.a1', '1092.e1.a1', '1092.e1.b1', '1092.e1.c1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [9480, -1, 844, -1, 9827, -1, 147, -1], 'generators': [801250460, 448893330, 724242170, 265474550], 'label': '30576.b.156.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '156.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '156.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178993
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '156.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '78.a1.a1'], 'contains': ['312.a1.a1', '1092.f1.a1', '1092.g1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8279, -1, 1324, -1, 9037, -1, 1094, -1], 'generators': [67560272, 801250460, 724242170, 265474550], 'label': '30576.b.156.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '156.c1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '156.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 65178994
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '84.a1.a1', '84.b1.a1', '84.c1.a1'], 'contains': ['336.a1.a1', '1176.a1.a1', '2184.a1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1630, -1, 6167, -1, 2686, -1, 6839, -1], 'generators': [483724728, 801250460, 265474550], 'label': '30576.b.168.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 65178995
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '84.a1.a1'], 'contains': ['336.a1.a1', '1176.b1.a1', '2184.d1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [676, -1, 5891, -1, 1696, -1, 8189, -1], 'generators': [483724728, 746691038, 265474550], 'label': '30576.b.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.b1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178996
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a2', '84.a1.a1'], 'contains': ['336.a1.a1', '1176.b1.a2', '2184.d1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [676, -1, 6524, -1, 1696, -1, 7857, -1], 'generators': [483724728, 313612573, 265474550], 'label': '30576.b.168.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '168.b1.a2', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a2', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65178997
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '182.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1', '91.b1.a1'], 'contains': ['364.a1.a1', '364.c1.a1', '364.d1.a1', '546.a1.a1', '1274.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [2901, -1, 5831, -1, 4905, -1, 4152, -1], 'generators': [716814548, 801250460, 448893330, 274410285, 265474550], 'label': '30576.b.182.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '182.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '182.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65178998
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '182.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['91.b1.a1'], 'contains': ['364.b1.a1', '364.c1.a1', '364.e1.a1', '546.a1.a1', '1274.b1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3750, -1, 4977, -1, 5785, -1, 3493, -1], 'generators': [801250460, 448893330, 413697563, 265474550, 177590821], 'label': '30576.b.182.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '182.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '182.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65178999
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '182.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['91.b1.a1'], 'contains': ['364.b1.a2', '364.c1.a1', '364.e1.a2', '546.a1.a1', '1274.b1.a2'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3750, -1, 3582, -1, 5785, -1, 3821, -1], 'generators': [611803378, 801250460, 448893330, 265474550, 177590821], 'label': '30576.b.182.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '182.b1.a2', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '182.b1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65179000
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': ['4368.c1.c1', '4368.c1.b1', '4368.c1.a1', '4368.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '98.a1.a1', '546.c1.a1', '637.a1.a1', '637.b1.a1'], 'core': '7.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7210, 2149, 8636, 9015, 7490, 1613, 1810, 1613], 'generators': [228729465, 72469057, 57921720, 24134050], 'label': '30576.b.7.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1', '7644.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '7.a1.a1', 'projective_image': None, 'quotient_action_image': '7.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1092.25'}
id: 65179001
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id: 65179002
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id: 65179003
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id: 65179004
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '182.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '91.b1.a1'], 'contains': ['364.d1.a1', '364.e1.a1', '364.e1.a2', '546.d1.a1', '1274.e1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [5807, -1, 5325, -1, 6856, -1, 3158, -1], 'generators': [801250460, 654490155, 739236111, 106830130, 265474550], 'label': '30576.b.182.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '182.e1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '182.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65179005
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '182.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '91.a1.a1'], 'contains': ['546.d1.a1', '728.a1.a1', '1274.f1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [7408, -1, 6893, -1, 7985, -1, 2120, -1], 'generators': [658177982, 328356958, 801250460, 120984722, 265474550], 'label': '30576.b.182.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '182.f1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '182.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65179006
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id: 65179007
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '196.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.b1.a1', '98.a1.a1'], 'contains': ['392.a1.a1', '588.b1.a1', '2548.c1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4305, -1, 8238, -1, 2124, -1, 6782, -1], 'generators': [57921720, 31536929, 285962998, 24134050], 'label': '30576.b.196.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '196.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '196.b1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179008
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '196.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '28.c1.a1', '98.a1.a1'], 'contains': ['392.a1.a1', '588.c1.a1', '2548.d1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6404, -1, 8917, -1, 3154, -1, 7853, -1], 'generators': [30249993, 7899068, 483724728, 57921720], 'label': '30576.b.196.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '196.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '196.c1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179009
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '273.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['91.a1.a1', '91.b1.a1'], 'contains': ['546.a1.a1', '546.b1.a1', '546.d1.a1', '1911.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [6821, -1, 2972, -1, 7256, -1, 2501, -1], 'generators': [611803378, 801250460, 448893330, 739236111, 265474550], 'label': '30576.b.273.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '273.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '273.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65179010
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '294.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.a1.a1', '98.a1.a1'], 'contains': ['588.a1.a1', '588.b1.a1', '588.c1.a1', '3822.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4562, -1, 7725, -1, 2784, -1, 7145, -1], 'generators': [30249993, 57921720, 285962998, 24134050], 'label': '30576.b.294.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '294.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '294.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179011
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': ['2184.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['196.c1.a1', '1092.g1.a1', '1274.e1.a1', '1274.f1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6885, 5040, 9078, 5887, 8275, 3548, 1869, 3548], 'generators': [228729465, 72469057, 57921720], 'label': '30576.b.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1', '7.a1.a1'], 'normal_contains': ['15288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1092.25'}
id: 65179012
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '312.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.a1.a1', '156.b1.a1', '156.c1.a1'], 'contains': ['624.a1.a1', '2184.a1.a1', '2184.b1.a1', '2184.c1.a1', '2184.c1.b1', '2184.c1.c1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [9221, -1, 390, -1, 9037, -1, 1149, -1], 'generators': [801250460, 724242170, 265474550], 'label': '30576.b.312.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '312.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '312.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65179013
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '312.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.a1.a1'], 'contains': ['624.a1.a1', '2184.d1.a1', '2184.e1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8637, -1, 1990, -1, 8679, -1, 1633, -1], 'generators': [69967934, 751430811, 265474550], 'label': '30576.b.312.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '312.b1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '312.b1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 65179014
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id: 65179015
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id: 65179016
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id: 65179017
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id: 65179018
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id: 65179019
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id: 65179020
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id: 65179021
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '364.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['182.b1.a1', '182.c1.a1', '182.e1.a1'], 'contains': ['728.a1.a1', '1092.f1.a1', '2548.e1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3778, -1, 5190, -1, 5807, -1, 3803, -1], 'generators': [801250460, 654490155, 413697563, 265474550], 'label': '30576.b.364.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '364.e1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '364.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65179022
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.a1.a1', '98.a1.a1', '182.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3714, -1, 6140, -1, 3245, -1, 6754, -1], 'generators': [716814548, 801250460, 448893330, 274410285, 642694551, 265474550], 'label': '30576.b.14.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '14.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179023
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '364.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['182.b1.a2', '182.c1.a2', '182.e1.a1'], 'contains': ['728.a1.a1', '1092.f1.a1', '2548.e1.a2'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3778, -1, 4838, -1, 5807, -1, 4142, -1], 'generators': [801250460, 654490155, 106830130, 265474550], 'label': '30576.b.364.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '364.e1.a2', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '364.e1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65179024
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id: 65179025
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id: 65179026
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id: 65179027
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id: 65179028
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id: 65179029
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '546.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '78.a1.a1'], 'contains': ['1092.c1.a1', '1092.d1.a1', '1092.g1.a1', '3822.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8637, -1, 1669, -1, 8674, -1, 786, -1], 'generators': [256972910, 57921720, 116836285, 24134050], 'label': '30576.b.546.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '546.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '546.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 65179030
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '546.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['182.e1.a1', '182.f1.a1', '273.a1.a1'], 'contains': ['1092.f1.a1', '3822.c1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [6913, -1, 3001, -1, 8047, -1, 1917, -1], 'generators': [801250460, 739236111, 106830130, 265474550], 'label': '30576.b.546.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '546.d1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '546.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65179031
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '588.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '196.a1.a1', '294.a1.a1'], 'contains': ['1176.a1.a1', '1176.b1.a1', '1176.b1.a2', '7644.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1392, -1, 8740, -1, 2463, -1, 7599, -1], 'generators': [483724728, 20176919, 57921720], 'label': '30576.b.588.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '588.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '588.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179032
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '588.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.b1.a1', '196.b1.a1', '294.a1.a1'], 'contains': ['1176.a1.a1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4367, -1, 7403, -1, 2908, -1, 6409, -1], 'generators': [57921720, 285962998, 24134050], 'label': '30576.b.588.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '588.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '588.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 65179033
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.b1.a2', '84.a1.a1', '196.a1.a1', '364.a1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1160, -1, 7072, -1, 1416, -1, 8643, -1], 'generators': [483724728, 313612573, 801250460, 274410285, 265474550], 'label': '30576.b.28.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179034
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '588.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.c1.a1', '196.c1.a1', '294.a1.a1'], 'contains': ['1176.a1.a1', '7644.c1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5416, -1, 7958, -1, 3157, -1, 6620, -1], 'generators': [30249993, 483724728, 57921720], 'label': '30576.b.588.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '588.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '588.c1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179035
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '624.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['312.a1.a1', '312.b1.a1', '312.b1.a2'], 'contains': ['4368.a1.a1', '4368.b1.a1', '4368.c1.a1', '4368.c1.b1', '4368.c1.c1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [9053, -1, 284, -1, 8633, -1, 1767, -1], 'generators': [69967934, 265474550], 'label': '30576.b.624.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '624.a1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '624.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65179036
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '637.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '91.a1.a1'], 'contains': ['1274.f1.a1', '1911.a1.a1', '2548.c1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [7917, -1, 6396, -1, 7595, -1, 1644, -1], 'generators': [350455415, 57921720, 303294956, 447400550, 24134050], 'label': '30576.b.637.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.a1.a1', 'old_label': '637.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '637.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 65179037
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '637.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '91.b1.a1'], 'contains': ['1274.a1.a1', '1274.b1.a1', '1274.b1.a2', '1274.c1.a1', '1274.c1.a2', '1274.d1.a1', '1274.e1.a1', '1911.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [6294, -1, 7157, -1, 6514, -1, 2868, -1], 'generators': [451549837, 57921720, 589426760, 677577488, 24134050], 'label': '30576.b.637.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '637.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '637.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 65179038
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '182.f1.a1', '364.a1.a1', '364.b1.a1', '364.b1.a2', '364.c1.a1', '364.d1.a1', '364.e1.a1', '364.e1.a2'], 'contains': ['1456.a1.a1', '2184.a1.a1', '5096.a1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3318, -1, 5253, -1, 4852, -1, 5152, -1], 'generators': [660312193, 801250460, 265474550], 'label': '30576.b.728.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '728.a1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '728.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65179039
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '728.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '56.b1.a2', '364.a1.a1'], 'contains': ['1456.a1.a1', '2184.d1.a1', '5096.b1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 182, 'diagramx': [1168, -1, 5759, -1, 3991, -1, 7419, -1], 'generators': [313612573, 274410285, 265474550], 'label': '30576.b.728.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '182.a1.a1', 'old_label': '728.b1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '728.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65179040
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '728.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.b1.a1'], 'contains': ['1456.a1.a1', '2184.d1.a1', '5096.c1.a1'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 182, 'diagramx': [2222, -1, 5017, -1, 4259, -1, 5928, -1], 'generators': [793333338, 654490155, 265474550], 'label': '30576.b.728.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '182.b1.a1', 'old_label': '728.c1.a1', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '728.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 65179041
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '728.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['364.b1.a2'], 'contains': ['1456.a1.a1', '2184.d1.a1', '5096.c1.a2'], 'core': '4368.a1.a1', 'coset_action_label': None, 'count': 182, 'diagramx': [2222, -1, 4732, -1, 4259, -1, 5654, -1], 'generators': [611803378, 654490155, 265474550], 'label': '30576.b.728.c1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '182.b1.a2', 'old_label': '728.c1.a2', 'projective_image': '4368.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '728.c1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 65179042
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '784.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '392.a1.a1', '392.b1.a1', '392.b1.a2'], 'contains': ['2352.a1.a1', '10192.a1.a1'], 'core': '30576.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [803, -1, 9817, -1, 2124, -1, 8270, -1], 'generators': [483724728, 36440461], 'label': '30576.b.784.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '784.a1.a1', 'projective_image': '30576.b', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '784.a1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179043
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['84.b1.a1', '156.b1.a1', '364.c1.a1', '546.a1.a1'], 'contains': ['2184.a1.a1', '7644.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3161, 7851, 1904, 985, 5838, 9316, 3185, 9316], 'generators': [801250460, 448893330, 265474550], 'label': '30576.b.1092.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1092, 'normal_closure': '1092.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['2184.a1.a1', '7644.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1092.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1092.25', 'quotient_action_kernel_order': 1092, 'quotient_fusion': None, 'short_label': '1092.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65179044
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1.a1'], 'contains': ['56.a1.a1', '84.b1.a1', '196.b1.a1', '364.c1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2521, -1, 6140, -1, 2289, -1, 6336, -1], 'generators': [660312193, 801250460, 448893330, 642694551, 265474550], 'label': '30576.b.28.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '28.b1.a1', 'projective_image': '1092.25', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '78.1'}
id: 65179045
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '156.a1.a1', '364.a1.a1', '364.b1.a1', '364.b1.a2', '546.a1.a1', '546.b1.a1'], 'contains': ['2184.a1.a1', '2184.d1.a1', '7644.b1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [3840, -1, 3948, -1, 5536, -1, 4896, -1], 'generators': [313612573, 801250460, 265474550], 'label': '30576.b.1092.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '1092.b1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65179046
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1092.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.a1.a1', '546.c1.a1'], 'contains': ['2184.b1.a1', '2184.e1.a1', '2184.e1.a2', '7644.b1.a1'], 'core': '15288.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [8822, -1, 2346, -1, 8408, -1, 2140, -1], 'generators': [256972910, 57921720, 116836285], 'label': '30576.b.1092.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '1092.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 65179047
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.b1.a1', '546.c1.a1'], 'contains': ['2184.b1.a1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 78, 'diagramx': [9442, -1, 1274, -1, 8196, -1, 2321, -1], 'generators': [57921720, 116836285, 24134050], 'label': '30576.b.1092.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '78.a1.a1', 'old_label': '1092.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 65179048
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.b1.a1'], 'contains': ['2184.c1.a1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 156, 'diagramx': [9774, -1, 742, -1, 9339, -1, 1404, -1], 'generators': [57921720, 724242170, 24134050], 'label': '30576.b.1092.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '156.b1.a1', 'old_label': '1092.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65179049
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.b1.a1'], 'contains': ['2184.c1.b1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 156, 'diagramx': [9774, -1, 928, -1, 9339, -1, 715, -1], 'generators': [57921720, 150962848, 24134050], 'label': '30576.b.1092.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '156.b1.a1', 'old_label': '1092.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65179050
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '156.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['156.b1.a1'], 'contains': ['2184.c1.c1', '7644.a1.a1'], 'core': '7644.a1.a1', 'coset_action_label': None, 'count': 156, 'diagramx': [9774, -1, 476, -1, 9339, -1, 893, -1], 'generators': [57921720, 563936054, 24134050], 'label': '30576.b.1092.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '156.b1.a1', 'old_label': '1092.e1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.e1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 65179051
{'ambient': '30576.b', 'aut_centralizer_order': None, 'aut_label': '1092.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '182.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.c1.a1', '156.c1.a1', '364.d1.a1', '364.e1.a1', '364.e1.a2', '546.a1.a1', '546.b1.a1', '546.d1.a1'], 'contains': ['2184.a1.a1', '7644.c1.a1'], 'core': '2184.a1.a1', 'coset_action_label': None, 'count': 91, 'diagramx': [5761, -1, 2795, -1, 6804, -1, 4024, -1], 'generators': [716814548, 801250460, 265474550], 'label': '30576.b.1092.f1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '91.b1.a1', 'old_label': '1092.f1.a1', 'projective_image': '2184.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1092.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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