LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-09-29T05:17:23.955416

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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [2, 6, 42, 7], 'aut_gens': [[1, 2, 28], [14, 113, 4], [13, 118, 140], [1, 90, 28], [17, 2, 28]], 'aut_group': '3528.br', 'aut_hash': 519392570028930314, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3528, 'aut_permdeg': 14, 'aut_perms': [64422659859, 58531649341, 27788271481, 4355079416], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 2, 1], [2, 49, 1, 1], [7, 2, 6, 1], [7, 4, 9, 1], [14, 14, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_7\\wr C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '3528.br', 'autcentquo_hash': 519392570028930314, 'autcentquo_nilpotent': False, 'autcentquo_order': 3528, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_7\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 7, 2], [2, 49, 1], [7, 2, 6], [7, 4, 9], [14, 14, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '196.9', 'commutator_count': 1, 'commutator_label': '49.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '7.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['14.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 2], [2, 49, 1, 1], [7, 2, 3, 2], [7, 4, 3, 3], [14, 14, 3, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 14, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[4, 1, 9]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '196.9', 'hash': 9, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 14, 7], 'inner_gens': [[1, 26, 28], [5, 2, 168], [1, 58, 28]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 196, 'inner_split': True, 'inner_tex': 'D_7^2', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 12], [4, 9]], 'label': '196.9', 'linC_count': 45, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 7, 'linQ_dim': 12, 'linQ_dim_count': 7, 'linR_count': 45, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D7^2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 25, 'number_divisions': 11, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 26, 'number_subgroups': 212, 'old_label': None, 'order': 196, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 63], [7, 48], [14, 84]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [15, 15], 'outer_gens': [[14, 141, 16], [1, 10, 84]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [541, 311], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [6, 4], [12, 3]], 'representations': {'PC': {'code': 25878846041027, 'gens': [1, 2, 4], 'pres': [4, -2, -2, -7, -7, 209, 21, 290, 1351]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [20383256, 31885375, 6473102, 1372909]}, 'Perm': {'d': 14, 'gens': [49816162079, 47249833680, 20248707456, 37362129120]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_7^2', 'transitive_degree': 14, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema

id: 109163378
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 9, 'group_order': 196, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 109163389
{'aut_label': '2A', 'centralizer': '7.a1.a1', 'counter': 2, 'group_counter': 9, 'group_order': 196, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 14, 'size': 7}
id: 109163396
{'aut_label': '2A', 'centralizer': '7.a1.b1', 'counter': 3, 'group_counter': 9, 'group_order': 196, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 1, 'size': 7}
id: 109163397
{'aut_label': '2C', 'centralizer': '49.a1.a1', 'counter': 4, 'group_counter': 9, 'group_order': 196, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 55, 'size': 49}
id: 109163398
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 9, 'group_order': 196, 'label': '7A1', 'order': 7, 'powers': [6, 7, 1], 'representative': 4, 'size': 2}
id: 109163399
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 6, 'group_counter': 9, 'group_order': 196, 'label': '7A2', 'order': 7, 'powers': [7, 5, 1], 'representative': 8, 'size': 2}
id: 109163400
{'aut_label': '7A1', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 9, 'group_order': 196, 'label': '7A3', 'order': 7, 'powers': [5, 6, 1], 'representative': 12, 'size': 2}
id: 109163401
{'aut_label': '7A1', 'centralizer': '2.a1.b1', 'counter': 8, 'group_counter': 9, 'group_order': 196, 'label': '7B1', 'order': 7, 'powers': [9, 10, 1], 'representative': 56, 'size': 2}
id: 109163402
{'aut_label': '7A1', 'centralizer': '2.a1.b1', 'counter': 9, 'group_counter': 9, 'group_order': 196, 'label': '7B2', 'order': 7, 'powers': [10, 8, 1], 'representative': 112, 'size': 2}
id: 109163379
{'aut_label': '7A1', 'centralizer': '2.a1.b1', 'counter': 10, 'group_counter': 9, 'group_order': 196, 'label': '7B3', 'order': 7, 'powers': [8, 9, 1], 'representative': 168, 'size': 2}
id: 109163380
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 9, 'group_order': 196, 'label': '7C1', 'order': 7, 'powers': [12, 13, 1], 'representative': 32, 'size': 4}
id: 109163381
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 12, 'group_counter': 9, 'group_order': 196, 'label': '7C2', 'order': 7, 'powers': [13, 11, 1], 'representative': 64, 'size': 4}
id: 109163382
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 13, 'group_counter': 9, 'group_order': 196, 'label': '7C3', 'order': 7, 'powers': [11, 12, 1], 'representative': 96, 'size': 4}
id: 109163383
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 9, 'group_order': 196, 'label': '7D1', 'order': 7, 'powers': [15, 16, 1], 'representative': 60, 'size': 4}
id: 109163384
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 15, 'group_counter': 9, 'group_order': 196, 'label': '7D2', 'order': 7, 'powers': [16, 14, 1], 'representative': 92, 'size': 4}
id: 109163385
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 16, 'group_counter': 9, 'group_order': 196, 'label': '7D3', 'order': 7, 'powers': [14, 15, 1], 'representative': 40, 'size': 4}
id: 109163386
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 17, 'group_counter': 9, 'group_order': 196, 'label': '7E1', 'order': 7, 'powers': [18, 19, 1], 'representative': 36, 'size': 4}
id: 109163387
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 18, 'group_counter': 9, 'group_order': 196, 'label': '7E2', 'order': 7, 'powers': [19, 17, 1], 'representative': 68, 'size': 4}
id: 109163388
{'aut_label': '7C1', 'centralizer': '4.a1.a1', 'counter': 19, 'group_counter': 9, 'group_order': 196, 'label': '7E3', 'order': 7, 'powers': [17, 18, 1], 'representative': 88, 'size': 4}
id: 109163390
{'aut_label': '14A1', 'centralizer': '14.b1.a1', 'counter': 20, 'group_counter': 9, 'group_order': 196, 'label': '14A1', 'order': 14, 'powers': [5, 21, 2], 'representative': 2, 'size': 14}
id: 109163391
{'aut_label': '14A1', 'centralizer': '14.b1.a1', 'counter': 21, 'group_counter': 9, 'group_order': 196, 'label': '14A3', 'order': 14, 'powers': [7, 22, 2], 'representative': 6, 'size': 14}
id: 109163392
{'aut_label': '14A1', 'centralizer': '14.b1.a1', 'counter': 22, 'group_counter': 9, 'group_order': 196, 'label': '14A5', 'order': 14, 'powers': [6, 20, 2], 'representative': 10, 'size': 14}
id: 109163393
{'aut_label': '14A1', 'centralizer': '14.b1.b1', 'counter': 23, 'group_counter': 9, 'group_order': 196, 'label': '14B1', 'order': 14, 'powers': [8, 24, 3], 'representative': 29, 'size': 14}
id: 109163394
{'aut_label': '14A1', 'centralizer': '14.b1.b1', 'counter': 24, 'group_counter': 9, 'group_order': 196, 'label': '14B3', 'order': 14, 'powers': [10, 25, 3], 'representative': 85, 'size': 14}
id: 109163395
{'aut_label': '14A1', 'centralizer': '14.b1.b1', 'counter': 25, 'group_counter': 9, 'group_order': 196, 'label': '14B5', 'order': 14, 'powers': [9, 23, 3], 'representative': 57, 'size': 14}

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: 4167265
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.1a', '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], 'schur_index': 1}
id: 4167268
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.1b', '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], 'schur_index': 1}
id: 4167269
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1], 'schur_index': 1}
id: 4167270
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1], 'schur_index': 1}
id: 4167271
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.2a', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 0, 6, 0, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -1, 0, -1, -1], 'schur_index': 1}
id: 4167272
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.2b', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -1, -1, -1, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, -1, 0, 0], 'schur_index': 1}
id: 4167273
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.2c', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -1, -1, -1, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 0, 0], 'schur_index': 1}
id: 4167274
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.2d', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 0, -6, 0, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 1, 0, 1, 1], 'schur_index': 1}
id: 4167275
{'cdim': 4, 'counter': 9, 'faithful': True, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.4a', 'multiplicity': 3, 'nt': [14, 13], 'qdim': 12, 'qvalues': [12, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 5, 5, -2, -2, 5, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4167266
{'cdim': 4, 'counter': 10, 'faithful': True, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.4b', 'multiplicity': 3, 'nt': [14, 13], 'qdim': 12, 'qvalues': [12, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 5, -2, -2, -2, -2, 5, -2, 5, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4167267
{'cdim': 4, 'counter': 11, 'faithful': True, 'group': '196.9', 'group_order': 196, 'image': None, 'label': '196.9.4c', 'multiplicity': 3, 'nt': [14, 13], 'qdim': 12, 'qvalues': [12, 0, 0, 0, -2, -2, -2, -2, -2, -2, 5, -2, 5, -2, -2, 5, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 6071075
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 196, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 196, 'label': '196.9.1a', '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]]]}
id: 6071086
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 196, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 98, 'label': '196.9.1b', '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]]]}
id: 6071093
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 196, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 98, 'label': '196.9.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 6071094
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 196, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 98, 'label': '196.9.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 6071095
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id: 6071096
{'center': '14.a1.b1', 'center_index': 14, 'center_order': 14, 'counter': 6, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.b1', 'kernel_order': 14, 'label': '196.9.2a2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]]]}
id: 6071097
{'center': '14.a1.b1', 'center_index': 14, 'center_order': 14, 'counter': 7, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.b1', 'kernel_order': 14, 'label': '196.9.2a3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
id: 6071098
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 8, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 14, 'label': '196.9.2b1', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]]]}
id: 6071099
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 9, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 14, 'label': '196.9.2b2', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[0, 0]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]]]}
id: 6071076
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 10, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '14.1', 'image_order': 14, 'indicator': 1, 'kernel': '14.a1.a1', 'kernel_order': 14, 'label': '196.9.2b3', 'nt': [7, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
id: 6071077
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 11, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 7, 'label': '196.9.2c1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[0, 0]]]}
id: 6071078
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 12, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 7, 'label': '196.9.2c2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[0, 0]]]}
id: 6071079
{'center': '14.a1.a1', 'center_index': 14, 'center_order': 14, 'counter': 13, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.b1', 'kernel_order': 7, 'label': '196.9.2c3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
id: 6071080
{'center': '14.a1.b1', 'center_index': 14, 'center_order': 14, 'counter': 14, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 7, 'label': '196.9.2d1', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 3], [1, -3]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[0, 0]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]]]}
id: 6071081
{'center': '14.a1.b1', 'center_index': 14, 'center_order': 14, 'counter': 15, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 7, 'label': '196.9.2d2', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[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, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]]]}
id: 6071082
{'center': '14.a1.b1', 'center_index': 14, 'center_order': 14, 'counter': 16, 'cyclotomic_n': 7, 'dim': 2, 'faithful': False, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '28.3', 'image_order': 28, 'indicator': 1, 'kernel': '28.a1.a1', 'kernel_order': 7, 'label': '196.9.2d3', 'nt': [14, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
id: 6071083
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4a1', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 3], [1, -3]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071084
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4a2', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071085
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4a3', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 1], [1, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071087
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4b1', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071088
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 21, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4b2', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 3], [1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071089
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 22, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4b3', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071090
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 23, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4c1', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071091
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 24, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4c2', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 2], [-1, -2]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 3], [-1, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 6071092
{'center': '196.a1.a1', 'center_index': 196, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 7, 'dim': 4, 'faithful': True, 'field': [1, -2, -1, 1], 'group': '196.9', 'group_counter': 9, 'group_order': 196, 'image': None, 'image_isoclass': '196.9', 'image_order': 196, 'indicator': 1, 'kernel': '196.a1.a1', 'kernel_order': 1, 'label': '196.9.4c3', 'nt': [14, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 2], [2, -2]], [[2, 3], [2, -3]], [[2, 1], [2, -1]], [[2, 0], [1, 3], [1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 1], [1, -1]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 1], [-1, -1]], [[2, 0], [1, 2], [1, -2]], [[-1, 0], [-1, 3], [-1, -3]], [[-1, 0], [-1, 2], [-1, -2]], [[-1, 0], [-1, 2], [-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 63626108
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 196, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 14, 'label': '196.9.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '196.9', 'subgroup_hash': 9, 'subgroup_order': 196, 'subgroup_tex': 'D_7^2', 'supersolvable': True, 'sylow': 0}
id: 63626119
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': False, 'core_order': 98, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '196.9.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, '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': True, 'special_labels': [], 'split': True, '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: 63626127
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 7, 'characteristic': False, 'core_order': 98, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '196.9.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, '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: 63626128
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 98, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '196.9.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '98.4', 'subgroup_hash': 4, 'subgroup_order': 98, 'subgroup_tex': 'C_7:D_7', 'supersolvable': True, 'sylow': 0}
id: 63626129
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': True, 'core_order': 49, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 7, 'label': '196.9.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '49.2', 'subgroup_hash': 2, 'subgroup_order': 49, 'subgroup_tex': 'C_7^2', 'supersolvable': True, 'sylow': 7}
id: 63626130
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 14, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.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': 7, '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: 63626131
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 14, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.7.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.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': 7, '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: 63626132
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': True, 'centralizer_order': 14, 'characteristic': False, 'core_order': 14, 'counter': 8, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '196.9.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626133
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': True, 'centralizer_order': 14, 'characteristic': False, 'core_order': 14, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '196.9.14.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626109
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 7, 'counter': 10, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 63626110
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 7, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.14.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 63626111
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 7, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626112
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 7, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.14.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626113
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626114
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.14.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.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': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626115
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '196.9.14.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.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': 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': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 63626116
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 98, 'characteristic': False, 'core_order': 7, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '196.9.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
id: 63626117
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 98, 'characteristic': False, 'core_order': 7, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '196.9.28.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '28.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
id: 63626118
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
id: 63626120
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.28.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
id: 63626121
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 49, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.28.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.b1.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': 28, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 0}
id: 63626122
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '196.9.49.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '49.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': 49, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
id: 63626123
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.98.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 63626124
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.98.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '98.a1.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': 98, '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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 63626125
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '196.9.98.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '98.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': 98, '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': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 63626126
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '196.9', 'ambient_counter': 9, 'ambient_order': 196, 'ambient_tex': 'D_7^2', 'central': True, 'central_factor': False, 'centralizer_order': 196, 'characteristic': True, 'core_order': 1, 'counter': 26, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '196.9.196.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '196.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '196.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 196, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 63626121
{'ambient': '196.9', 'aut_centralizer_order': 98, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.d1.c1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': '28T36', 'count': 2, 'diagramx': [7795, -1, 7863, -1, 2311, -1, 1283, -1], 'generators': [88], 'label': '196.9.28.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '28.b1.c1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 63626108
{'ambient': '196.9', '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': '196.a1.a1', 'complements': ['196.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '7.a1.a1', '7.a1.b1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3947, 5026, 3579, 5000, 5000, 4445, 6162, 5000], 'generators': [1, 4, 28, 14], 'label': '196.9.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '196.9', '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': '196.9'}
id: 63626109
{'ambient': '196.9', 'aut_centralizer_order': 42, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '14.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '98.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [857, -1, 374, -1, 5800, -1, 5775, -1], 'generators': [14, 4], 'label': '196.9.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '196.9', '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': '2.1'}
id: 63626110
{'ambient': '196.9', 'aut_centralizer_order': 42, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '14.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.b1'], 'contains': ['28.a1.b1', '98.a1.b1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [857, -1, 4840, -1, 5800, -1, 9576, -1], 'generators': [1, 28], 'label': '196.9.14.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.b1', 'old_label': '14.b1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 63626111
{'ambient': '196.9', 'aut_centralizer_order': 6, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '98.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '98.b1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6446, -1, 2809, -1, 4022, -1, 3935, -1], 'generators': [3, 4], 'label': '196.9.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626112
{'ambient': '196.9', 'aut_centralizer_order': 6, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '98.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.b1'], 'contains': ['28.a1.b1', '98.b1.a1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6446, -1, 6100, -1, 4022, -1, 4806, -1], 'generators': [3, 28], 'label': '196.9.14.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.b1', 'old_label': '14.c1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626113
{'ambient': '196.9', 'aut_centralizer_order': 2, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '196.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['28.b1.a1', '98.b1.a1'], 'core': '196.a1.a1', 'coset_action_label': '14T13', 'count': 14, 'diagramx': [9143, -1, 6869, -1, 600, -1, 1199, -1], 'generators': [3, 32], 'label': '196.9.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '14.d1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626114
{'ambient': '196.9', 'aut_centralizer_order': 2, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '196.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['28.b1.b1', '98.b1.a1'], 'core': '196.a1.a1', 'coset_action_label': '14T13', 'count': 14, 'diagramx': [9143, -1, 9626, -1, 600, -1, 2070, -1], 'generators': [3, 60], 'label': '196.9.14.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.b1', 'old_label': '14.d1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626115
{'ambient': '196.9', 'aut_centralizer_order': 2, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '196.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['28.b1.c1', '98.b1.a1'], 'core': '196.a1.a1', 'coset_action_label': '14T13', 'count': 14, 'diagramx': [9143, -1, 8451, -1, 600, -1, 327, -1], 'generators': [3, 88], 'label': '196.9.14.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.c1', 'old_label': '14.d1.c1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.c1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626116
{'ambient': '196.9', 'aut_centralizer_order': 294, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '2.a1.a1', 'complements': ['7.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.b1', '14.b1.a1', '14.c1.a1'], 'contains': ['196.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3505, 6507, 1335, 5631, 5622, 5343, 4770, 6032], 'generators': [4], 'label': '196.9.28.a1.a1', 'mobius_quo': -1, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.a1.a1', '14.a1.b1'], 'normal_contains': ['196.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '196.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 63626117
{'ambient': '196.9', 'aut_centralizer_order': 294, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '2.a1.b1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.a1.a1', '14.b1.b1', '14.c1.b1'], 'contains': ['196.a1.a1'], 'core': '28.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3505, 6507, 5513, 3567, 5622, 5343, 5642, 3968], 'generators': [28], 'label': '196.9.28.a1.b1', 'mobius_quo': -1, 'mobius_sub': -14, 'normal_closure': '28.a1.b1', 'normal_contained_in': ['4.a1.a1', '14.a1.a1'], 'normal_contains': ['196.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.b1', 'projective_image': '196.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 63626118
{'ambient': '196.9', 'aut_centralizer_order': 98, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.d1.a1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': '28T36', 'count': 2, 'diagramx': [7795, -1, 7094, -1, 2311, -1, 2155, -1], 'generators': [32], 'label': '196.9.28.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '28.b1.a1', 'projective_image': '196.9', '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': '2.1'}
id: 63626119
{'ambient': '196.9', 'aut_centralizer_order': 7, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '252.28', 'aut_weyl_index': 14, 'centralizer': '28.a1.a1', 'complements': ['98.a1.b1', '98.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '14.a1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1790, 8042, 2639, 1704, 5000, 7187, 4794, 1705], 'generators': [14, 28, 4], 'label': '196.9.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '196.9', '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': '28.3'}
id: 63626120
{'ambient': '196.9', 'aut_centralizer_order': 98, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 588, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.d1.b1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': '28T36', 'count': 2, 'diagramx': [7795, -1, 9038, -1, 2311, -1, 3027, -1], 'generators': [60], 'label': '196.9.28.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '28.b1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 63626122
{'ambient': '196.9', 'aut_centralizer_order': 36, 'aut_label': '49.a1', 'aut_quo_index': None, 'aut_stab_index': 49, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1764, 'centralizer': '49.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1.a1', '7.a1.b1'], 'contains': ['98.a1.a1', '98.a1.b1', '98.b1.a1'], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 49, 'diagramx': [4976, -1, 3878, -1, 9289, -1, 7676, -1], 'generators': [1, 14], 'label': '196.9.49.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '49.a1.a1', 'old_label': '49.a1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '49.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 63626123
{'ambient': '196.9', 'aut_centralizer_order': 252, 'aut_label': '98.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3528, 'centralizer': '7.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.a1', '14.b1.a1', '49.a1.a1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2157, -1, 2949, -1, 7400, -1, 6622, -1], 'generators': [14], 'label': '196.9.98.a1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '98.a1.a1', 'projective_image': '196.9', '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': '1.1'}
id: 63626124
{'ambient': '196.9', 'aut_centralizer_order': 252, 'aut_label': '98.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3528, 'centralizer': '7.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1.b1', '14.b1.b1', '49.a1.a1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2157, -1, 4135, -1, 7400, -1, 8136, -1], 'generators': [1], 'label': '196.9.98.a1.b1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.b1', 'old_label': '98.a1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '98.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 63626125
{'ambient': '196.9', 'aut_centralizer_order': 72, 'aut_label': '98.b1', 'aut_quo_index': None, 'aut_stab_index': 49, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3528, 'centralizer': '49.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.c1.a1', '14.c1.b1', '14.d1.a1', '14.d1.b1', '14.d1.c1', '49.a1.a1'], 'contains': ['196.a1.a1'], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 49, 'diagramx': [5711, -1, 6100, -1, 4022, -1, 3898, -1], 'generators': [3], 'label': '196.9.98.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '49.a1.a1', 'old_label': '98.b1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '98.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 63626126
{'ambient': '196.9', 'aut_centralizer_order': None, 'aut_label': '196.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1', '28.a1.b1', '28.b1.a1', '28.b1.b1', '28.b1.c1', '98.a1.a1', '98.a1.b1', '98.b1.a1'], 'contains': [], 'core': '196.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4976, 6507, 5513, 4599, 4822, 5343, 4334, 5000], 'generators': [], 'label': '196.9.196.a1.a1', 'mobius_quo': 1, 'mobius_sub': 98, 'normal_closure': '196.a1.a1', 'normal_contained_in': ['28.a1.b1', '28.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '196.a1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '196.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 63626127
{'ambient': '196.9', 'aut_centralizer_order': 7, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '252.28', 'aut_weyl_index': 14, 'centralizer': '28.a1.b1', 'complements': ['98.a1.a1', '98.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '14.a1.b1', '14.b1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1790, 8042, 4540, 8296, 5000, 7187, 8608, 8295], 'generators': [1, 4, 28], 'label': '196.9.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '14.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '196.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 63626128
{'ambient': '196.9', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3528.br', 'aut_weyl_index': 1, 'centralizer': '196.a1.a1', 'complements': ['98.a1.a1', '98.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '14.c1.a1', '14.c1.b1', '14.d1.a1', '14.d1.b1', '14.d1.c1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7475, 1958, 7821, 5000, 2400, 1749, 3002, 5000], 'generators': [3, 28, 4], 'label': '196.9.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '196.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '196.9'}
id: 63626129
{'ambient': '196.9', 'aut_centralizer_order': 49, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '72.30', 'aut_weyl_index': 49, 'centralizer': '4.a1.a1', 'complements': ['49.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['28.a1.a1', '28.a1.b1', '28.b1.a1', '28.b1.b1', '28.b1.c1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6078, 4868, 5705, 5000, 2311, 3546, 3002, 5000], 'generators': [4, 28], 'label': '196.9.4.a1.a1', 'mobius_quo': 1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.b1.a1'], 'normal_contains': ['28.a1.b1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '196.9', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 63626130
{'ambient': '196.9', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '98.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.b1', '14.b1.a1', '14.c1.a1', '49.a1.a1'], 'core': '14.a1.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [3358, -1, 2393, -1, 7511, -1, 6162, -1], 'generators': [1, 4, 14], 'label': '196.9.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626131
{'ambient': '196.9', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '98.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.b1', '14.c1.b1', '49.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3358, -1, 4166, -1, 7511, -1, 7240, -1], 'generators': [1, 28, 14], 'label': '196.9.7.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.b1', 'old_label': '7.a1.b1', 'projective_image': '196.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626132
{'ambient': '196.9', 'aut_centralizer_order': 42, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '14.a1.b1', 'complements': ['14.a1.b1', '14.c1.a1', '14.d1.a1', '14.d1.b1', '14.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.b1'], 'contains': ['28.a1.b1', '98.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2819, 7936, 3579, 2307, 7578, 7187, 6743, 2249], 'generators': [14, 28], 'label': '196.9.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['28.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '196.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 63626133
{'ambient': '196.9', 'aut_centralizer_order': 42, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '42.1', 'aut_weyl_index': 84, 'centralizer': '14.a1.a1', 'complements': ['14.a1.a1', '14.c1.b1', '14.d1.a1', '14.d1.c1', '14.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '7.a1.a1'], 'contains': ['28.a1.a1', '98.a1.b1'], 'core': '14.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2819, 7936, 1634, 7006, 7578, 7187, 8608, 7751], 'generators': [1, 4], 'label': '196.9.14.a1.b1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.b1', 'normal_contained_in': ['2.a1.b1'], 'normal_contains': ['28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.b1', 'projective_image': '196.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '14.1', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '14.a1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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.