LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.3', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 156, 'aut_gen_orders': [2, 12, 2, 52], 'aut_gens': [[1, 4], [1, 204], [1, 388], [1, 212], [73, 4]], 'aut_group': '2496.m', 'aut_hash': 203795305191032416, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2496, 'aut_permdeg': 56, 'aut_perms': [375255912943571649608758266282692034355446318039910280167027600124860110699, 677589312679247996073606266072674447529905821634091604993951237490298668339, 413332299908359263057503103589173484823083967513180090512085688479081373004, 657870009361306646304447708362532377142151620858788439755690031911498039302], 'aut_phi_ratio': 13.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 13, 2, 1], [4, 1, 2, 1], [4, 13, 2, 1], [4, 13, 4, 2], [8, 1, 4, 1], [8, 13, 4, 3], [13, 4, 3, 1], [26, 4, 3, 1], [52, 4, 6, 1], [104, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4\\times F_{13}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 156, 'autcentquo_group': '156.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 156, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{13}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 13, 2], [4, 1, 2], [4, 13, 10], [8, 1, 4], [8, 13, 12], [13, 4, 3], [26, 4, 3], [52, 4, 6], [104, 4, 12]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '52.3', 'commutator_count': 1, 'commutator_label': '13.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '13.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 66, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['52.3', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 13, 1, 2], [4, 1, 2, 1], [4, 13, 2, 5], [8, 1, 4, 1], [8, 13, 4, 3], [13, 4, 3, 1], [26, 4, 3, 1], [52, 4, 6, 1], [104, 4, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 104, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 13], 'faithful_reps': [[4, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '104.12', 'hash': 66, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 52, 'inner_gen_orders': [4, 13], 'inner_gens': [[1, 228], [193, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 52, 'inner_split': True, 'inner_tex': 'C_{13}:C_4', 'inner_used': [1, 2], 'irrC_degree': 4, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [4, 24]], 'label': '416.66', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 8, 'linQ_dim': 16, 'linQ_dim_count': 8, 'linR_count': 48, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C104:C4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 56, 'number_divisions': 18, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 44, 'number_subgroups': 260, 'old_label': None, 'order': 416, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 27], [4, 132], [8, 160], [13, 12], [26, 12], [52, 24], [104, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 12], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 308], [1, 204], [105, 356]], 'outer_group': '48.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 9, 'outer_perms': [24, 10800, 46107], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [4, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [12, 2], [24, 1], [48, 1]], 'representations': {'PC': {'code': 2229695061671779145326799672747753719812107, 'gens': [1, 3], 'pres': [6, -2, -2, -2, -2, -2, -13, 12, 4106, 908, 50, 963, 2409, 69, 2404, 6010, 88, 5765, 6923]}, 'GLFq': {'d': 2, 'q': 169, 'gens': [58921344, 57921720, 395130710, 91709390, 61491841, 38614480]}, 'Perm': {'d': 21, 'gens': [128821980471172861, 12443, 262581480247986498, 6781, 18498, 2823515358096787200]}}, 'schur_multiplier': [4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 8], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{104}:C_4', 'transitive_degree': 104, '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: 110176197
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 66, 'group_order': 416, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 110176208
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 66, 'group_order': 416, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 208, 'size': 1}
id: 110176219
{'aut_label': '2B', 'centralizer': '13.a1.a1', 'counter': 3, 'group_counter': 66, 'group_order': 416, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 2, 'size': 13}
id: 110176230
{'aut_label': '2B', 'centralizer': '13.a1.a1', 'counter': 4, 'group_counter': 66, 'group_order': 416, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 50, 'size': 13}
id: 110176241
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 66, 'group_order': 416, 'label': '4A1', 'order': 4, 'powers': [2, 6, 5], 'representative': 104, 'size': 1}
id: 110176249
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 66, 'group_order': 416, 'label': '4A-1', 'order': 4, 'powers': [2, 5, 6], 'representative': 312, 'size': 1}
id: 110176250
{'aut_label': '4B1', 'centralizer': '13.a1.a1', 'counter': 7, 'group_counter': 66, 'group_order': 416, 'label': '4B1', 'order': 4, 'powers': [3, 8, 7], 'representative': 1, 'size': 13}
id: 110176251
{'aut_label': '4B-1', 'centralizer': '13.a1.a1', 'counter': 8, 'group_counter': 66, 'group_order': 416, 'label': '4B-1', 'order': 4, 'powers': [3, 7, 8], 'representative': 3, 'size': 13}
id: 110176252
{'aut_label': '4B1', 'centralizer': '13.a1.a1', 'counter': 9, 'group_counter': 66, 'group_order': 416, 'label': '4C1', 'order': 4, 'powers': [3, 10, 9], 'representative': 17, 'size': 13}
id: 110176198
{'aut_label': '4B-1', 'centralizer': '13.a1.a1', 'counter': 10, 'group_counter': 66, 'group_order': 416, 'label': '4C-1', 'order': 4, 'powers': [3, 9, 10], 'representative': 19, 'size': 13}
id: 110176199
{'aut_label': '4B1', 'centralizer': '13.a1.a1', 'counter': 11, 'group_counter': 66, 'group_order': 416, 'label': '4D1', 'order': 4, 'powers': [4, 12, 11], 'representative': 9, 'size': 13}
id: 110176200
{'aut_label': '4B-1', 'centralizer': '13.a1.a1', 'counter': 12, 'group_counter': 66, 'group_order': 416, 'label': '4D-1', 'order': 4, 'powers': [4, 11, 12], 'representative': 27, 'size': 13}
id: 110176201
{'aut_label': '4B1', 'centralizer': '13.a1.a1', 'counter': 13, 'group_counter': 66, 'group_order': 416, 'label': '4E1', 'order': 4, 'powers': [4, 14, 13], 'representative': 25, 'size': 13}
id: 110176202
{'aut_label': '4B-1', 'centralizer': '13.a1.a1', 'counter': 14, 'group_counter': 66, 'group_order': 416, 'label': '4E-1', 'order': 4, 'powers': [4, 13, 14], 'representative': 11, 'size': 13}
id: 110176203
{'aut_label': '4F1', 'centralizer': '13.a1.a1', 'counter': 15, 'group_counter': 66, 'group_order': 416, 'label': '4F1', 'order': 4, 'powers': [2, 16, 15], 'representative': 234, 'size': 13}
id: 110176204
{'aut_label': '4F1', 'centralizer': '13.a1.a1', 'counter': 16, 'group_counter': 66, 'group_order': 416, 'label': '4F-1', 'order': 4, 'powers': [2, 15, 16], 'representative': 26, 'size': 13}
id: 110176205
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 66, 'group_order': 416, 'label': '8A1', 'order': 8, 'powers': [5, 19, 20], 'representative': 52, 'size': 1}
id: 110176206
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 66, 'group_order': 416, 'label': '8A-1', 'order': 8, 'powers': [6, 20, 19], 'representative': 364, 'size': 1}
id: 110176207
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 66, 'group_order': 416, 'label': '8A3', 'order': 8, 'powers': [6, 17, 18], 'representative': 156, 'size': 1}
id: 110176209
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 66, 'group_order': 416, 'label': '8A-3', 'order': 8, 'powers': [5, 18, 17], 'representative': 260, 'size': 1}
id: 110176210
{'aut_label': '8B1', 'centralizer': '13.a1.a1', 'counter': 21, 'group_counter': 66, 'group_order': 416, 'label': '8B1', 'order': 8, 'powers': [5, 23, 24], 'representative': 6, 'size': 13}
id: 110176211
{'aut_label': '8B1', 'centralizer': '13.a1.a1', 'counter': 22, 'group_counter': 66, 'group_order': 416, 'label': '8B-1', 'order': 8, 'powers': [6, 24, 23], 'representative': 30, 'size': 13}
id: 110176212
{'aut_label': '8B1', 'centralizer': '13.a1.a1', 'counter': 23, 'group_counter': 66, 'group_order': 416, 'label': '8B3', 'order': 8, 'powers': [6, 21, 22], 'representative': 14, 'size': 13}
id: 110176213
{'aut_label': '8B1', 'centralizer': '13.a1.a1', 'counter': 24, 'group_counter': 66, 'group_order': 416, 'label': '8B-3', 'order': 8, 'powers': [5, 22, 21], 'representative': 22, 'size': 13}
id: 110176214
{'aut_label': '8C1', 'centralizer': '13.a1.a1', 'counter': 25, 'group_counter': 66, 'group_order': 416, 'label': '8C1', 'order': 8, 'powers': [15, 27, 28], 'representative': 5, 'size': 13}
id: 110176215
{'aut_label': '8C-1', 'centralizer': '13.a1.a1', 'counter': 26, 'group_counter': 66, 'group_order': 416, 'label': '8C-1', 'order': 8, 'powers': [16, 28, 27], 'representative': 31, 'size': 13}
id: 110176216
{'aut_label': '8C-1', 'centralizer': '13.a1.a1', 'counter': 27, 'group_counter': 66, 'group_order': 416, 'label': '8C3', 'order': 8, 'powers': [16, 25, 26], 'representative': 15, 'size': 13}
id: 110176217
{'aut_label': '8C1', 'centralizer': '13.a1.a1', 'counter': 28, 'group_counter': 66, 'group_order': 416, 'label': '8C-3', 'order': 8, 'powers': [15, 26, 25], 'representative': 21, 'size': 13}
id: 110176218
{'aut_label': '8C1', 'centralizer': '13.a1.a1', 'counter': 29, 'group_counter': 66, 'group_order': 416, 'label': '8D1', 'order': 8, 'powers': [16, 31, 32], 'representative': 13, 'size': 13}
id: 110176220
{'aut_label': '8C-1', 'centralizer': '13.a1.a1', 'counter': 30, 'group_counter': 66, 'group_order': 416, 'label': '8D-1', 'order': 8, 'powers': [15, 32, 31], 'representative': 23, 'size': 13}
id: 110176221
{'aut_label': '8C-1', 'centralizer': '13.a1.a1', 'counter': 31, 'group_counter': 66, 'group_order': 416, 'label': '8D3', 'order': 8, 'powers': [15, 29, 30], 'representative': 7, 'size': 13}
id: 110176222
{'aut_label': '8C1', 'centralizer': '13.a1.a1', 'counter': 32, 'group_counter': 66, 'group_order': 416, 'label': '8D-3', 'order': 8, 'powers': [16, 30, 29], 'representative': 29, 'size': 13}
id: 110176223
{'aut_label': '13A1', 'centralizer': '4.c1.a1', 'counter': 33, 'group_counter': 66, 'group_order': 416, 'label': '13A1', 'order': 13, 'powers': [34, 34, 1], 'representative': 32, 'size': 4}
id: 110176224
{'aut_label': '13A1', 'centralizer': '4.c1.a1', 'counter': 34, 'group_counter': 66, 'group_order': 416, 'label': '13A2', 'order': 13, 'powers': [35, 35, 1], 'representative': 64, 'size': 4}
id: 110176225
{'aut_label': '13A1', 'centralizer': '4.c1.a1', 'counter': 35, 'group_counter': 66, 'group_order': 416, 'label': '13A4', 'order': 13, 'powers': [33, 33, 1], 'representative': 128, 'size': 4}
id: 110176226
{'aut_label': '26A1', 'centralizer': '4.c1.a1', 'counter': 36, 'group_counter': 66, 'group_order': 416, 'label': '26A1', 'order': 26, 'powers': [33, 37, 2], 'representative': 16, 'size': 4}
id: 110176227
{'aut_label': '26A1', 'centralizer': '4.c1.a1', 'counter': 37, 'group_counter': 66, 'group_order': 416, 'label': '26A3', 'order': 26, 'powers': [34, 38, 2], 'representative': 48, 'size': 4}
id: 110176228
{'aut_label': '26A1', 'centralizer': '4.c1.a1', 'counter': 38, 'group_counter': 66, 'group_order': 416, 'label': '26A7', 'order': 26, 'powers': [35, 36, 2], 'representative': 112, 'size': 4}
id: 110176229
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 39, 'group_counter': 66, 'group_order': 416, 'label': '52A1', 'order': 52, 'powers': [36, 41, 5], 'representative': 8, 'size': 4}
id: 110176231
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 40, 'group_counter': 66, 'group_order': 416, 'label': '52A-1', 'order': 52, 'powers': [36, 42, 6], 'representative': 408, 'size': 4}
id: 110176232
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 41, 'group_counter': 66, 'group_order': 416, 'label': '52A3', 'order': 52, 'powers': [37, 44, 6], 'representative': 24, 'size': 4}
id: 110176233
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 42, 'group_counter': 66, 'group_order': 416, 'label': '52A-3', 'order': 52, 'powers': [37, 43, 5], 'representative': 392, 'size': 4}
id: 110176234
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 43, 'group_counter': 66, 'group_order': 416, 'label': '52A7', 'order': 52, 'powers': [38, 39, 6], 'representative': 56, 'size': 4}
id: 110176235
{'aut_label': '52A1', 'centralizer': '4.c1.a1', 'counter': 44, 'group_counter': 66, 'group_order': 416, 'label': '52A-7', 'order': 52, 'powers': [38, 40, 5], 'representative': 360, 'size': 4}
id: 110176236
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 45, 'group_counter': 66, 'group_order': 416, 'label': '104A1', 'order': 104, 'powers': [39, 47, 17], 'representative': 4, 'size': 4}
id: 110176237
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 46, 'group_counter': 66, 'group_order': 416, 'label': '104A-1', 'order': 104, 'powers': [40, 48, 18], 'representative': 124, 'size': 4}
id: 110176238
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 47, 'group_counter': 66, 'group_order': 416, 'label': '104A3', 'order': 104, 'powers': [41, 52, 19], 'representative': 12, 'size': 4}
id: 110176239
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 48, 'group_counter': 66, 'group_order': 416, 'label': '104A-3', 'order': 104, 'powers': [42, 51, 20], 'representative': 116, 'size': 4}
id: 110176240
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 49, 'group_counter': 66, 'group_order': 416, 'label': '104A5', 'order': 104, 'powers': [39, 53, 20], 'representative': 20, 'size': 4}
id: 110176242
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 50, 'group_counter': 66, 'group_order': 416, 'label': '104A-5', 'order': 104, 'powers': [40, 54, 19], 'representative': 108, 'size': 4}
id: 110176243
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 51, 'group_counter': 66, 'group_order': 416, 'label': '104A7', 'order': 104, 'powers': [43, 49, 18], 'representative': 28, 'size': 4}
id: 110176244
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 52, 'group_counter': 66, 'group_order': 416, 'label': '104A-7', 'order': 104, 'powers': [44, 50, 17], 'representative': 36, 'size': 4}
id: 110176245
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 53, 'group_counter': 66, 'group_order': 416, 'label': '104A15', 'order': 104, 'powers': [41, 56, 18], 'representative': 60, 'size': 4}
id: 110176246
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 54, 'group_counter': 66, 'group_order': 416, 'label': '104A-15', 'order': 104, 'powers': [42, 55, 17], 'representative': 164, 'size': 4}
id: 110176247
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 55, 'group_counter': 66, 'group_order': 416, 'label': '104A19', 'order': 104, 'powers': [43, 45, 19], 'representative': 76, 'size': 4}
id: 110176248
{'aut_label': '104A1', 'centralizer': '4.c1.a1', 'counter': 56, 'group_counter': 66, 'group_order': 416, 'label': '104A-19', 'order': 104, 'powers': [44, 46, 20], 'representative': 180, 'size': 4}

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: 4544392
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4544402
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4544403
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4544404
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4544405
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, -2, 2, 2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544406
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, -2, 2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544407
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2], 'schur_index': 1}
id: 4544408
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1h', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 0, -2, 0, 0, 0, 0, -2, 0, 0, 0, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'schur_index': 1}
id: 4544409
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544393
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, 2, -2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544394
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1k', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 0, 4, 0, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544395
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1l', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, 0, -4, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544396
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, -4, 0, -4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544397
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.1n', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 4, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544398
{'cdim': 4, 'counter': 15, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.4a', 'multiplicity': 3, 'nt': [13, 4], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4544399
{'cdim': 4, 'counter': 16, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.4b', 'multiplicity': 3, 'nt': [26, 7], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4544400
{'cdim': 4, 'counter': 17, 'faithful': False, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.4c', 'multiplicity': 6, 'nt': [52, 0], 'qdim': 24, 'qvalues': [24, 24, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4544401
{'cdim': 4, 'counter': 18, 'faithful': True, 'group': '416.66', 'group_order': 416, 'image': None, 'label': '416.66.4d', 'multiplicity': 12, 'nt': [104, 0], 'qdim': 48, 'qvalues': [48, -48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 7083656
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 416, 'label': '416.66.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7083667
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 208, 'label': '416.66.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 7083678
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 208, 'label': '416.66.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7083689
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 208, 'label': '416.66.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 7083700
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 104, 'label': '416.66.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 7083708
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 104, 'label': '416.66.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 7083709
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 104, 'label': '416.66.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 7083710
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 104, 'label': '416.66.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 7083711
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 104, 'label': '416.66.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 7083657
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 104, 'label': '416.66.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 7083658
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 104, 'label': '416.66.1h1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 7083659
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 104, 'label': '416.66.1h2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 7083660
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 104, 'label': '416.66.1i1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 7083661
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 14, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 104, 'label': '416.66.1i2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 7083662
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 15, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 104, 'label': '416.66.1j1', 'nt': [4, 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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 7083663
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 16, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 104, 'label': '416.66.1j2', 'nt': [4, 2], '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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 7083664
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 17, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.c1', 'kernel_order': 52, 'label': '416.66.1k1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
id: 7083665
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 18, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.c1', 'kernel_order': 52, 'label': '416.66.1k2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
id: 7083666
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 19, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.c1', 'kernel_order': 52, 'label': '416.66.1k3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
id: 7083668
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 20, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.c1', 'kernel_order': 52, 'label': '416.66.1k4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
id: 7083669
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 21, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.d1', 'kernel_order': 52, 'label': '416.66.1l1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
id: 7083670
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 22, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.d1', 'kernel_order': 52, 'label': '416.66.1l2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
id: 7083671
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 23, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.d1', 'kernel_order': 52, 'label': '416.66.1l3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
id: 7083672
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 24, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.d1', 'kernel_order': 52, 'label': '416.66.1l4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
id: 7083673
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 25, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 52, 'label': '416.66.1m1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
id: 7083674
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 26, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 52, 'label': '416.66.1m2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
id: 7083675
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 27, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 52, 'label': '416.66.1m3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
id: 7083676
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 28, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 52, 'label': '416.66.1m4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
id: 7083677
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 29, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 52, 'label': '416.66.1n1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 3]]]}
id: 7083679
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 30, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 52, 'label': '416.66.1n2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
id: 7083680
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 31, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 52, 'label': '416.66.1n3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 3]]]}
id: 7083681
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 416, 'counter': 32, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.a1', 'kernel_order': 52, 'label': '416.66.1n4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
id: 7083682
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 13, 'dim': 4, 'faithful': False, 'field': [-1, -4, -1, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '52.3', 'image_order': 52, 'indicator': 1, 'kernel': '52.a1.a1', 'kernel_order': 8, 'label': '416.66.4a1', 'nt': [13, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]]]}
id: 7083683
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 13, 'dim': 4, 'faithful': False, 'field': [-1, -4, -1, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '52.3', 'image_order': 52, 'indicator': 1, 'kernel': '52.a1.a1', 'kernel_order': 8, 'label': '416.66.4a2', 'nt': [13, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 2], [1, 3], [1, -3], [1, -2]], [[1, 1], [1, 5], [1, -5], [1, -1]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 4], [1, 6], [1, -6], [1, -4]], [[1, 1], [1, 5], [1, -5], [1, -1]]]}
id: 7083684
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id: 7083685
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id: 7083686
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id: 7083687
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id: 7083688
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id: 7083690
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id: 7083691
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id: 7083692
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id: 7083693
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 43, 'cyclotomic_n': 52, 'dim': 4, 'faithful': False, 'field': [1, 0, 14, 0, 9, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '208.30', 'image_order': 208, 'indicator': 0, 'kernel': '208.a1.a1', 'kernel_order': 2, 'label': '416.66.4c5', 'nt': [52, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 13]], [[4, 13]], [[4, 13]], [[-4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, 12], [-1, 14], [-1, 18]], [[-1, 0], [-1, 4], [1, 6], [-1, 8], [-1, 12], [1, 14], [1, 18], [-1, 20], [1, 22]], [[1, 4], [-1, 6], [1, 20], [-1, 22]], [[1, 4], [-1, 6], [1, 20], [-1, 22]], [[1, 8], [1, 12], [-1, 14], [-1, 18]], [[-1, 0], [-1, 4], [1, 6], [-1, 8], [-1, 12], [1, 14], [1, 18], [-1, 20], [1, 22]], [[1, 0], [1, 4], [-1, 6], [1, 8], [1, 12], [-1, 14], [-1, 18], [1, 20], [-1, 22]], [[1, 0], [1, 4], [-1, 6], [1, 8], [1, 12], [-1, 14], [-1, 18], [1, 20], [-1, 22]], [[-1, 4], [1, 6], [-1, 20], [1, 22]], [[-1, 4], [1, 6], [-1, 20], [1, 22]], [[-1, 8], [-1, 12], [1, 14], [1, 18]], [[-1, 8], [-1, 12], [1, 14], [1, 18]], [[1, 3], [1, 11], [1, 15], [1, 23]], [[-1, 3], [-1, 11], [-1, 15], [-1, 23]], [[-1, 7], [1, 9], [1, 17], [-1, 19]], [[1, 3], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19], [1, 23]], [[-1, 3], [-1, 11], [-1, 15], [-1, 23]], [[-1, 3], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19], [-1, 23]], [[1, 7], [-1, 9], [-1, 17], [1, 19]], [[1, 3], [1, 11], [1, 15], [1, 23]], [[-1, 3], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19], [-1, 23]], [[1, 7], [-1, 9], [-1, 17], [1, 19]], [[-1, 7], [1, 9], [1, 17], [-1, 19]], [[1, 3], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19], [1, 23]]]}
id: 7083694
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 44, 'cyclotomic_n': 52, 'dim': 4, 'faithful': False, 'field': [1, 0, 14, 0, 9, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '208.30', 'image_order': 208, 'indicator': 0, 'kernel': '208.a1.a1', 'kernel_order': 2, 'label': '416.66.4c6', 'nt': [52, 6], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 13]], [[-4, 13]], [[-4, 13]], [[4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [1, 12], [-1, 14], [-1, 18]], [[-1, 0], [-1, 4], [1, 6], [-1, 8], [-1, 12], [1, 14], [1, 18], [-1, 20], [1, 22]], [[1, 4], [-1, 6], [1, 20], [-1, 22]], [[1, 4], [-1, 6], [1, 20], [-1, 22]], [[1, 8], [1, 12], [-1, 14], [-1, 18]], [[-1, 0], [-1, 4], [1, 6], [-1, 8], [-1, 12], [1, 14], [1, 18], [-1, 20], [1, 22]], [[1, 0], [1, 4], [-1, 6], [1, 8], [1, 12], [-1, 14], [-1, 18], [1, 20], [-1, 22]], [[1, 0], [1, 4], [-1, 6], [1, 8], [1, 12], [-1, 14], [-1, 18], [1, 20], [-1, 22]], [[-1, 4], [1, 6], [-1, 20], [1, 22]], [[-1, 4], [1, 6], [-1, 20], [1, 22]], [[-1, 8], [-1, 12], [1, 14], [1, 18]], [[-1, 8], [-1, 12], [1, 14], [1, 18]], [[-1, 3], [-1, 11], [-1, 15], [-1, 23]], [[1, 3], [1, 11], [1, 15], [1, 23]], [[1, 7], [-1, 9], [-1, 17], [1, 19]], [[-1, 3], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19], [-1, 23]], [[1, 3], [1, 11], [1, 15], [1, 23]], [[1, 3], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19], [1, 23]], [[-1, 7], [1, 9], [1, 17], [-1, 19]], [[-1, 3], [-1, 11], [-1, 15], [-1, 23]], [[1, 3], [1, 7], [-1, 9], [1, 11], [-1, 13], [1, 15], [-1, 17], [1, 19], [1, 23]], [[-1, 7], [1, 9], [1, 17], [-1, 19]], [[1, 7], [-1, 9], [-1, 17], [1, 19]], [[-1, 3], [-1, 7], [1, 9], [-1, 11], [1, 13], [-1, 15], [1, 17], [-1, 19], [-1, 23]]]}
id: 7083695
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 45, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d1', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 13]], [[4, 39]], [[-4, 39]], [[4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 7], [1, 19], [1, 35], [1, 43]]]}
id: 7083705
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 54, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d10', 'nt': [104, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 26]], [[-4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 39]], [[4, 13]], [[-4, 13]], [[4, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]]]}
id: 7083706
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 55, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d11', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 13]], [[-4, 39]], [[4, 39]], [[-4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]]]}
id: 7083707
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id: 7083696
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 46, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d2', 'nt': [104, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 26]], [[-4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 39]], [[-4, 13]], [[4, 13]], [[-4, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]]]}
id: 7083697
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d3', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 13]], [[4, 39]], [[-4, 39]], [[4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]]]}
id: 7083698
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d4', 'nt': [104, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 26]], [[-4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 39]], [[-4, 13]], [[4, 13]], [[-4, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]]]}
id: 7083699
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d5', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 13]], [[4, 39]], [[-4, 39]], [[4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]]]}
id: 7083701
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d6', 'nt': [104, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 26]], [[-4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 39]], [[-4, 13]], [[4, 13]], [[-4, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]]]}
id: 7083702
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d7', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 13]], [[-4, 39]], [[4, 39]], [[-4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]]]}
id: 7083703
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d8', 'nt': [104, 12], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 26]], [[-4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 39]], [[4, 13]], [[-4, 13]], [[4, 39]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 9], [1, 17], [1, 33], [-1, 45]]]}
id: 7083704
{'center': '52.a1.a1', 'center_index': 52, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 104, 'dim': 4, 'faithful': True, 'field': [1, 0, 0, 0, 178, 0, 0, 0, 53, 0, 0, 0, 1], 'group': '416.66', 'group_counter': 66, 'group_order': 416, 'image': None, 'image_isoclass': '416.66', 'image_order': 416, 'indicator': 0, 'kernel': '416.a1.a1', 'kernel_order': 1, 'label': '416.66.4d9', 'nt': [104, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 26]], [[4, 26]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 13]], [[-4, 39]], [[4, 39]], [[-4, 13]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 8], [-1, 12], [1, 40], [-1, 44]], [[1, 16], [1, 24], [-1, 28], [-1, 36]], [[-1, 0], [-1, 8], [1, 12], [-1, 16], [-1, 24], [1, 28], [1, 36], [-1, 40], [1, 44]], [[1, 0], [1, 8], [-1, 12], [1, 16], [1, 24], [-1, 28], [-1, 36], [1, 40], [-1, 44]], [[-1, 8], [1, 12], [-1, 40], [1, 44]], [[-1, 16], [-1, 24], [1, 28], [1, 36]], [[-1, 6], [-1, 14], [1, 18], [-1, 22], [1, 26], [-1, 30], [1, 34], [-1, 38], [-1, 46]], [[1, 6], [1, 14], [-1, 18], [1, 22], [-1, 26], [1, 30], [-1, 34], [1, 38], [1, 46]], [[-1, 6], [-1, 22], [-1, 30], [-1, 46]], [[1, 6], [1, 22], [1, 30], [1, 46]], [[-1, 14], [1, 18], [1, 34], [-1, 38]], [[1, 14], [-1, 18], [-1, 34], [1, 38]], [[-1, 1], [1, 5], [-1, 9], [1, 13], [-1, 17], [1, 21], [-1, 25], [-1, 33], [1, 45]], [[1, 3], [1, 11], [-1, 15], [-1, 23]], [[1, 7], [-1, 19], [-1, 35], [-1, 43]], [[-1, 3], [1, 7], [-1, 11], [1, 15], [-1, 19], [1, 23], [-1, 35], [1, 39], [-1, 43]], [[-1, 3], [-1, 11], [1, 15], [1, 23]], [[-1, 1], [1, 5], [1, 21], [-1, 25]], [[1, 9], [1, 17], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [1, 9], [-1, 13], [1, 17], [-1, 21], [1, 25], [1, 33], [-1, 45]], [[1, 1], [-1, 5], [-1, 21], [1, 25]], [[-1, 9], [-1, 17], [-1, 33], [1, 45]], [[-1, 7], [1, 19], [1, 35], [1, 43]], [[1, 3], [-1, 7], [1, 11], [-1, 15], [1, 19], [-1, 23], [1, 35], [-1, 39], [1, 43]]]}

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: 66505827
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 416, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 26, 'label': '416.66.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '416.66', 'subgroup_hash': 66, 'subgroup_order': 416, 'subgroup_tex': 'C_{104}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505838
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 208, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '208.30', 'subgroup_hash': 30, 'subgroup_order': 208, 'subgroup_tex': 'C_{52}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505849
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 208, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '208.4', 'subgroup_hash': 4, 'subgroup_order': 208, 'subgroup_tex': 'C_8\\times D_{13}', 'supersolvable': True, 'sylow': 0}
id: 66505860
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 208, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '208.28', 'subgroup_hash': 28, 'subgroup_order': 208, 'subgroup_tex': 'D_{13}:C_8', 'supersolvable': True, 'sylow': 0}
id: 66505866
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 104, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '104.5', 'subgroup_hash': 5, 'subgroup_order': 104, 'subgroup_tex': 'C_4\\times D_{13}', 'supersolvable': True, 'sylow': 0}
id: 66505867
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 104, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '104.12', 'subgroup_hash': 12, 'subgroup_order': 104, 'subgroup_tex': 'C_{26}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505868
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 104, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '104.12', 'subgroup_hash': 12, 'subgroup_order': 104, 'subgroup_tex': 'C_{26}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505869
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 104, 'characteristic': True, 'core_order': 104, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '416.66.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104.2', 'subgroup_hash': 2, 'subgroup_order': 104, 'subgroup_tex': 'C_{104}', 'supersolvable': True, 'sylow': 0}
id: 66505870
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 104, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104.1', 'subgroup_hash': 1, 'subgroup_order': 104, 'subgroup_tex': 'C_{13}:C_8', 'supersolvable': True, 'sylow': 0}
id: 66505828
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 104, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104.3', 'subgroup_hash': 3, 'subgroup_order': 104, 'subgroup_tex': 'C_{13}:C_8', 'supersolvable': True, 'sylow': 0}
id: 66505829
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 104, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104.3', 'subgroup_hash': 3, 'subgroup_order': 104, 'subgroup_tex': 'C_{13}:C_8', 'supersolvable': True, 'sylow': 0}
id: 66505830
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 52, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '52.4', 'subgroup_hash': 4, 'subgroup_order': 52, 'subgroup_tex': 'D_{26}', 'supersolvable': True, 'sylow': 0}
id: 66505831
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 104, 'characteristic': True, 'core_order': 52, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '416.66.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '52.2', 'subgroup_hash': 2, 'subgroup_order': 52, 'subgroup_tex': 'C_{52}', 'supersolvable': True, 'sylow': 0}
id: 66505832
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 52, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '52.1', 'subgroup_hash': 1, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505833
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 52, 'counter': 15, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '416.66.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '52.3', 'subgroup_hash': 3, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505834
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 52, 'counter': 16, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '416.66.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '52.3', 'subgroup_hash': 3, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505835
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 52, 'counter': 17, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '416.66.8.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '52.3', 'subgroup_hash': 3, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505836
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': False, 'core_order': 52, 'counter': 18, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '416.66.8.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '52.3', 'subgroup_hash': 3, 'subgroup_order': 52, 'subgroup_tex': 'C_{13}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66505837
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '416.66.13.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '13.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': 13, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 2}
id: 66505839
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 104, 'characteristic': True, 'core_order': 26, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '416.66.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '26.2', 'subgroup_hash': 2, 'subgroup_order': 26, 'subgroup_tex': 'C_{26}', 'supersolvable': True, 'sylow': 0}
id: 66505840
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 26, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '26.1', 'subgroup_hash': 1, 'subgroup_order': 26, 'subgroup_tex': 'D_{13}', 'supersolvable': True, 'sylow': 0}
id: 66505841
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 26, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '416.66.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '26.1', 'subgroup_hash': 1, 'subgroup_order': 26, 'subgroup_tex': 'D_{13}', 'supersolvable': True, 'sylow': 0}
id: 66505842
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.26.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '26.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': 26, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 66505843
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.26.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '26.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': 26, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 66505844
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.26.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '26.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': 26, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 66505845
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 104, 'characteristic': True, 'core_order': 13, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 13, 'label': '416.66.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.3', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times C_8', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '13.1', 'subgroup_hash': 1, 'subgroup_order': 13, 'subgroup_tex': 'C_{13}', 'supersolvable': True, 'sylow': 13}
id: 66505846
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 416, 'characteristic': True, 'core_order': 8, 'counter': 27, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '416.66.52.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '52.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '52.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 52, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{13}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 66505847
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.52.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.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': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 66505848
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.52.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.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': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 66505850
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.52.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.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': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 66505851
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.52.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.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': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 66505852
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.52.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 66505853
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.52.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '52.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 52, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 66505854
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 416, 'characteristic': True, 'core_order': 4, 'counter': 34, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '416.66.104.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '104.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '104.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 104, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{26}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505855
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '416.66.104.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.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': 104, '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': 0}
id: 66505856
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.104.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.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': 104, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505857
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.104.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.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': 104, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505858
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.104.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.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': 104, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505859
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.104.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.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': 104, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505861
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.104.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '104.d1.d1', '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': 104, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 66505862
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 416, 'characteristic': True, 'core_order': 2, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '416.66.208.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '208.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '208.30', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 208, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{52}:C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 66505863
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.208.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '208.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': 208, '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: 66505864
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '416.66.208.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '208.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': 208, '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: 66505865
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '416.66', 'ambient_counter': 66, 'ambient_order': 416, 'ambient_tex': 'C_{104}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 416, 'characteristic': True, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '416.66.416.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '416.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '416.66', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 66, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 416, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{104}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C6'], '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: 66505827
{'ambient': '416.66', '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': '52.a1.a1', 'complements': ['416.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '13.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6002, 5338, 7657, 6039, 6221, 5721, 6681, 6253], 'generators': [1, 32, 2, 104, 52, 208], 'label': '416.66.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '52.3', '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': '52.3'}
id: 66505828
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': ['104.d1.c1', '104.d1.d1', '104.d1.a1', '104.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '52.e1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5196, 3379, 5283, 7229, 9510, 3622, 9670, 7410], 'generators': [5, 208, 32, 234], 'label': '416.66.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '208.30', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505829
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': ['104.d1.a1', '104.d1.b1', '104.d1.d1', '104.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '52.e1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5196, 3379, 6136, 6039, 9510, 3622, 8894, 6253], 'generators': [13, 208, 32, 282], 'label': '416.66.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '208.30', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505830
{'ambient': '416.66', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '104.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2283, 3904, 3095, 2732, 3241, 4183, 2679, 4971], 'generators': [2, 32, 208], 'label': '416.66.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.b1', '4.b1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505831
{'ambient': '416.66', 'aut_centralizer_order': 104, 'aut_label': '8.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.9', 'aut_weyl_index': 104, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '104.a1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7293, 7132, 8669, 7748, 4105, 7539, 5702, 7828], 'generators': [104, 208, 32], 'label': '416.66.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'normal_contains': ['16.a1.a1', '104.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '104.12', 'quotient_action_image': '4.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 66505832
{'ambient': '416.66', 'aut_centralizer_order': 8, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.a1.a1', '104.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4153, 5338, 5972, 6149, 7831, 5721, 8678, 6166], 'generators': [10, 32, 208], 'label': '416.66.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.e1.a1', '4.e1.b1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505833
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': ['52.a1.a1', '52.d1.a1', '52.e1.a1', '52.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '104.d1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1209, 1848, 2349, 1694, 903, 1981, 330, 491], 'generators': [1, 32, 2], 'label': '416.66.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '416.66', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505834
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': ['52.a1.a1', '52.d1.a1', '52.e1.a1', '52.e1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.b1.a1', '104.d1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1209, 1848, 3842, 505, 903, 1981, 1106, 1647], 'generators': [17, 32, 98], 'label': '416.66.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '416.66', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505835
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': ['52.a1.a1', '52.d1.a1', '52.e1.b1', '52.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.b1.b1', '104.d1.c1'], 'core': '8.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1209, 1848, 363, 4960, 903, 1981, 4135, 3960], 'generators': [9, 32, 50], 'label': '416.66.8.d1.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.c1', 'normal_contained_in': ['4.b1.b1'], 'normal_contains': ['16.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.c1', 'projective_image': '416.66', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.d1.c1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505836
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': ['52.a1.a1', '52.d1.a1', '52.e1.b1', '52.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.b1.b1', '104.d1.d1'], 'core': '8.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [1209, 1848, 1216, 3771, 903, 1981, 3358, 2804], 'generators': [25, 32, 146], 'label': '416.66.8.d1.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.d1', 'normal_contained_in': ['4.b1.b1'], 'normal_contains': ['16.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.d1', 'projective_image': '416.66', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.d1.d1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505837
{'ambient': '416.66', 'aut_centralizer_order': 12, 'aut_label': '13.a1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '16.11', 'aut_weyl_index': 156, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['26.a1.a1', '26.b1.a1', '26.c1.a1'], 'core': '52.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [6653, -1, 8167, -1, 6948, -1, 7170, -1], 'generators': [1, 52], 'label': '416.66.13.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '13.a1.a1', 'projective_image': '52.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '13.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505838
{'ambient': '416.66', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1248.1162', 'aut_weyl_index': 2, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '26.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3212, 3173, 4716, 3652, 2795, 3400, 3972, 3931], 'generators': [1, 2, 208, 104, 32], 'label': '416.66.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.b1', '4.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505839
{'ambient': '416.66', 'aut_centralizer_order': 208, 'aut_label': '16.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '12.2', 'aut_weyl_index': 208, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['32.a1.a1', '208.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2655, 5338, 4802, 5710, 4260, 5721, 5558, 5437], 'generators': [208, 32], 'label': '416.66.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '208.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '208.30', 'quotient_action_image': '4.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 66505840
{'ambient': '416.66', 'aut_centralizer_order': 8, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.a1.a1', '208.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1301, 3904, 2887, 2213, 2601, 4183, 1857, 2842], 'generators': [2, 32], 'label': '416.66.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505841
{'ambient': '416.66', 'aut_centralizer_order': 8, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '156.7', 'aut_weyl_index': 16, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.c1', '8.d1.d1'], 'contains': ['32.a1.a1', '208.b1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1301, 3904, 1323, 3992, 2601, 4183, 3358, 4504], 'generators': [18, 32], 'label': '416.66.16.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1', '8.d1.c1', '8.d1.d1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505842
{'ambient': '416.66', 'aut_centralizer_order': 24, 'aut_label': '26.a1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '8.3', 'aut_weyl_index': 312, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '13.a1.a1'], 'contains': ['52.b1.a1', '52.c1.a1', '52.c1.b1'], 'core': '104.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [3956, -1, 5326, -1, 2193, -1, 3972, -1], 'generators': [1, 104], 'label': '416.66.26.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '26.a1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505843
{'ambient': '416.66', 'aut_centralizer_order': 24, 'aut_label': '26.b1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '8.5', 'aut_weyl_index': 312, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '13.a1.a1'], 'contains': ['52.a1.a1', '52.b1.a1', '52.d1.a1'], 'core': '52.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [7944, -1, 9637, -1, 6948, -1, 7170, -1], 'generators': [2, 52], 'label': '416.66.26.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '26.b1.a1', 'projective_image': '52.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505844
{'ambient': '416.66', 'aut_centralizer_order': 24, 'aut_label': '26.c1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '8.3', 'aut_weyl_index': 312, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '13.a1.a1'], 'contains': ['52.b1.a1', '52.e1.a1', '52.e1.b1'], 'core': '104.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [5867, -1, 7895, -1, 8268, -1, 8058, -1], 'generators': [5, 104], 'label': '416.66.26.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '26.c1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505845
{'ambient': '416.66', 'aut_centralizer_order': 208, 'aut_label': '32.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.2', 'aut_weyl_index': 208, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['416.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1539, 4910, 2163, 4211, 3455, 5129, 3378, 4621], 'generators': [32], 'label': '416.66.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.b1', '16.b1.a1'], 'normal_contains': ['416.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '416.66', 'quotient_action_image': '4.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 66505846
{'ambient': '416.66', 'aut_centralizer_order': 624, 'aut_label': '52.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 624, 'centralizer': '1.a1.a1', 'complements': ['8.d1.a1', '8.d1.b1', '8.d1.c1', '8.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '26.b1.a1'], 'contains': ['104.a1.a1'], 'core': '52.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7944, 8332, 9637, 8847, 6201, 9061, 7582, 9062], 'generators': [52], 'label': '416.66.52.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '52.a1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['104.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '52.a1.a1', 'projective_image': '52.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '52.3', 'quotient_action_kernel_order': 52, 'quotient_fusion': None, 'short_label': '52.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505847
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.b1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '4.2', 'aut_weyl_index': 624, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '26.a1.a1', '26.b1.a1', '26.c1.a1'], 'contains': ['104.a1.a1', '104.b1.a1', '104.c1.a1'], 'core': '104.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [4524, -1, 7628, -1, 5192, -1, 6433, -1], 'generators': [2, 104], 'label': '416.66.52.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.b1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505848
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.c1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '26.a1.a1'], 'contains': ['104.b1.a1', '104.d1.a1', '104.d1.b1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [1466, -1, 4056, -1, 2145, -1, 1942, -1], 'generators': [1, 208], 'label': '416.66.52.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.c1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505849
{'ambient': '416.66', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1248.1435', 'aut_weyl_index': 2, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1', '26.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7902, 7298, 8877, 7937, 5493, 7820, 6191, 8100], 'generators': [2, 104, 208, 52, 32], 'label': '416.66.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '52.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505850
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.c1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '26.a1.a1'], 'contains': ['104.b1.a1', '104.d1.c1', '104.d1.d1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [1466, -1, 1990, -1, 2145, -1, 4970, -1], 'generators': [9, 208], 'label': '416.66.52.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.c1.b1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505851
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.d1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '4.2', 'aut_weyl_index': 624, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '26.b1.a1'], 'contains': ['104.a1.a1'], 'core': '104.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [9235, -1, 9013, -1, 6900, -1, 7112, -1], 'generators': [102], 'label': '416.66.52.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.d1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505852
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.e1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '26.c1.a1'], 'contains': ['104.c1.a1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [5599, -1, 6266, -1, 8763, -1, 9305, -1], 'generators': [5], 'label': '416.66.52.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.e1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505853
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '52.e1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '26.c1.a1'], 'contains': ['104.c1.a1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [5599, -1, 6782, -1, 8763, -1, 8052, -1], 'generators': [13], 'label': '416.66.52.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '52.e1.b1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505854
{'ambient': '416.66', 'aut_centralizer_order': 1248, 'aut_label': '104.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '52.a1.a1', '52.b1.a1', '52.d1.a1'], 'contains': ['208.a1.a1'], 'core': '104.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7045, 7132, 8575, 7748, 5192, 7539, 6433, 7828], 'generators': [104], 'label': '416.66.104.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '104.a1.a1', 'normal_contained_in': ['8.b1.a1', '52.a1.a1'], 'normal_contains': ['208.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '104.a1.a1', 'projective_image': '104.12', 'quotient_action_image': '1.1', 'quotient_action_kernel': '104.12', 'quotient_action_kernel_order': 104, 'quotient_fusion': None, 'short_label': '104.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505855
{'ambient': '416.66', 'aut_centralizer_order': 96, 'aut_label': '104.b1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '52.b1.a1', '52.c1.a1', '52.c1.b1'], 'contains': ['208.a1.a1', '208.b1.a1', '208.b1.b1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [2169, -1, 3834, -1, 3435, -1, 3920, -1], 'generators': [2, 208], 'label': '416.66.104.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.b1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505856
{'ambient': '416.66', 'aut_centralizer_order': 96, 'aut_label': '104.c1', 'aut_quo_index': None, 'aut_stab_index': 13, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1248, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '52.b1.a1', '52.e1.a1', '52.e1.b1'], 'contains': ['208.a1.a1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [4050, -1, 6266, -1, 6861, -1, 8052, -1], 'generators': [10], 'label': '416.66.104.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.c1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505857
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '104.d1', 'aut_quo_index': None, 'aut_stab_index': 52, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '52.c1.a1'], 'contains': ['208.b1.a1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 3282, -1, 1815, -1, 1328, -1], 'generators': [1], 'label': '416.66.104.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.d1.a1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505858
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '104.d1', 'aut_quo_index': None, 'aut_stab_index': 52, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '52.c1.a1'], 'contains': ['208.b1.a1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 4387, -1, 1815, -1, 2386, -1], 'generators': [17], 'label': '416.66.104.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.d1.b1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505859
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '104.d1', 'aut_quo_index': None, 'aut_stab_index': 52, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '52.c1.b1'], 'contains': ['208.b1.b1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 1489, -1, 1815, -1, 4892, -1], 'generators': [9], 'label': '416.66.104.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.d1.c1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.d1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505860
{'ambient': '416.66', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1248.1162', 'aut_weyl_index': 2, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.e1.b1', '26.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5475, 5338, 7155, 6039, 8229, 5721, 8058, 6253], 'generators': [5, 234, 208, 104, 32], 'label': '416.66.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.e1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505861
{'ambient': '416.66', 'aut_centralizer_order': 48, 'aut_label': '104.d1', 'aut_quo_index': None, 'aut_stab_index': 52, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '52.c1.b1'], 'contains': ['208.b1.b1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 2005, -1, 1815, -1, 4422, -1], 'generators': [25], 'label': '416.66.104.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '104.d1.d1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '104.d1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505862
{'ambient': '416.66', 'aut_centralizer_order': 2496, 'aut_label': '208.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '104.a1.a1', '104.b1.a1', '104.c1.a1'], 'contains': ['416.a1.a1'], 'core': '208.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2789, 5780, 4953, 5710, 4260, 6312, 5558, 5437], 'generators': [208], 'label': '416.66.208.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '208.a1.a1', 'normal_contained_in': ['16.a1.a1', '104.a1.a1'], 'normal_contains': ['416.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '208.a1.a1', 'projective_image': '208.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '208.30', 'quotient_action_kernel_order': 208, 'quotient_fusion': None, 'short_label': '208.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505863
{'ambient': '416.66', 'aut_centralizer_order': 96, 'aut_label': '208.b1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '104.b1.a1', '104.d1.a1', '104.d1.b1'], 'contains': ['416.a1.a1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 3282, -1, 2630, -1, 2386, -1], 'generators': [2], 'label': '416.66.208.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '208.b1.a1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '208.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505864
{'ambient': '416.66', 'aut_centralizer_order': 96, 'aut_label': '208.b1', 'aut_quo_index': None, 'aut_stab_index': 26, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2496, 'centralizer': '13.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '104.b1.a1', '104.d1.c1', '104.d1.d1'], 'contains': ['416.a1.a1'], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 13, 'diagramx': [279, -1, 2005, -1, 2630, -1, 3920, -1], 'generators': [18], 'label': '416.66.208.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '13.a1.a1', 'old_label': '208.b1.b1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '208.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505865
{'ambient': '416.66', 'aut_centralizer_order': None, 'aut_label': '416.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': ['32.a1.a1', '208.a1.a1', '208.b1.a1', '208.b1.b1'], 'contains': [], 'core': '416.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [847, 5379, 2952, 5420, 3455, 5721, 3659, 5010], 'generators': [], 'label': '416.66.416.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '416.a1.a1', 'normal_contained_in': ['32.a1.a1', '208.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '416.a1.a1', 'projective_image': '416.66', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '416.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66505866
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '624.239', 'aut_weyl_index': 4, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '52.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3729, 5338, 7155, 4620, 3387, 5721, 4775, 4874], 'generators': [2, 208, 32, 104], 'label': '416.66.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '104.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505867
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '52.c1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1466, 1213, 3842, 894, 854, 1301, 1805, 1249], 'generators': [1, 2, 32, 208], 'label': '416.66.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505868
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '312.45', 'aut_weyl_index': 8, 'centralizer': '52.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.c1', '8.d1.d1', '52.c1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1466, 1213, 1782, 2833, 854, 1301, 3071, 3134], 'generators': [9, 50, 32, 208], 'label': '416.66.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.c1', '8.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '208.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '52.3'}
id: 66505869
{'ambient': '416.66', 'aut_centralizer_order': 52, 'aut_label': '4.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.44', 'aut_weyl_index': 52, 'centralizer': '4.c1.a1', 'complements': ['104.d1.a1', '104.d1.b1', '104.d1.c1', '104.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '52.a1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8605, 8787, 9494, 9495, 4658, 9416, 6407, 9616], 'generators': [52, 104, 208, 32], 'label': '416.66.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.b1.a1', '52.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '52.3', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 66505870
{'ambient': '416.66', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '624.239', 'aut_weyl_index': 4, 'centralizer': '52.a1.a1', 'complements': ['104.d1.a1', '104.d1.b1', '104.d1.c1', '104.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '52.d1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9721, 7298, 8718, 8417, 5706, 7820, 5702, 8566], 'generators': [102, 208, 32, 104], 'label': '416.66.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '104.12', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '52.3'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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