LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-02-04T05:47:36.484004

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 42, 'aut_gen_orders': [6, 14], 'aut_gens': [[16784385, 101521990, 16979969, 68817028, 1938688, 16849409, 16880641, 84383621], [16881153, 118592839, 16948225, 51844803, 101585478, 16849409, 16912897, 68852868], [16945153, 51745987, 16817665, 84153221, 34182594, 16979969, 16948225, 101453894]], 'aut_group': '688128.bi', 'aut_hash': 3039706533391825331, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 688128, 'aut_permdeg': 80, 'aut_perms': [13396347712416937746516208439108090430173680860182257005289956640941011959428386309747026007831966668024381263186405874, 54426467517091005268294851063997407059167849746613838974953759665683943551652706638820937482634295484722310693916301406], 'aut_phi_ratio': 5376.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1], [2, 4, 14, 1], [2, 8, 3, 1], [4, 8, 21, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^{12}.C_{14}:A_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': None, 'autcent_hash': 3946057693156513511, 'autcent_nilpotent': True, 'autcent_order': 32768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^{15}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 21, 'autcentquo_group': '21.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 21, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_7:C_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 4, 14], [2, 8, 3], [4, 8, 21]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '32.51', 'commutator_count': 1, 'commutator_label': '8.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 46157, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 4, 1, 14], [2, 8, 1, 3], [4, 8, 1, 21]], 'element_repr_type': 'GLFq', 'elementary': 2, 'eulerian_function': 476160, 'exponent': 4, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '32.51', 'hash': 46157, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2, 1, 2, 2, 1, 1, 2], 'inner_gens': [[16784385, 101585478, 16979969, 68785796, 2038016, 16849409, 16880641, 84319621], [16978945, 101521990, 16979969, 68853380, 1938688, 16849409, 16880641, 84383621], [16784385, 101521990, 16979969, 68817028, 1938688, 16849409, 16880641, 84383621], [17013249, 101553222, 16979969, 68817028, 2070272, 16849409, 16880641, 84189061], [16945153, 101521990, 16979969, 68686468, 1938688, 16849409, 16880641, 84383621], [16784385, 101521990, 16979969, 68817028, 1938688, 16849409, 16880641, 84383621], [16784385, 101521990, 16979969, 68817028, 1938688, 16849409, 16880641, 84383621], [16848385, 101521990, 16979969, 68753540, 1938688, 16849409, 16880641, 84383621]], 'inner_hash': 51, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': True, 'inner_tex': 'C_2^5', 'inner_used': [1, 2, 4, 5, 8], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [4, 14]], 'label': '256.46157', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:C2^3', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 46, 'number_divisions': 46, 'number_normal_subgroups': 403, 'number_subgroup_autclasses': 73, 'number_subgroup_classes': 1648, 'number_subgroups': 5063, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 87], [4, 168]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 42, 'outer_gen_orders': [7, 6], 'outer_gen_pows': [16784385, 16781313], 'outer_gens': [[16978945, 118529863, 16880641, 101553734, 68852868, 16817665, 16912897, 51646659], [16784897, 68754052, 16948225, 51679939, 34182594, 16817665, 16979969, 1938688]], 'outer_group': '21504.bp', 'outer_hash': 5385334024956809412, 'outer_nilpotent': False, 'outer_order': 21504, 'outer_permdeg': 22, 'outer_perms': [211798041582424527351, 512164798383892555593], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^{10}:C_7:C_3', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [4, 14]], 'representations': {'PC': {'code': 12389868118267742598268785744, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1924, 1132, 1460, 116, 11206, 6510, 3158, 166]}, 'GLFq': {'d': 3, 'q': 8, 'gens': [16784385, 101521990, 16979969, 68817028, 1938688, 16849409, 16880641, 84383621]}, 'Perm': {'d': 24, 'gens': [29645551604542253553919, 57551323693113285247793, 79140122006718417926400, 110261561163181339162247, 136525096875771419561436, 111745636804617587229499, 84811344950403599633280, 138824189357015259820800]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:C_2^3', 'transitive_degree': 32, '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: 102971253
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 46157, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 16781313, 'size': 1}
id: 102971264
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 46157, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16817665, 'size': 1}
id: 102971275
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 46157, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 16912897, 'size': 1}
id: 102971286
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 46157, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 16948225, 'size': 1}
id: 102971294
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 46157, 'group_order': 256, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 16880641, 'size': 1}
id: 102971295
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 46157, 'group_order': 256, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 17012225, 'size': 1}
id: 102971296
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 46157, 'group_order': 256, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 16849409, 'size': 1}
id: 102971297
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 46157, 'group_order': 256, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 16979969, 'size': 1}
id: 102971298
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 9, 'group_counter': 46157, 'group_order': 256, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 1839360, 'size': 4}
id: 102971254
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 10, 'group_counter': 46157, 'group_order': 256, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 1938688, 'size': 4}
id: 102971255
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 11, 'group_counter': 46157, 'group_order': 256, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 34083266, 'size': 4}
id: 102971256
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 12, 'group_counter': 46157, 'group_order': 256, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 68685956, 'size': 4}
id: 102971257
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 13, 'group_counter': 46157, 'group_order': 256, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 51646659, 'size': 4}
id: 102971258
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 14, 'group_counter': 46157, 'group_order': 256, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 101453894, 'size': 4}
id: 102971259
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 15, 'group_counter': 46157, 'group_order': 256, 'label': '2N', 'order': 2, 'powers': [1], 'representative': 118493511, 'size': 4}
id: 102971260
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 16, 'group_counter': 46157, 'group_order': 256, 'label': '2O', 'order': 2, 'powers': [1], 'representative': 84152709, 'size': 4}
id: 102971261
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 17, 'group_counter': 46157, 'group_order': 256, 'label': '2P', 'order': 2, 'powers': [1], 'representative': 34281922, 'size': 4}
id: 102971262
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 18, 'group_counter': 46157, 'group_order': 256, 'label': '2Q', 'order': 2, 'powers': [1], 'representative': 68817540, 'size': 4}
id: 102971263
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 19, 'group_counter': 46157, 'group_order': 256, 'label': '2R', 'order': 2, 'powers': [1], 'representative': 51778243, 'size': 4}
id: 102971265
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 20, 'group_counter': 46157, 'group_order': 256, 'label': '2S', 'order': 2, 'powers': [1], 'representative': 101585478, 'size': 4}
id: 102971266
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 21, 'group_counter': 46157, 'group_order': 256, 'label': '2T', 'order': 2, 'powers': [1], 'representative': 118625095, 'size': 4}
id: 102971267
{'aut_label': '2H', 'centralizer': '4.f1', 'counter': 22, 'group_counter': 46157, 'group_order': 256, 'label': '2U', 'order': 2, 'powers': [1], 'representative': 84252037, 'size': 4}
id: 102971268
{'aut_label': '2V', 'centralizer': '8.e1', 'counter': 23, 'group_counter': 46157, 'group_order': 256, 'label': '2V', 'order': 2, 'powers': [1], 'representative': 16814081, 'size': 8}
id: 102971269
{'aut_label': '2V', 'centralizer': '8.e1', 'counter': 24, 'group_counter': 46157, 'group_order': 256, 'label': '2W', 'order': 2, 'powers': [1], 'representative': 16912385, 'size': 8}
id: 102971270
{'aut_label': '2V', 'centralizer': '8.e1', 'counter': 25, 'group_counter': 46157, 'group_order': 256, 'label': '2X', 'order': 2, 'powers': [1], 'representative': 16945153, 'size': 8}
id: 102971271
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 26, 'group_counter': 46157, 'group_order': 256, 'label': '4A', 'order': 4, 'powers': [2], 'representative': 1872128, 'size': 8}
id: 102971272
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 27, 'group_counter': 46157, 'group_order': 256, 'label': '4B', 'order': 4, 'powers': [3], 'representative': 1970432, 'size': 8}
id: 102971273
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 28, 'group_counter': 46157, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 2003200, 'size': 8}
id: 102971274
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 29, 'group_counter': 46157, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [5], 'representative': 34116034, 'size': 8}
id: 102971276
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 30, 'group_counter': 46157, 'group_order': 256, 'label': '4E', 'order': 4, 'powers': [6], 'representative': 34214338, 'size': 8}
id: 102971277
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 31, 'group_counter': 46157, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 34247106, 'size': 8}
id: 102971278
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 32, 'group_counter': 46157, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 68718724, 'size': 8}
id: 102971279
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 33, 'group_counter': 46157, 'group_order': 256, 'label': '4H', 'order': 4, 'powers': [7], 'representative': 68817028, 'size': 8}
id: 102971280
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 34, 'group_counter': 46157, 'group_order': 256, 'label': '4I', 'order': 4, 'powers': [6], 'representative': 68849796, 'size': 8}
id: 102971281
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 35, 'group_counter': 46157, 'group_order': 256, 'label': '4J', 'order': 4, 'powers': [7], 'representative': 51679427, 'size': 8}
id: 102971282
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 36, 'group_counter': 46157, 'group_order': 256, 'label': '4K', 'order': 4, 'powers': [5], 'representative': 51777731, 'size': 8}
id: 102971283
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 37, 'group_counter': 46157, 'group_order': 256, 'label': '4L', 'order': 4, 'powers': [2], 'representative': 51810499, 'size': 8}
id: 102971284
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 38, 'group_counter': 46157, 'group_order': 256, 'label': '4M', 'order': 4, 'powers': [6], 'representative': 101486662, 'size': 8}
id: 102971285
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 39, 'group_counter': 46157, 'group_order': 256, 'label': '4N', 'order': 4, 'powers': [2], 'representative': 101584966, 'size': 8}
id: 102971287
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 40, 'group_counter': 46157, 'group_order': 256, 'label': '4O', 'order': 4, 'powers': [8], 'representative': 101617734, 'size': 8}
id: 102971288
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 41, 'group_counter': 46157, 'group_order': 256, 'label': '4P', 'order': 4, 'powers': [8], 'representative': 118526279, 'size': 8}
id: 102971289
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 42, 'group_counter': 46157, 'group_order': 256, 'label': '4Q', 'order': 4, 'powers': [4], 'representative': 118624583, 'size': 8}
id: 102971290
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 43, 'group_counter': 46157, 'group_order': 256, 'label': '4R', 'order': 4, 'powers': [5], 'representative': 118657351, 'size': 8}
id: 102971291
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 44, 'group_counter': 46157, 'group_order': 256, 'label': '4S', 'order': 4, 'powers': [3], 'representative': 84185477, 'size': 8}
id: 102971292
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 45, 'group_counter': 46157, 'group_order': 256, 'label': '4T', 'order': 4, 'powers': [8], 'representative': 84283781, 'size': 8}
id: 102971293
{'aut_label': '4A', 'centralizer': '8.f2', 'counter': 46, 'group_counter': 46157, 'group_order': 256, 'label': '4U', 'order': 4, 'powers': [7], 'representative': 84316549, 'size': 8}

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: 1843484
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1a', '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], 'schur_index': 1}
id: 1843495
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1b', '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], 'schur_index': 1}
id: 1843506
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1c', '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], 'schur_index': 1}
id: 1843517
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1d', '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], 'schur_index': 1}
id: 1843525
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1e', '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], 'schur_index': 1}
id: 1843526
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1f', '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], 'schur_index': 1}
id: 1843527
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1g', '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], 'schur_index': 1}
id: 1843528
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1h', '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], 'schur_index': 1}
id: 1843529
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1i', '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], 'schur_index': 1}
id: 1843485
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1j', '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], 'schur_index': 1}
id: 1843486
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1k', '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], 'schur_index': 1}
id: 1843487
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1l', '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], 'schur_index': 1}
id: 1843488
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1m', '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], 'schur_index': 1}
id: 1843489
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1n', '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], 'schur_index': 1}
id: 1843490
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1o', '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], 'schur_index': 1}
id: 1843491
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1p', '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], 'schur_index': 1}
id: 1843492
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1q', '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], 'schur_index': 1}
id: 1843493
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1r', '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], 'schur_index': 1}
id: 1843494
{'cdim': 1, 'counter': 19, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1s', '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], 'schur_index': 1}
id: 1843496
{'cdim': 1, 'counter': 20, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1t', '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], 'schur_index': 1}
id: 1843497
{'cdim': 1, 'counter': 21, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1u', '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], 'schur_index': 1}
id: 1843498
{'cdim': 1, 'counter': 22, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1v', '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], 'schur_index': 1}
id: 1843499
{'cdim': 1, 'counter': 23, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1w', '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], 'schur_index': 1}
id: 1843500
{'cdim': 1, 'counter': 24, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1x', '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], 'schur_index': 1}
id: 1843501
{'cdim': 1, 'counter': 25, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1y', '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], 'schur_index': 1}
id: 1843502
{'cdim': 1, 'counter': 26, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1z', '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], 'schur_index': 1}
id: 1843503
{'cdim': 1, 'counter': 27, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1aa', '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], 'schur_index': 1}
id: 1843504
{'cdim': 1, 'counter': 28, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1ab', '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], 'schur_index': 1}
id: 1843505
{'cdim': 1, 'counter': 29, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1ac', '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], 'schur_index': 1}
id: 1843507
{'cdim': 1, 'counter': 30, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1ad', '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], 'schur_index': 1}
id: 1843508
{'cdim': 1, 'counter': 31, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1ae', '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], 'schur_index': 1}
id: 1843509
{'cdim': 1, 'counter': 32, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.1af', '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], 'schur_index': 1}
id: 1843510
{'cdim': 4, 'counter': 33, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4a', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, -4, -4, 4, 4, 4, 0, -4, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1843511
{'cdim': 4, 'counter': 34, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4b', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, -4, -4, 4, 4, 4, 0, 4, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1843512
{'cdim': 4, 'counter': 35, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4c', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 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, 0, 0, 0], 'schur_index': 1}
id: 1843513
{'cdim': 4, 'counter': 36, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4d', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 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, 0, 0, 0], 'schur_index': 1}
id: 1843514
{'cdim': 4, 'counter': 37, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4e', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, -4, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 1843515
{'cdim': 4, 'counter': 38, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4f', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 1843516
{'cdim': 4, 'counter': 39, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4g', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, -4, 0, 0, 0, 0, 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, 0, 0], 'schur_index': 1}
id: 1843518
{'cdim': 4, 'counter': 40, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4h', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 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, 0, 0], 'schur_index': 1}
id: 1843519
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4i', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 1843520
{'cdim': 4, 'counter': 42, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4j', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 1843521
{'cdim': 4, 'counter': 43, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4k', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, -4, 0, 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, 0, 0, 0, 0], 'schur_index': 1}
id: 1843522
{'cdim': 4, 'counter': 44, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4l', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 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, 0, 0, 0, 0], 'schur_index': 1}
id: 1843523
{'cdim': 4, 'counter': 45, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4m', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 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, 0], 'schur_index': 1}
id: 1843524
{'cdim': 4, 'counter': 46, 'faithful': False, 'group': '256.46157', 'group_order': 256, 'image': None, 'label': '256.46157.4n', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 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, 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: 2377351
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 256, 'label': '256.46157.1a', '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]]]}
id: 2377370
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 27, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1aa', '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]]]}
id: 2377371
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 28, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1ab', '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]]]}
id: 2377372
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 29, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.46157.1ac', '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]]]}
id: 2377374
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 30, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.46157.1ad', '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]]]}
id: 2377375
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 31, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.46157.1ae', '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]]]}
id: 2377376
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 32, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 128, 'label': '256.46157.1af', '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]]]}
id: 2377362
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1b', '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]]]}
id: 2377373
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1c', '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]]]}
id: 2377384
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1d', '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]]]}
id: 2377392
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.46157.1e', '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]]]}
id: 2377393
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1f', '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]]]}
id: 2377394
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1g', '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]]]}
id: 2377395
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1h', '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]]]}
id: 2377396
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 128, 'label': '256.46157.1i', '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]]]}
id: 2377352
{'center': '1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 128, 'label': '256.46157.1j', '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]]]}
id: 2377353
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id: 2377354
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id: 2377355
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id: 2377356
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id: 2377357
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id: 2377358
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id: 2377359
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id: 2377360
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id: 2377361
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id: 2377363
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id: 2377364
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id: 2377365
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id: 2377366
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id: 2377367
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id: 2377368
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id: 2377369
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id: 2377377
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id: 2377378
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4b', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377379
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4c', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377380
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 36, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4d', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377381
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4e', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377382
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4f', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377383
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4g', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377385
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 40, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4h', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377386
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4i', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 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]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377387
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4j', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 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]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377388
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4k', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377389
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4l', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377390
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4m', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 2377391
{'center': '16.a1', 'center_index': 16, 'center_order': 16, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '256.46157', 'group_counter': 46157, 'group_order': 256, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.a1', 'kernel_order': 8, 'label': '256.46157.4n', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 43335338
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.46157.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.46157', 'subgroup_hash': 46157, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:C_2^3', 'supersolvable': True, 'sylow': 2}
id: 43335349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1417', 'subgroup_hash': 1417, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3.C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1411', 'subgroup_hash': 1411, 'subgroup_order': 128, 'subgroup_tex': 'C_2.D_4^2', 'supersolvable': True, 'sylow': 0}
id: 43335371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 43335382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.71', 'subgroup_hash': 71, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a2', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
id: 43335404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.a3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a3', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.75', 'subgroup_hash': 75, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
id: 43335409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
id: 43335410
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.77', 'subgroup_hash': 77, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
id: 43335339
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c2', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.80', 'subgroup_hash': 80, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.Q_8', 'supersolvable': True, 'sylow': 0}
id: 43335340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.c3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c3', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.69', 'subgroup_hash': 69, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335341
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.c4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c4', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.209', 'subgroup_hash': 209, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335342
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
id: 43335343
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335344
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
id: 43335345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 43335346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.b3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335350
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 32, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 43335351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 43335353
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
id: 43335354
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
id: 43335355
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.f3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
id: 43335356
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.8.f4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.2', 'subgroup_hash': 2, 'subgroup_order': 32, 'subgroup_tex': 'C_2.C_4^2', 'supersolvable': True, 'sylow': 0}
id: 43335357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 43335358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.33', 'subgroup_hash': 33, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
id: 43335359
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 43335361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 43335362
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335363
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335364
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 43335365
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335366
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 43335367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 43335368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.e3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 43335369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.f3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335373
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335374
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335375
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.g3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335376
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 43335378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 43335379
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.16.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 43335380
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335381
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.51', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'D', 'Phi', 'S', 'U1', 'L1', 'D1', 'C5'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 43335384
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335385
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335386
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.d3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335387
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335388
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335389
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335390
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 43335392
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.h2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 43335394
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.h3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 43335395
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 43335396
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.46157.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335397
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335398
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.b3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.b3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335400
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335401
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.46157.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 43335402
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335403
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.46157.64.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 43335405
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.46157.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2264', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2264, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4^2:C_2', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 43335406
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.46157.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 43335407
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.46157.128.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, '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: 43335408
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.46157', 'ambient_counter': 46157, 'ambient_order': 256, 'ambient_tex': 'C_2^5:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.46157.256.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '256.46157', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46157, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^5:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C8'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 43335369
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.b1', '8.i1'], 'contains': ['32.f2', '32.h1', '32.h2'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4435, -1, 4435, -1], 'generators': [1938688, 16948225, 84316549, 17012225], 'label': '256.46157.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.f1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335370
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.f2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.b2', '8.i1'], 'contains': ['32.f1', '32.h1', '32.h3'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3478, -1, 3477, -1], 'generators': [1938688, 16948225, 101588550, 16979969], 'label': '256.46157.16.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.f2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335367
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.e2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.a1', '8.i1'], 'contains': ['32.c1', '32.f1', '32.g1', '32.h2'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6383, -1, 6383, -1], 'generators': [1938688, 16948225, 16784385, 16979969], 'label': '256.46157.16.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.e2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335368
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.e3', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.a1', '8.i1'], 'contains': ['32.c1', '32.f2', '32.g1', '32.h3'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5746, -1, 5746, -1], 'generators': [1938688, 16948225, 16784385, 17012225], 'label': '256.46157.16.e3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.e3', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e3', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335338
{'ambient': '256.46157', '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': '32.b1', 'complements': ['256.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4751, 4234, 4751, 4116], 'generators': [1938688, 16948225, 101521990, 68817028, 16784385, 17012225, 84383621, 16979969], 'label': '256.46157.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335339
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.c2', 'aut_quo_index': 2, 'aut_stab_index': 7, 'aut_weyl_group': '1536.408544622', 'aut_weyl_index': 448, 'centralizer': '32.b1', 'complements': ['64.e1', '64.f1'], 'conjugacy_class_count': 7, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.f1', '8.f4'], 'core': '4.c2', 'coset_action_label': None, 'count': 7, 'diagramx': [6290, 8780, 6290, 8535], 'generators': [1938688, 16948225, 51845827, 84316549, 17012225, 16979969], 'label': '256.46157.4.c2', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c2', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.f1', '8.f4'], 'normalizer': '1.a1', 'old_label': '4.c2', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335340
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.c3', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': ['64.e1', '64.f1'], 'conjugacy_class_count': 21, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.b2', '8.b3', '8.f1', '8.f2', '8.f3', '8.f4'], 'core': '4.c3', 'coset_action_label': None, 'count': 21, 'diagramx': [4082, 7878, 4082, 7659], 'generators': [84383109, 16948225, 101521990, 68786820, 17012225, 16979969], 'label': '256.46157.4.c3', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c3', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.b2', '8.b3', '8.f1', '8.f2', '8.f3', '8.f4'], 'normalizer': '1.a1', 'old_label': '4.c3', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c3', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335341
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.c4', 'aut_quo_index': 2, 'aut_stab_index': 7, 'aut_weyl_group': '1536.408544622', 'aut_weyl_index': 448, 'centralizer': '32.b1', 'complements': ['64.f1', '64.e1'], 'conjugacy_class_count': 7, 'contained_in': ['2.a1'], 'contains': ['8.b3', '8.f1', '8.f2', '8.h1'], 'core': '4.c4', 'coset_action_label': None, 'count': 7, 'diagramx': [1646, 9827, 1646, 9554], 'generators': [84383109, 16948225, 1842944, 101521990, 17012225, 16979969], 'label': '256.46157.4.c4', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c4', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b3', '8.f1', '8.f2'], 'normalizer': '1.a1', 'old_label': '4.c4', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c4', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335342
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.b2', '8.b3', '8.c1', '8.i1'], 'core': '4.d1', 'coset_action_label': None, 'count': 21, 'diagramx': [3189, 2413, 3189, 2346], 'generators': [1938688, 16948225, 101521990, 16784385, 17012225, 16979969], 'label': '256.46157.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.b2', '8.b3', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335343
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': ['64.f1'], 'conjugacy_class_count': 21, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.b2', '8.b3', '8.c1'], 'core': '4.e1', 'coset_action_label': None, 'count': 21, 'diagramx': [2348, 3391, 2348, 3297], 'generators': [1938688, 16948225, 101521990, 68786820, 17012225, 16979969], 'label': '256.46157.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '8.b2', '8.b3', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335344
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '10752.bk', 'aut_weyl_index': 64, 'centralizer': '4.f1', 'complements': ['64.f1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1'], 'contains': ['8.c1', '8.j1'], 'core': '4.f1', 'coset_action_label': None, 'count': 1, 'diagramx': [530, 173, 530, 168], 'generators': [1938688, 16948225, 101521990, 17012225, 84383621, 16979969], 'label': '256.46157.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['8.c1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335345
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['4.a1', '4.a2', '4.a3', '4.b1', '4.d1'], 'contains': ['16.a1', '16.b1', '16.c1', '16.e1', '16.e2', '16.e3'], 'core': '8.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7610, 2225, 7610, 2163], 'generators': [1938688, 16948225, 16784385, 17012225, 16979969], 'label': '256.46157.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.a2', '4.a3', '4.b1', '4.d1'], 'normal_contains': ['16.a1', '16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335346
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['4.a1', '4.a2', '4.c2', '4.c3', '4.d1', '4.e1'], 'contains': ['16.a1', '16.c1', '16.f1'], 'core': '8.b1', 'coset_action_label': None, 'count': 21, 'diagramx': [4165, 5189, 4165, 5045], 'generators': [1938688, 16948225, 84316549, 17012225, 16979969], 'label': '256.46157.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.a2', '4.c2', '4.c3', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335347
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.b2', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['4.a1', '4.a3', '4.c1', '4.c3', '4.d1', '4.e1'], 'contains': ['16.a1', '16.c1', '16.f2'], 'core': '8.b2', 'coset_action_label': None, 'count': 21, 'diagramx': [3292, 4173, 3291, 4058], 'generators': [1938688, 16948225, 101588550, 17012225, 16979969], 'label': '256.46157.8.b2', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b2', 'normal_contained_in': ['4.a1', '4.a3', '4.c1', '4.c3', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b2', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335348
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.b3', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['4.a2', '4.a3', '4.c3', '4.c4', '4.d1', '4.e1'], 'contains': ['16.a1', '16.c1', '16.f3'], 'core': '8.b3', 'coset_action_label': None, 'count': 21, 'diagramx': [2418, 6204, 2417, 6031], 'generators': [1938688, 16948225, 68786820, 17012225, 16979969], 'label': '256.46157.8.b3', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b3', 'normal_contained_in': ['4.a2', '4.a3', '4.c3', '4.c4', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b3', 'projective_image': '32.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b3', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335349
{'ambient': '256.46157', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 21, 'aut_weyl_group': '4096.bri', 'aut_weyl_index': 168, 'centralizer': '32.b1', 'complements': ['128.c1', '128.b1'], 'conjugacy_class_count': 21, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.a2', '4.a3', '4.c1', '4.c2', '4.c3', '4.c4', '4.d1', '4.e1'], 'core': '2.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4751, 5664, 4751, 5506], 'generators': [1938688, 16948225, 101521990, 68817028, 16784385, 17012225, 16979969], 'label': '256.46157.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.a2', '4.a3', '4.c1', '4.c2', '4.c3', '4.c4', '4.d1', '4.e1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335350
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.c1', 'aut_quo_index': 56, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 7, 'contained_in': ['4.d1', '4.e1', '4.f1'], 'contains': ['16.a1', '16.g1', '16.g2', '16.g3'], 'core': '8.c1', 'coset_action_label': None, 'count': 7, 'diagramx': [530, 1577, 530, 1533], 'generators': [1938688, 16948225, 101521990, 17012225, 16979969], 'label': '256.46157.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.d1', '4.e1', '4.f1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335351
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.d1', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': ['32.i1'], 'conjugacy_class_count': 21, 'contained_in': ['4.a1', '4.a2', '4.a3', '4.b1'], 'contains': ['16.b1', '16.c1', '16.h1'], 'core': '8.d1', 'coset_action_label': None, 'count': 21, 'diagramx': [8414, 3159, 8415, 3071], 'generators': [84383109, 16948225, 16784385, 17012225, 16979969], 'label': '256.46157.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.a1', '4.a2', '4.a3', '4.b1'], 'normal_contains': ['16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335352
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11690', 'aut_weyl_index': 512, 'centralizer': '8.e1', 'complements': ['32.i1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1'], 'contains': ['16.b1', '16.i1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [9851, 1101, 9851, 1071], 'generators': [16948225, 16980481, 16784385, 17012225, 16979969], 'label': '256.46157.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.b1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335353
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.f1', 'aut_quo_index': 168, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': ['32.i1'], 'conjugacy_class_count': 21, 'contained_in': ['4.a1', '4.a2', '4.a3', '4.c1', '4.c2', '4.c3', '4.c4'], 'contains': ['16.c1', '16.j1'], 'core': '8.f1', 'coset_action_label': None, 'count': 21, 'diagramx': [6327, 7775, 6327, 7559], 'generators': [84383109, 16948225, 101588550, 17012225, 16979969], 'label': '256.46157.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.a1', '4.a2', '4.a3', '4.c1', '4.c2', '4.c3', '4.c4'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335354
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.f2', 'aut_quo_index': 56, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '8.f2', 'complements': ['32.i1'], 'conjugacy_class_count': 7, 'contained_in': ['4.a1', '4.c3', '4.c4'], 'contains': ['16.c1', '16.j2'], 'core': '8.f2', 'coset_action_label': None, 'count': 7, 'diagramx': [1613, 8650, 1613, 8410], 'generators': [84383109, 16948225, 1842944, 17012225, 16979969], 'label': '256.46157.8.f2', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f2', 'normal_contained_in': ['4.a1', '4.c3', '4.c4'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.f2', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f2', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335355
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.f3', 'aut_quo_index': 56, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '32.b1', 'complements': ['32.i1'], 'conjugacy_class_count': 7, 'contained_in': ['4.a2', '4.c1', '4.c3'], 'contains': ['16.c1'], 'core': '8.f3', 'coset_action_label': None, 'count': 7, 'diagramx': [5676, 7019, 5676, 6824], 'generators': [84383109, 16948225, 51878083, 17012225, 16979969], 'label': '256.46157.8.f3', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f3', 'normal_contained_in': ['4.a2', '4.c1', '4.c3'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.f3', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f3', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335356
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '8.f4', 'aut_quo_index': 56, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '32.b1', 'complements': ['32.i1'], 'conjugacy_class_count': 7, 'contained_in': ['4.a3', '4.c2', '4.c3'], 'contains': ['16.c1'], 'core': '8.f4', 'coset_action_label': None, 'count': 7, 'diagramx': [6977, 9379, 6978, 9118], 'generators': [84383109, 16948225, 34116546, 17012225, 16979969], 'label': '256.46157.8.f4', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f4', 'normal_contained_in': ['4.a3', '4.c2', '4.c3'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.f4', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.f4', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335357
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 14, 'contained_in': ['4.b1'], 'contains': ['16.e1', '16.h1', '16.i1'], 'core': '32.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [9256, -1, 9256, -1], 'generators': [101521990, 16980481, 16784385, 17012225, 16979969], 'label': '256.46157.8.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.g1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335358
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 14, 'contained_in': ['4.c4'], 'contains': ['16.f3', '16.j1', '16.j2'], 'core': '32.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [986, -1, 986, -1], 'generators': [84383109, 1842944, 101521990, 17012225, 16979969], 'label': '256.46157.8.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c4', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c4', 'old_label': '8.h1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335359
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '64.267', 'aut_weyl_index': 10752, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['4.d1'], 'contains': ['16.e1', '16.e2', '16.e3', '16.f1', '16.f2', '16.f3', '16.g1'], 'core': '32.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [5006, -1, 5007, -1], 'generators': [1938688, 16948225, 101521990, 16784385, 16979969], 'label': '256.46157.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.i1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335360
{'ambient': '256.46157', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 7, 'aut_weyl_group': '12288.bmv', 'aut_weyl_index': 56, 'centralizer': '32.b1', 'complements': ['128.b1'], 'conjugacy_class_count': 7, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.a2', '4.a3', '4.b1', '4.d1'], 'core': '2.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [6341, 4234, 6341, 4116], 'generators': [68817540, 16948225, 101521990, 68817028, 16784385, 17012225, 16979969], 'label': '256.46157.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.a2', '4.a3', '4.b1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335361
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 3584, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 14, 'contained_in': ['4.f1'], 'contains': ['16.d1', '16.g1', '16.g2', '16.g3'], 'core': '32.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [149, -1, 149, -1], 'generators': [1938688, 16948225, 101521990, 17012225, 84383621], 'label': '256.46157.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '8.j1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335362
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '16.a1', 'aut_quo_index': 6720, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 28672, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 7, 'contained_in': ['8.a1', '8.b1', '8.b2', '8.b3', '8.c1'], 'contains': ['32.a1', '32.b1', '32.f1', '32.f2'], 'core': '16.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2497, 4173, 2497, 4058], 'generators': [1938688, 16948225, 17012225, 16979969], 'label': '256.46157.16.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.b2', '8.b3', '8.c1'], 'normal_contains': ['32.a1', '32.b1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335363
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '16.b1', 'aut_quo_index': 2880, 'aut_stab_index': 3, 'aut_weyl_group': '56.11', 'aut_weyl_index': 12288, 'centralizer': '8.e1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '8.d1', '8.e1'], 'contains': ['32.b1', '32.g1'], 'core': '16.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7610, 2694, 7610, 2619], 'generators': [16948225, 16784385, 17012225, 16979969], 'label': '256.46157.16.b1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.d1', '8.e1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335364
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '16.c1', 'aut_quo_index': 20160, 'aut_stab_index': 21, 'aut_weyl_group': '8.5', 'aut_weyl_index': 86016, 'centralizer': '8.f2', 'complements': [], 'conjugacy_class_count': 21, 'contained_in': ['8.a1', '8.b1', '8.b2', '8.b3', '8.d1', '8.f1', '8.f2', '8.f3', '8.f4'], 'contains': ['32.b1', '32.h1', '32.h2', '32.h3'], 'core': '16.c1', 'coset_action_label': None, 'count': 21, 'diagramx': [5062, 5696, 5063, 5538], 'generators': [16948225, 2036992, 17012225, 16979969], 'label': '256.46157.16.c1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.c1', 'normal_contained_in': ['8.a1', '8.b1', '8.b2', '8.b3', '8.d1', '8.f1', '8.f2', '8.f3', '8.f4'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '32.51', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335365
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 448, 'aut_weyl_group': '24.13', 'aut_weyl_index': 28672, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 112, 'contained_in': ['8.j1'], 'contains': ['32.d1', '32.d2', '32.d3', '32.i1'], 'core': '128.a1', 'coset_action_label': None, 'count': 448, 'diagramx': [590, -1, 590, -1], 'generators': [1938688, 16948225, 101521990, 84383621], 'label': '256.46157.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335366
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['8.a1', '8.g1', '8.i1'], 'contains': ['32.a1', '32.c1', '32.g1', '32.h1'], 'core': '32.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [7020, -1, 7020, -1], 'generators': [16817665, 1938688, 16948225, 16784385], 'label': '256.46157.16.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '16.e1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 43335371
{'ambient': '256.46157', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '28672.m', 'aut_weyl_index': 24, 'centralizer': '32.b1', 'complements': ['128.c1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.d1', '4.e1', '4.f1'], 'core': '2.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [2770, 2905, 2771, 2824], 'generators': [1938688, 16948225, 101521990, 16784385, 17012225, 84383621, 16979969], 'label': '256.46157.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.d1', '4.e1', '4.f1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '32.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335372
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.f3', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['8.b3', '8.h1', '8.i1'], 'contains': ['32.a1', '32.h2', '32.h3'], 'core': '32.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2952, -1, 2952, -1], 'generators': [16817665, 1938688, 16948225, 68786820], 'label': '256.46157.16.f3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b3', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.f3', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f3', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 43335373
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['8.c1', '8.i1', '8.j1'], 'contains': ['32.a1', '32.d1', '32.d2', '32.f1', '32.f2'], 'core': '32.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [1734, -1, 1734, -1], 'generators': [16817665, 1938688, 16948225, 101521990], 'label': '256.46157.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.g1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335374
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.g2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.c1', '8.j1'], 'contains': ['32.d1', '32.d2', '32.d3', '32.f1', '32.f2'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [971, -1, 972, -1], 'generators': [1938688, 16948225, 101521990, 17012225], 'label': '256.46157.16.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.g2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335375
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.g3', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.49', 'aut_weyl_index': 14336, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 7, 'contained_in': ['8.c1', '8.j1'], 'contains': ['32.d2', '32.f2'], 'core': '64.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1352, -1, 1353, -1], 'generators': [1938688, 16880641, 101521990, 17012225], 'label': '256.46157.16.g3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '16.g3', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335376
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.d1', '8.g1'], 'contains': ['32.g1', '32.h1'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [8242, -1, 8238, -1], 'generators': [16849409, 84383109, 16784385, 16979969], 'label': '256.46157.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.h1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335377
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.49', 'aut_weyl_index': 14336, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 7, 'contained_in': ['8.e1', '8.g1'], 'contains': ['32.e1', '32.g1'], 'core': '64.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8977, -1, 8973, -1], 'generators': [16948225, 16980481, 16784385, 17012225], 'label': '256.46157.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '16.i1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335378
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 43008, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['8.f1', '8.h1'], 'contains': ['32.h2', '32.h3'], 'core': '64.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3956, -1, 3956, -1], 'generators': [84383109, 16948225, 101588550, 16979969], 'label': '256.46157.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c4', 'old_label': '16.j1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 43335379
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '16.j2', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.49', 'aut_weyl_index': 14336, 'centralizer': '8.f2', 'complements': None, 'conjugacy_class_count': 7, 'contained_in': ['8.f2', '8.h1'], 'contains': ['32.h3'], 'core': '64.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2116, -1, 2115, -1], 'generators': [84383109, 1842944, 17012225, 16979969], 'label': '256.46157.16.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f2', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c4', 'old_label': '16.j2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335380
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.a1', 'aut_quo_index': 24, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 57344, 'centralizer': '4.f1', 'complements': [], 'conjugacy_class_count': 14, 'contained_in': ['16.a1', '16.e1', '16.f3', '16.g1'], 'contains': ['64.a1', '64.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2934, 3953, 2934, 3843], 'generators': [16817665, 1938688, 16948225], 'label': '256.46157.32.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '64.264', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335381
{'ambient': '256.46157', 'aut_centralizer_order': 32768, 'aut_label': '32.b1', 'aut_quo_index': 476160, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 32768, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1'], 'contains': ['64.a1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4607, 4395, 4607, 4273], 'generators': [16948225, 17012225, 16979969], 'label': '256.46157.32.b1', 'mobius_quo': -8, 'mobius_sub': -1024, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335382
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': ['64.e1'], 'conjugacy_class_count': 21, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.b2', '8.d1', '8.f1', '8.f2'], 'core': '4.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5467, 5189, 5467, 5045], 'generators': [16948225, 101521990, 16980481, 84316549, 17012225, 16979969], 'label': '256.46157.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.b2', '8.d1', '8.f1', '8.f2'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335383
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '32.b1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['16.e1', '16.e2', '16.e3'], 'contains': ['64.b1', '64.c1', '64.d1'], 'core': '128.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [5886, -1, 5825, -1], 'generators': [1938688, 16948225, 16784385], 'label': '256.46157.32.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '32.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335384
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 84, 'contained_in': ['16.d1', '16.g1', '16.g2'], 'contains': ['64.b1', '64.b2', '64.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [1352, -1, 1353, -1], 'generators': [1938688, 16948225, 101521990], 'label': '256.46157.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335385
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '32.d2', 'aut_quo_index': None, 'aut_stab_index': 336, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 84, 'contained_in': ['16.d1', '16.g1', '16.g2', '16.g3'], 'contains': ['64.b1', '64.b2', '64.b3', '64.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 336, 'diagramx': [1734, -1, 1734, -1], 'generators': [1938688, 16880641, 101521990], 'label': '256.46157.32.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.d2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335386
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '32.d3', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.3', 'aut_weyl_index': 57344, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 28, 'contained_in': ['16.d1', '16.g2'], 'contains': ['64.b2', '64.e1'], 'core': '128.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [971, -1, 972, -1], 'generators': [1938688, 16849409, 101521990], 'label': '256.46157.32.d3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.d3', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335387
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '12.3', 'aut_weyl_index': 57344, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 14, 'contained_in': ['16.i1'], 'contains': ['64.c1', '64.f1'], 'core': '128.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [6764, -1, 6764, -1], 'generators': [16948225, 16980481, 16784385], 'label': '256.46157.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '32.e1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335388
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.a1', '16.e2', '16.f2', '16.g1', '16.g2'], 'contains': ['64.a1', '64.b1', '64.b2'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2515, -1, 2515, -1], 'generators': [16817665, 1938688, 16880641], 'label': '256.46157.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.f1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335389
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.f2', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.a1', '16.e3', '16.f1', '16.g1', '16.g2', '16.g3'], 'contains': ['64.a1', '64.b1', '64.b2', '64.b3'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2134, -1, 2134, -1], 'generators': [1938688, 16948225, 17012225], 'label': '256.46157.32.f2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.f2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335390
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.b1', '16.e1', '16.e2', '16.e3', '16.h1', '16.i1'], 'contains': ['64.a1', '64.c1'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6383, -1, 6383, -1], 'generators': [16948225, 16784385, 17012225], 'label': '256.46157.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.g1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335391
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '8.f2', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.c1', '16.e1', '16.f1', '16.f2', '16.h1'], 'contains': ['64.a1', '64.d1'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5114, -1, 5114, -1], 'generators': [16817665, 16948225, 2036992], 'label': '256.46157.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '32.h1', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335392
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.h2', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '8.f2', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.c1', '16.e2', '16.f1', '16.f3', '16.j1'], 'contains': ['64.a1', '64.d1'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [4101, -1, 4100, -1], 'generators': [16948225, 2036992, 16979969], 'label': '256.46157.32.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.h2', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335393
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.a2', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': ['64.e1'], 'conjugacy_class_count': 21, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.b3', '8.d1', '8.f1', '8.f3'], 'core': '4.a2', 'coset_action_label': None, 'count': 21, 'diagramx': [7215, 4234, 7215, 4116], 'generators': [84383109, 16948225, 101521990, 16784385, 17012225, 16979969], 'label': '256.46157.4.a2', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a2', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.b3', '8.d1', '8.f1', '8.f3'], 'normalizer': '1.a1', 'old_label': '4.a2', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a2', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335394
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '32.h3', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 172032, 'centralizer': '8.f2', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['16.c1', '16.e3', '16.f2', '16.f3', '16.j1', '16.j2'], 'contains': ['64.a1', '64.d1'], 'core': '64.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3468, -1, 3468, -1], 'generators': [16948225, 2036992, 17012225], 'label': '256.46157.32.h3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.h3', 'projective_image': '64.264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h3', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 43335395
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 512, 'aut_weyl_group': '21.1', 'aut_weyl_index': 32768, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 128, 'contained_in': ['16.d1'], 'contains': ['64.e1'], 'core': '256.a1', 'coset_action_label': '32T3677', 'count': 512, 'diagramx': [590, -1, 590, -1], 'generators': [1938688, 101521990, 84383621], 'label': '256.46157.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '32.i1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335396
{'ambient': '256.46157', 'aut_centralizer_order': 32768, 'aut_label': '64.a1', 'aut_quo_index': 384, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 229376, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 7, 'contained_in': ['32.a1', '32.b1', '32.f1', '32.f2', '32.g1', '32.h1', '32.h2', '32.h3'], 'contains': ['128.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3468, 4173, 3468, 4058], 'generators': [16948225, 17012225], 'label': '256.46157.64.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.264', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335397
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 344064, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 42, 'contained_in': ['32.a1', '32.c1', '32.d1', '32.d2', '32.f1', '32.f2'], 'contains': ['128.a1', '128.b1'], 'core': '128.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2515, -1, 2515, -1], 'generators': [1938688, 16948225], 'label': '256.46157.64.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '64.b1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335398
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '64.b2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 344064, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['32.d1', '32.d2', '32.d3', '32.f1', '32.f2'], 'contains': ['128.a1', '128.b1'], 'core': '128.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [1753, -1, 1753, -1], 'generators': [1938688, 16849409], 'label': '256.46157.64.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '64.b2', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335399
{'ambient': '256.46157', 'aut_centralizer_order': 12288, 'aut_label': '64.b3', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 344064, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 7, 'contained_in': ['32.d2', '32.f2'], 'contains': ['128.a1', '128.b1'], 'core': '128.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2134, -1, 2134, -1], 'generators': [1938688, 17012225], 'label': '256.46157.64.b3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '64.b3', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335400
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 344064, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['32.c1', '32.e1', '32.g1'], 'contains': ['128.a1', '128.c1'], 'core': '128.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6011, -1, 5983, -1], 'generators': [16948225, 16784385], 'label': '256.46157.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '64.c1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335401
{'ambient': '256.46157', 'aut_centralizer_order': 4096, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 344064, 'centralizer': '8.f2', 'complements': None, 'conjugacy_class_count': 21, 'contained_in': ['32.c1', '32.h1', '32.h2', '32.h3'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4101, -1, 4100, -1], 'generators': [16948225, 2036992], 'label': '256.46157.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.d1', 'projective_image': '128.2264', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 43335402
{'ambient': '256.46157', 'aut_centralizer_order': 512, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 448, 'aut_weyl_group': '3.1', 'aut_weyl_index': 229376, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 112, 'contained_in': ['32.d1', '32.d2', '32.d3', '32.i1'], 'contains': ['128.b1'], 'core': '256.a1', 'coset_action_label': None, 'count': 448, 'diagramx': [1352, -1, 1353, -1], 'generators': [1938688, 101521990], 'label': '256.46157.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '64.e1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335403
{'ambient': '256.46157', 'aut_centralizer_order': 3584, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 229376, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['32.e1'], 'contains': ['128.c1'], 'core': '256.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [6518, -1, 6681, -1], 'generators': [16980481, 16784385], 'label': '256.46157.64.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '64.f1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335404
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.a3', 'aut_quo_index': 6, 'aut_stab_index': 21, 'aut_weyl_group': '512.10494213', 'aut_weyl_index': 1344, 'centralizer': '32.b1', 'complements': ['64.e1'], 'conjugacy_class_count': 21, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b2', '8.b3', '8.d1', '8.f1', '8.f4'], 'core': '4.a3', 'coset_action_label': None, 'count': 21, 'diagramx': [8140, 6145, 8140, 5974], 'generators': [84383109, 16948225, 101521990, 84316549, 17012225, 16979969], 'label': '256.46157.4.a3', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a3', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b2', '8.b3', '8.d1', '8.f1', '8.f4'], 'normalizer': '1.a1', 'old_label': '4.a3', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a3', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335405
{'ambient': '256.46157', 'aut_centralizer_order': 98304, 'aut_label': '128.a1', 'aut_quo_index': 2, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 688128, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 7, 'contained_in': ['64.a1', '64.b1', '64.b2', '64.b3', '64.c1', '64.d1'], 'contains': ['256.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2980, 4173, 2980, 4058], 'generators': [16948225], 'label': '256.46157.128.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': '128.2264', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2264', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335406
{'ambient': '256.46157', 'aut_centralizer_order': 12288, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 688128, 'centralizer': '4.f1', 'complements': None, 'conjugacy_class_count': 14, 'contained_in': ['64.b1', '64.b2', '64.b3', '64.e1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [2134, -1, 2134, -1], 'generators': [1938688], 'label': '256.46157.128.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1', 'old_label': '128.b1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335407
{'ambient': '256.46157', 'aut_centralizer_order': 28672, 'aut_label': '128.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 688128, 'centralizer': '8.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['64.c1', '64.f1'], 'contains': ['256.a1'], 'core': '256.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6011, -1, 5983, -1], 'generators': [16784385], 'label': '256.46157.128.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1', 'old_label': '128.c1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335408
{'ambient': '256.46157', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1', '128.b1', '128.c1'], 'contains': [], 'core': '256.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2980, 4173, 2980, 4058], 'generators': [], 'label': '256.46157.256.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1', 'normal_contained_in': ['128.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '256.a1', 'projective_image': '256.46157', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 43335409
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 2, 'aut_stab_index': 7, 'aut_weyl_group': '1536.408544622', 'aut_weyl_index': 448, 'centralizer': '32.b1', 'complements': ['64.e1'], 'conjugacy_class_count': 7, 'contained_in': ['2.b1'], 'contains': ['8.a1', '8.d1', '8.e1', '8.g1'], 'core': '4.b1', 'coset_action_label': None, 'count': 7, 'diagramx': [9182, 1069, 9182, 1039], 'generators': [16948225, 101521990, 16980481, 16784385, 17012225, 16979969], 'label': '256.46157.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.a1', '8.d1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '32.51'}
id: 43335410
{'ambient': '256.46157', 'aut_centralizer_order': 64, 'aut_label': '4.c1', 'aut_quo_index': 2, 'aut_stab_index': 7, 'aut_weyl_group': '1536.408544622', 'aut_weyl_index': 448, 'centralizer': '32.b1', 'complements': ['64.f1', '64.e1'], 'conjugacy_class_count': 7, 'contained_in': ['2.a1'], 'contains': ['8.b2', '8.f1', '8.f3'], 'core': '4.c1', 'coset_action_label': None, 'count': 7, 'diagramx': [4751, 7100, 4751, 6903], 'generators': [68817540, 16948225, 1842944, 51845827, 17012225, 16979969], 'label': '256.46157.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b2', '8.f1', '8.f3'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '32.51', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '32.51'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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