LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-09-21T18:07:32.424025

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': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 16, 'aut_gen_orders': [8, 2, 16, 2, 2, 2], 'aut_gens': [[1, 2, 64], [153, 202, 192], [253, 94, 64], [253, 194, 192], [161, 98, 192], [161, 2, 64], [33, 162, 64]], 'aut_group': '2048.ib', 'aut_hash': 7805229136759487691, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 30, 'aut_perms': [3071080737514666463810123588034, 21038661543945985836950237566222, 133957373708140247257087531140622, 13412407680, 6266956942, 382222], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 16, 2, 2], [8, 2, 2, 2], [8, 2, 4, 1], [8, 16, 4, 1], [16, 2, 4, 2], [16, 2, 8, 1], [32, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times D_{16}:C_8', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': '64.123', 'autcentquo_hash': 123, 'autcentquo_nilpotent': True, 'autcentquo_order': 64, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_8:C_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 1, 4], [4, 2, 4], [4, 16, 4], [8, 2, 8], [8, 16, 4], [16, 2, 16], [32, 2, 32]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '32.18', 'commutator_count': 1, 'commutator_label': '16.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 372, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 16, 1, 2], [4, 16, 2, 1], [8, 2, 2, 2], [8, 2, 4, 1], [8, 16, 4, 1], [16, 2, 4, 2], [16, 2, 8, 1], [32, 2, 16, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 12, 'exponent': 32, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '64.26', 'frattini_quotient': '4.2', 'hash': 372, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 16, 'inner_gen_orders': [2, 16, 1], 'inner_gens': [[1, 94, 64], [229, 2, 64], [1, 2, 64]], 'inner_hash': 18, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': True, 'inner_tex': 'D_{16}', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 60]], 'label': '256.372', 'linC_count': 256, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 10, 'linQ_dim': 20, 'linQ_dim_count': 5, 'linR_count': 80, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'Q32:C8', 'ngens': 2, 'nilpotency_class': 5, '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': 19, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 76, 'number_divisions': 21, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 63, 'number_subgroups': 187, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 3], [4, 76], [8, 80], [16, 32], [32, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 8], 'outer_gen_pows': [8, 0, 0, 0], 'outer_gens': [[9, 2, 64], [1, 190, 192], [1, 130, 64], [1, 10, 64]], 'outer_group': '64.246', 'outer_hash': 246, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 14, 'outer_perms': [362880, 6227045260, 6266937600, 39927090], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_8', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 40, 'pgroup': 2, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 7], [8, 2], [16, 3], [32, 1]], 'representations': {'PC': {'code': 656715372420455558888917202634719, 'gens': [1, 2, 7], 'pres': [8, -2, 2, -2, -2, -2, -2, 2, -2, 256, 1505, 41, 4514, 66, 1795, 91, 1924, 116, 166]}, 'GLZN': {'d': 2, 'p': 93, 'gens': [25739456, 65722316, 56907994, 61624723, 27612973, 49065838, 26281429, 58800169]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [33025, 106701, 32897, 294921, 33281, 491617, 557073, 835913]}, 'Perm': {'d': 40, 'gens': [2728696234801185019148805973435969543923942057, 22618457096625397207034098907407667935281406080, 43551586463038126297286618037655967915680358400, 12568, 64446824499942635556740276985773218655870244480, 18498, 85407852568729923668065803437515040736132574080, 106344098755135128628362244407000629091951377280]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_{32}:C_8', 'transitive_degree': 256, 'wreath_data': None, 'wreath_product': False}

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

gps_conj_classes • Show schema

id: 102460156
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 372, 'group_order': 256, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
id: 102460167
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 372, 'group_order': 256, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 128, 'size': 1}
id: 102460178
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 372, 'group_order': 256, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 160, 'size': 1}
id: 102460189
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 372, 'group_order': 256, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 32, 'size': 1}
id: 102460200
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 372, 'group_order': 256, 'label': '4A1', 'order': 4, 'powers': [2], 'representative': 96, 'size': 1}
id: 102460211
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 372, 'group_order': 256, 'label': '4A-1', 'order': 4, 'powers': [2], 'representative': 224, 'size': 1}
id: 102460222
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 372, 'group_order': 256, 'label': '4B1', 'order': 4, 'powers': [2], 'representative': 64, 'size': 1}
id: 102460230
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 372, 'group_order': 256, 'label': '4B-1', 'order': 4, 'powers': [2], 'representative': 192, 'size': 1}
id: 102460231
{'aut_label': '4C', 'centralizer': '2.c1.a1', 'counter': 9, 'group_counter': 372, 'group_order': 256, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 144, 'size': 2}
id: 102460157
{'aut_label': '4D', 'centralizer': '2.c1.a1', 'counter': 10, 'group_counter': 372, 'group_order': 256, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 16, 'size': 2}
id: 102460158
{'aut_label': '4E1', 'centralizer': '2.c1.a1', 'counter': 11, 'group_counter': 372, 'group_order': 256, 'label': '4E1', 'order': 4, 'powers': [3], 'representative': 80, 'size': 2}
id: 102460159
{'aut_label': '4E1', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 372, 'group_order': 256, 'label': '4E-1', 'order': 4, 'powers': [3], 'representative': 208, 'size': 2}
id: 102460160
{'aut_label': '4F', 'centralizer': '16.f1.a1', 'counter': 13, 'group_counter': 372, 'group_order': 256, 'label': '4F', 'order': 4, 'powers': [4], 'representative': 1, 'size': 16}
id: 102460161
{'aut_label': '4F', 'centralizer': '16.f1.a1', 'counter': 14, 'group_counter': 372, 'group_order': 256, 'label': '4G', 'order': 4, 'powers': [4], 'representative': 129, 'size': 16}
id: 102460162
{'aut_label': '4H1', 'centralizer': '16.f1.a1', 'counter': 15, 'group_counter': 372, 'group_order': 256, 'label': '4H1', 'order': 4, 'powers': [3], 'representative': 65, 'size': 16}
id: 102460163
{'aut_label': '4H1', 'centralizer': '16.f1.a1', 'counter': 16, 'group_counter': 372, 'group_order': 256, 'label': '4H-1', 'order': 4, 'powers': [3], 'representative': 193, 'size': 16}
id: 102460164
{'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 17, 'group_counter': 372, 'group_order': 256, 'label': '8A1', 'order': 8, 'powers': [10], 'representative': 136, 'size': 2}
id: 102460165
{'aut_label': '8A1', 'centralizer': '2.c1.a1', 'counter': 18, 'group_counter': 372, 'group_order': 256, 'label': '8A3', 'order': 8, 'powers': [10], 'representative': 152, 'size': 2}
id: 102460166
{'aut_label': '8B1', 'centralizer': '2.c1.a1', 'counter': 19, 'group_counter': 372, 'group_order': 256, 'label': '8B1', 'order': 8, 'powers': [10], 'representative': 8, 'size': 2}
id: 102460168
{'aut_label': '8B1', 'centralizer': '2.c1.a1', 'counter': 20, 'group_counter': 372, 'group_order': 256, 'label': '8B3', 'order': 8, 'powers': [10], 'representative': 24, 'size': 2}
id: 102460169
{'aut_label': '8C1', 'centralizer': '2.c1.a1', 'counter': 21, 'group_counter': 372, 'group_order': 256, 'label': '8C1', 'order': 8, 'powers': [9], 'representative': 72, 'size': 2}
id: 102460170
{'aut_label': '8C1', 'centralizer': '2.c1.a1', 'counter': 22, 'group_counter': 372, 'group_order': 256, 'label': '8C-1', 'order': 8, 'powers': [9], 'representative': 200, 'size': 2}
id: 102460171
{'aut_label': '8C1', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 372, 'group_order': 256, 'label': '8C3', 'order': 8, 'powers': [9], 'representative': 232, 'size': 2}
id: 102460172
{'aut_label': '8C1', 'centralizer': '2.c1.a1', 'counter': 24, 'group_counter': 372, 'group_order': 256, 'label': '8C-3', 'order': 8, 'powers': [9], 'representative': 104, 'size': 2}
id: 102460173
{'aut_label': '8D1', 'centralizer': '16.g1.a1', 'counter': 25, 'group_counter': 372, 'group_order': 256, 'label': '8D1', 'order': 8, 'powers': [7], 'representative': 3, 'size': 16}
id: 102460174
{'aut_label': '8D1', 'centralizer': '16.g1.a1', 'counter': 26, 'group_counter': 372, 'group_order': 256, 'label': '8D-1', 'order': 8, 'powers': [8], 'representative': 195, 'size': 16}
id: 102460175
{'aut_label': '8D1', 'centralizer': '16.g1.a1', 'counter': 27, 'group_counter': 372, 'group_order': 256, 'label': '8D3', 'order': 8, 'powers': [8], 'representative': 67, 'size': 16}
id: 102460176
{'aut_label': '8D1', 'centralizer': '16.g1.a1', 'counter': 28, 'group_counter': 372, 'group_order': 256, 'label': '8D-3', 'order': 8, 'powers': [7], 'representative': 131, 'size': 16}
id: 102460177
{'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 29, 'group_counter': 372, 'group_order': 256, 'label': '16A1', 'order': 16, 'powers': [17], 'representative': 68, 'size': 2}
id: 102460179
{'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 30, 'group_counter': 372, 'group_order': 256, 'label': '16A3', 'order': 16, 'powers': [18], 'representative': 116, 'size': 2}
id: 102460180
{'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 31, 'group_counter': 372, 'group_order': 256, 'label': '16A5', 'order': 16, 'powers': [18], 'representative': 84, 'size': 2}
id: 102460181
{'aut_label': '16A1', 'centralizer': '2.c1.a1', 'counter': 32, 'group_counter': 372, 'group_order': 256, 'label': '16A7', 'order': 16, 'powers': [17], 'representative': 100, 'size': 2}
id: 102460182
{'aut_label': '16B1', 'centralizer': '2.c1.a1', 'counter': 33, 'group_counter': 372, 'group_order': 256, 'label': '16B1', 'order': 16, 'powers': [17], 'representative': 196, 'size': 2}
id: 102460183
{'aut_label': '16B1', 'centralizer': '2.c1.a1', 'counter': 34, 'group_counter': 372, 'group_order': 256, 'label': '16B3', 'order': 16, 'powers': [18], 'representative': 76, 'size': 2}
id: 102460184
{'aut_label': '16B1', 'centralizer': '2.c1.a1', 'counter': 35, 'group_counter': 372, 'group_order': 256, 'label': '16B5', 'order': 16, 'powers': [18], 'representative': 212, 'size': 2}
id: 102460185
{'aut_label': '16B1', 'centralizer': '2.c1.a1', 'counter': 36, 'group_counter': 372, 'group_order': 256, 'label': '16B7', 'order': 16, 'powers': [17], 'representative': 228, 'size': 2}
id: 102460186
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 37, 'group_counter': 372, 'group_order': 256, 'label': '16C1', 'order': 16, 'powers': [19], 'representative': 4, 'size': 2}
id: 102460187
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 38, 'group_counter': 372, 'group_order': 256, 'label': '16C-1', 'order': 16, 'powers': [19], 'representative': 60, 'size': 2}
id: 102460188
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 39, 'group_counter': 372, 'group_order': 256, 'label': '16C3', 'order': 16, 'powers': [20], 'representative': 12, 'size': 2}
id: 102460190
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 40, 'group_counter': 372, 'group_order': 256, 'label': '16C-3', 'order': 16, 'powers': [20], 'representative': 52, 'size': 2}
id: 102460191
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 41, 'group_counter': 372, 'group_order': 256, 'label': '16C5', 'order': 16, 'powers': [20], 'representative': 20, 'size': 2}
id: 102460192
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 42, 'group_counter': 372, 'group_order': 256, 'label': '16C-5', 'order': 16, 'powers': [20], 'representative': 44, 'size': 2}
id: 102460193
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 43, 'group_counter': 372, 'group_order': 256, 'label': '16C7', 'order': 16, 'powers': [19], 'representative': 28, 'size': 2}
id: 102460194
{'aut_label': '16C1', 'centralizer': '2.c1.a1', 'counter': 44, 'group_counter': 372, 'group_order': 256, 'label': '16C-7', 'order': 16, 'powers': [19], 'representative': 36, 'size': 2}
id: 102460195
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 45, 'group_counter': 372, 'group_order': 256, 'label': '32A1', 'order': 32, 'powers': [37], 'representative': 2, 'size': 2}
id: 102460196
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 46, 'group_counter': 372, 'group_order': 256, 'label': '32A-1', 'order': 32, 'powers': [38], 'representative': 226, 'size': 2}
id: 102460197
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 47, 'group_counter': 372, 'group_order': 256, 'label': '32A3', 'order': 32, 'powers': [39], 'representative': 6, 'size': 2}
id: 102460198
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 48, 'group_counter': 372, 'group_order': 256, 'label': '32A-3', 'order': 32, 'powers': [40], 'representative': 58, 'size': 2}
id: 102460199
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 49, 'group_counter': 372, 'group_order': 256, 'label': '32A5', 'order': 32, 'powers': [41], 'representative': 10, 'size': 2}
id: 102460201
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 50, 'group_counter': 372, 'group_order': 256, 'label': '32A-5', 'order': 32, 'powers': [42], 'representative': 54, 'size': 2}
id: 102460202
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 51, 'group_counter': 372, 'group_order': 256, 'label': '32A7', 'order': 32, 'powers': [43], 'representative': 14, 'size': 2}
id: 102460203
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 52, 'group_counter': 372, 'group_order': 256, 'label': '32A-7', 'order': 32, 'powers': [44], 'representative': 50, 'size': 2}
id: 102460204
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 53, 'group_counter': 372, 'group_order': 256, 'label': '32A9', 'order': 32, 'powers': [44], 'representative': 18, 'size': 2}
id: 102460205
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 54, 'group_counter': 372, 'group_order': 256, 'label': '32A-9', 'order': 32, 'powers': [43], 'representative': 46, 'size': 2}
id: 102460206
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 55, 'group_counter': 372, 'group_order': 256, 'label': '32A11', 'order': 32, 'powers': [42], 'representative': 22, 'size': 2}
id: 102460207
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 56, 'group_counter': 372, 'group_order': 256, 'label': '32A-11', 'order': 32, 'powers': [41], 'representative': 42, 'size': 2}
id: 102460208
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 57, 'group_counter': 372, 'group_order': 256, 'label': '32A13', 'order': 32, 'powers': [40], 'representative': 26, 'size': 2}
id: 102460209
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 58, 'group_counter': 372, 'group_order': 256, 'label': '32A-13', 'order': 32, 'powers': [39], 'representative': 38, 'size': 2}
id: 102460210
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 59, 'group_counter': 372, 'group_order': 256, 'label': '32A15', 'order': 32, 'powers': [38], 'representative': 194, 'size': 2}
id: 102460212
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 60, 'group_counter': 372, 'group_order': 256, 'label': '32A-15', 'order': 32, 'powers': [37], 'representative': 34, 'size': 2}
id: 102460213
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 61, 'group_counter': 372, 'group_order': 256, 'label': '32B1', 'order': 32, 'powers': [37], 'representative': 130, 'size': 2}
id: 102460214
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 62, 'group_counter': 372, 'group_order': 256, 'label': '32B-1', 'order': 32, 'powers': [38], 'representative': 98, 'size': 2}
id: 102460215
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 63, 'group_counter': 372, 'group_order': 256, 'label': '32B3', 'order': 32, 'powers': [39], 'representative': 134, 'size': 2}
id: 102460216
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 64, 'group_counter': 372, 'group_order': 256, 'label': '32B-3', 'order': 32, 'powers': [40], 'representative': 186, 'size': 2}
id: 102460217
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 65, 'group_counter': 372, 'group_order': 256, 'label': '32B5', 'order': 32, 'powers': [41], 'representative': 138, 'size': 2}
id: 102460218
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 66, 'group_counter': 372, 'group_order': 256, 'label': '32B-5', 'order': 32, 'powers': [42], 'representative': 106, 'size': 2}
id: 102460219
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 67, 'group_counter': 372, 'group_order': 256, 'label': '32B7', 'order': 32, 'powers': [43], 'representative': 82, 'size': 2}
id: 102460220
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 68, 'group_counter': 372, 'group_order': 256, 'label': '32B-7', 'order': 32, 'powers': [44], 'representative': 178, 'size': 2}
id: 102460221
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 69, 'group_counter': 372, 'group_order': 256, 'label': '32B9', 'order': 32, 'powers': [44], 'representative': 146, 'size': 2}
id: 102460223
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 70, 'group_counter': 372, 'group_order': 256, 'label': '32B-9', 'order': 32, 'powers': [43], 'representative': 114, 'size': 2}
id: 102460224
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 71, 'group_counter': 372, 'group_order': 256, 'label': '32B11', 'order': 32, 'powers': [42], 'representative': 74, 'size': 2}
id: 102460225
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 72, 'group_counter': 372, 'group_order': 256, 'label': '32B-11', 'order': 32, 'powers': [41], 'representative': 170, 'size': 2}
id: 102460226
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 73, 'group_counter': 372, 'group_order': 256, 'label': '32B13', 'order': 32, 'powers': [40], 'representative': 154, 'size': 2}
id: 102460227
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 74, 'group_counter': 372, 'group_order': 256, 'label': '32B-13', 'order': 32, 'powers': [39], 'representative': 166, 'size': 2}
id: 102460228
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 75, 'group_counter': 372, 'group_order': 256, 'label': '32B15', 'order': 32, 'powers': [38], 'representative': 66, 'size': 2}
id: 102460229
{'aut_label': '32A1', 'centralizer': '2.c1.a1', 'counter': 76, 'group_counter': 372, 'group_order': 256, 'label': '32B-15', 'order': 32, 'powers': [37], 'representative': 162, 'size': 2}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 1407302
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 1407313
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 1407316
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 1407317
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 1407318
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407319
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407322
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, -2, -2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407303
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407320
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1g', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, -4, 4, 0, -4, 0, 0, 0, -4, 0, 4, 4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407321
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.1h', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 4, -4, 0, -4, 0, 0, 0, -4, 0, 4, 4, 0, 0, 0, 0, 4, -4, 0, 0, 0, 4, -4, 0, 0, 0, 0, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407304
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2c', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407305
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2d', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -4, 0, 4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, -4, 4, 0, 0, 0, 0, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407306
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2e', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 0, 0, 0, 0, -4, 4, 4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407307
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2f', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, -2], 'schur_index': 1}
id: 1407308
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2g', 'multiplicity': 2, 'nt': [8, 17], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, -2, 2, -2, 2], 'schur_index': 1}
id: 1407309
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2h', 'multiplicity': 4, 'nt': [16, 55], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, -8, -8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407310
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2i', 'multiplicity': 4, 'nt': [16, 56], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, 8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407311
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2j', 'multiplicity': 8, 'nt': [32, 284], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407312
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2k', 'multiplicity': 8, 'nt': [32, 373], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 1407314
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2l', 'multiplicity': 8, 'nt': [64, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, -16, 16, 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 1407315
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '256.372', 'group_order': 256, 'image': None, 'label': '256.372.2m', 'multiplicity': 16, 'nt': [64, 0], 'qdim': 32, 'qvalues': [32, -32, 32, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 1866254
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 256, 'label': '256.372.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 1866265
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 128, 'label': '256.372.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 1866276
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 128, 'label': '256.372.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 1866287
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 128, 'label': '256.372.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 1866298
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 64, 'label': '256.372.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 1866309
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 64, 'label': '256.372.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 1866320
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 64, 'label': '256.372.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 1866328
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 64, 'label': '256.372.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]]]}
id: 1866329
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 9, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 32, 'label': '256.372.1g1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]]]}
id: 1866255
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 10, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 32, 'label': '256.372.1g2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]]]}
id: 1866256
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 11, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 32, 'label': '256.372.1g3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 1]]]}
id: 1866257
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 256, 'counter': 12, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.d1.b1', 'kernel_order': 32, 'label': '256.372.1g4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 3]]]}
id: 1866258
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id: 1866259
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id: 1866260
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id: 1866261
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id: 1866262
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id: 1866263
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id: 1866264
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id: 1866266
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.a1.a1', 'kernel_order': 16, 'label': '256.372.2c2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]]]}
id: 1866267
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id: 1866268
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '16.6', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 16, 'label': '256.372.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 1866269
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 16, 'label': '256.372.2e1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
id: 1866270
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id: 1866271
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id: 1866272
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id: 1866273
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id: 1866274
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id: 1866275
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id: 1866277
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id: 1866278
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id: 1866279
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id: 1866280
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id: 1866281
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id: 1866282
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id: 1866283
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id: 1866284
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id: 1866285
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id: 1866286
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id: 1866288
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id: 1866289
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id: 1866290
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id: 1866291
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id: 1866292
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id: 1866293
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id: 1866294
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id: 1866295
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id: 1866296
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id: 1866297
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id: 1866299
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id: 1866300
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id: 1866301
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id: 1866302
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id: 1866303
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id: 1866304
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id: 1866305
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id: 1866306
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id: 1866307
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id: 1866308
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id: 1866310
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id: 1866311
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id: 1866321
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id: 1866322
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id: 1866323
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id: 1866324
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id: 1866325
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id: 1866326
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id: 1866327
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id: 1866312
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id: 1866313
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id: 1866314
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 64, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m4', 'nt': [64, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 8]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[1, 4], [1, -4]], [[1, 4], [1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2], [-1, -2]], [[1, 6], [1, -6]], [[1, 2], [1, 14]], [[1, 2], [1, 14]], [[1, 6], [1, 10]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, 14]], [[1, 6], [1, 10]], [[-1, 6], [-1, 10]], [[-1, 2], [-1, 14]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 6], [-1, 10]], [[-1, 9], [-1, 15]], [[1, 1], [1, 7]], [[1, 11], [1, 13]], [[1, 11], [-1, 13]], [[1, 9], [1, 15]], [[1, 11], [-1, 13]], [[1, 3], [1, 5]], [[-1, 3], [-1, 5]], [[1, 9], [-1, 15]], [[1, 9], [-1, 15]], [[-1, 1], [-1, 7]], [[1, 9], [1, 15]], [[-1, 1], [1, 7]], [[1, 1], [-1, 7]], [[1, 3], [-1, 5]], [[1, 11], [1, 13]], [[-1, 9], [1, 15]], [[-1, 1], [1, 7]], [[-1, 9], [1, 15]], [[-1, 11], [1, 13]], [[1, 1], [1, 7]], [[-1, 3], [-1, 5]], [[1, 3], [-1, 5]], [[-1, 11], [-1, 13]], [[1, 3], [1, 5]], [[-1, 3], [1, 5]], [[-1, 9], [-1, 15]], [[1, 1], [-1, 7]], [[-1, 3], [1, 5]], [[-1, 11], [-1, 13]], [[-1, 1], [-1, 7]], [[-1, 11], [1, 13]]]}
id: 1866315
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 65, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m5', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, 14]], [[1, 2], [1, 14]], [[1, 6], [1, 10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 14]], [[1, 6], [1, 10]], [[-1, 6], [-1, 10]], [[-1, 2], [-1, 14]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, 10]], [[-1, 9], [1, 15]], [[-1, 1], [1, 7]], [[-1, 11], [1, 13]], [[1, 11], [1, 13]], [[1, 9], [-1, 15]], [[1, 11], [1, 13]], [[1, 3], [-1, 5]], [[-1, 3], [1, 5]], [[-1, 9], [-1, 15]], [[-1, 9], [-1, 15]], [[1, 1], [-1, 7]], [[1, 9], [-1, 15]], [[-1, 1], [-1, 7]], [[1, 1], [1, 7]], [[-1, 3], [-1, 5]], [[-1, 11], [1, 13]], [[1, 9], [1, 15]], [[-1, 1], [-1, 7]], [[1, 9], [1, 15]], [[-1, 11], [-1, 13]], [[-1, 1], [1, 7]], [[-1, 3], [1, 5]], [[-1, 3], [-1, 5]], [[1, 11], [-1, 13]], [[1, 3], [-1, 5]], [[1, 3], [1, 5]], [[-1, 9], [1, 15]], [[1, 1], [1, 7]], [[1, 3], [1, 5]], [[1, 11], [-1, 13]], [[1, 1], [-1, 7]], [[-1, 11], [-1, 13]]]}
id: 1866316
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 66, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m6', 'nt': [64, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 8]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[1, 4], [1, -4]], [[1, 4], [1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, 14]], [[-1, 2], [-1, 14]], [[-1, 6], [-1, 10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, 14]], [[-1, 6], [-1, 10]], [[1, 6], [1, 10]], [[1, 2], [1, 14]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, 10]], [[-1, 1], [1, 7]], [[-1, 9], [1, 15]], [[-1, 3], [1, 5]], [[-1, 3], [-1, 5]], [[1, 1], [-1, 7]], [[-1, 3], [-1, 5]], [[1, 11], [-1, 13]], [[-1, 11], [1, 13]], [[1, 1], [1, 7]], [[1, 1], [1, 7]], [[1, 9], [-1, 15]], [[1, 1], [-1, 7]], [[1, 9], [1, 15]], [[-1, 9], [-1, 15]], [[1, 11], [1, 13]], [[-1, 3], [1, 5]], [[-1, 1], [-1, 7]], [[1, 9], [1, 15]], [[-1, 1], [-1, 7]], [[1, 3], [1, 5]], [[-1, 9], [1, 15]], [[-1, 11], [1, 13]], [[1, 11], [1, 13]], [[1, 3], [-1, 5]], [[1, 11], [-1, 13]], [[-1, 11], [-1, 13]], [[-1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[-1, 11], [-1, 13]], [[1, 3], [-1, 5]], [[1, 9], [-1, 15]], [[1, 3], [1, 5]]]}
id: 1866317
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 67, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m7', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[1, 2], [1, 14]], [[1, 2], [1, 14]], [[1, 6], [1, 10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[-1, 2], [-1, 14]], [[1, 6], [1, 10]], [[-1, 6], [-1, 10]], [[-1, 2], [-1, 14]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, 10]], [[1, 9], [-1, 15]], [[1, 1], [-1, 7]], [[1, 11], [-1, 13]], [[-1, 11], [-1, 13]], [[-1, 9], [1, 15]], [[-1, 11], [-1, 13]], [[-1, 3], [1, 5]], [[1, 3], [-1, 5]], [[1, 9], [1, 15]], [[1, 9], [1, 15]], [[-1, 1], [1, 7]], [[-1, 9], [1, 15]], [[1, 1], [1, 7]], [[-1, 1], [-1, 7]], [[1, 3], [1, 5]], [[1, 11], [-1, 13]], [[-1, 9], [-1, 15]], [[1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[1, 11], [1, 13]], [[1, 1], [-1, 7]], [[1, 3], [-1, 5]], [[1, 3], [1, 5]], [[-1, 11], [1, 13]], [[-1, 3], [1, 5]], [[-1, 3], [-1, 5]], [[1, 9], [-1, 15]], [[-1, 1], [-1, 7]], [[-1, 3], [-1, 5]], [[-1, 11], [1, 13]], [[-1, 1], [1, 7]], [[1, 11], [1, 13]]]}
id: 1866318
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 68, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m8', 'nt': [64, 16], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 8]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[1, 4], [1, -4]], [[1, 4], [1, 12]], [[1, 4], [1, -4]], [[-1, 4], [-1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, 14]], [[-1, 2], [-1, 14]], [[-1, 6], [-1, 10]], [[-1, 6], [-1, -6]], [[1, 2], [1, -2]], [[1, 2], [1, 14]], [[-1, 6], [-1, 10]], [[1, 6], [1, 10]], [[1, 2], [1, 14]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 6], [1, 10]], [[1, 1], [-1, 7]], [[1, 9], [-1, 15]], [[1, 3], [-1, 5]], [[1, 3], [1, 5]], [[-1, 1], [1, 7]], [[1, 3], [1, 5]], [[-1, 11], [1, 13]], [[1, 11], [-1, 13]], [[-1, 1], [-1, 7]], [[-1, 1], [-1, 7]], [[-1, 9], [1, 15]], [[-1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[1, 9], [1, 15]], [[-1, 11], [-1, 13]], [[1, 3], [-1, 5]], [[1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[1, 1], [1, 7]], [[-1, 3], [-1, 5]], [[1, 9], [-1, 15]], [[1, 11], [-1, 13]], [[-1, 11], [-1, 13]], [[-1, 3], [1, 5]], [[-1, 11], [1, 13]], [[1, 11], [1, 13]], [[1, 1], [-1, 7]], [[1, 9], [1, 15]], [[1, 11], [1, 13]], [[-1, 3], [1, 5]], [[-1, 9], [1, 15]], [[-1, 3], [-1, 5]]]}
id: 1866319
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 8, 'counter': 69, 'cyclotomic_n': 32, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '256.372', 'group_counter': 372, 'group_order': 256, 'image': None, 'image_isoclass': '128.149', 'image_order': 128, 'indicator': 0, 'kernel': '128.b1.a1', 'kernel_order': 2, 'label': '256.372.2m9', 'nt': [64, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 8]], [[2, 8]], [[-2, 8]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 4], [1, -4]], [[-1, 4], [-1, 12]], [[1, 4], [1, 12]], [[-1, 4], [-1, 12]], [[-1, 4], [-1, -4]], [[1, 4], [1, 12]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 6], [1, 10]], [[1, 6], [1, 10]], [[-1, 2], [-1, 14]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, 10]], [[-1, 2], [-1, 14]], [[1, 2], [1, 14]], [[-1, 6], [-1, 10]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, 14]], [[-1, 11], [1, 13]], [[-1, 3], [1, 5]], [[-1, 1], [-1, 7]], [[-1, 1], [1, 7]], [[1, 11], [-1, 13]], [[-1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[1, 9], [1, 15]], [[1, 11], [1, 13]], [[1, 11], [1, 13]], [[1, 3], [-1, 5]], [[1, 11], [-1, 13]], [[1, 3], [1, 5]], [[-1, 3], [-1, 5]], [[-1, 9], [1, 15]], [[-1, 1], [-1, 7]], [[-1, 11], [-1, 13]], [[1, 3], [1, 5]], [[-1, 11], [-1, 13]], [[1, 1], [-1, 7]], [[-1, 3], [1, 5]], [[1, 9], [1, 15]], [[-1, 9], [1, 15]], [[1, 1], [1, 7]], [[-1, 9], [-1, 15]], [[1, 9], [-1, 15]], [[-1, 11], [1, 13]], [[-1, 3], [-1, 5]], [[1, 9], [-1, 15]], [[1, 1], [1, 7]], [[1, 3], [-1, 5]], [[1, 1], [-1, 7]]]}

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: 36121568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 256, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '256.372.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '256.372', 'subgroup_hash': 372, 'subgroup_order': 256, 'subgroup_tex': 'Q_{32}:C_8', 'supersolvable': True, 'sylow': 2}
id: 36121579
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.906', 'subgroup_hash': 906, 'subgroup_order': 128, 'subgroup_tex': 'C_4\\times Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.103', 'subgroup_hash': 103, 'subgroup_order': 128, 'subgroup_tex': 'C_{16}:C_8', 'supersolvable': True, 'sylow': 0}
id: 36121601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 128, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.128', 'subgroup_hash': 128, 'subgroup_order': 128, 'subgroup_tex': 'C_4\\times C_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121612
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.26', 'subgroup_hash': 26, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.188', 'subgroup_hash': 188, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.47', 'subgroup_hash': 47, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.120', 'subgroup_hash': 120, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.16', 'subgroup_hash': 16, 'subgroup_order': 64, 'subgroup_tex': 'C_8:C_8', 'supersolvable': True, 'sylow': 0}
id: 36121569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.39', 'subgroup_hash': 39, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121570
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.50', 'subgroup_hash': 50, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\times C_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121571
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 36121572
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121573
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 36121577
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
id: 36121578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.14', 'subgroup_hash': 14, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.20', 'subgroup_hash': 20, 'subgroup_order': 32, 'subgroup_tex': 'Q_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121583
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.1', 'subgroup_hash': 1, 'subgroup_order': 32, 'subgroup_tex': 'C_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121584
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 24, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.1', 'subgroup_hash': 1, 'subgroup_order': 32, 'subgroup_tex': 'C_{32}', 'supersolvable': True, 'sylow': 0}
id: 36121585
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': ['U3', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 36121586
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 36121587
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 36121588
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121589
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 16, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121591
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 36121592
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 36121593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 36121594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 36121596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121599
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 36121600
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.18', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{16}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U4', 'C5'], 'split': False, '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: 36121602
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.9', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 36121603
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.19', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 19, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{32}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 36121604
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_8', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 36121605
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 36121606
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.32.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 36121607
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.32.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 36121608
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.32.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 36121609
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.32.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 36121610
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.32.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 36121611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.32.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 36121613
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '256.372.32.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 36121614
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.372.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 36121615
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.54', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 54, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{64}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121616
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 4, 'counter': 53, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.53', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 53, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{64}', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121617
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.64.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121618
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.64.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_8', 'simple': False, 'solvable': True, 'special_labels': ['L3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121619
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.64.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 36121620
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.64.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 36121621
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.64.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121622
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '256.372.64.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 36121624
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.148', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 148, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{32}:C_4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 36121625
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_{16}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 36121626
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.372.128.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '128.63', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 63, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_8', 'simple': True, 'solvable': True, 'special_labels': ['L4'], '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: 36121627
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.372', 'ambient_counter': 372, 'ambient_order': 256, 'ambient_tex': 'Q_{32}:C_8', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '256.372.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '256.372', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 372, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{32}:C_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U5', 'L5', '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: 36121568
{'ambient': '256.372', '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.a1.a1', 'complements': ['256.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6304, 5404, 4804, 4774, 6270, 5305, 4829, 4915], 'generators': [1, 2], 'label': '256.372.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121569
{'ambient': '256.372', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '256.53142', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.i1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5378, -1, 3795, -1, 5348, -1, 3815, -1], 'generators': [1, 156], 'label': '256.372.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121570
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.36', 'aut_weyl_index': 64, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.c1.a1', '8.k1.a1', '8.k1.b1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8158, -1, 5664, -1, 8114, -1, 5694, -1], 'generators': [2, 128], 'label': '256.372.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.g1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121571
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4083, 3422, 6671, 2850, 4060, 3359, 6707, 2934], 'generators': [136, 64], 'label': '256.372.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '32.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121572
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '8.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.b1.a1', '16.d1.a1', '16.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7823, 7556, 2087, 6663, 7780, 7419, 2098, 6859], 'generators': [92, 128], 'label': '256.372.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.b1.a1', '16.e1.a1', '16.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121573
{'ambient': '256.372', 'aut_centralizer_order': 128, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.b1.a1', '16.m1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6751, 5404, 4668, 4677, 6715, 5305, 4693, 4815], 'generators': [156, 128], 'label': '256.372.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121574
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.913', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.e1.a1', '16.k1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9822, 9221, 218, 8198, 9768, 9053, 219, 8439], 'generators': [1, 92], 'label': '256.372.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121575
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '8.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.913', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': ['32.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.e1.a1', '16.k1.b1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9822, 9221, 766, 9281, 9768, 9053, 769, 9555], 'generators': [129, 92], 'label': '256.372.8.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.b1.a1'], 'normal_contains': ['16.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121576
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '16.h1.a1', '16.i1.a1', '16.j1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2577, -1, 8079, -1, 2563, -1, 8122, -1], 'generators': [1, 48, 64], 'label': '256.372.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.e1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121577
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.a1.a1', '16.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1821, -1, 8786, -1, 1811, -1, 8832, -1], 'generators': [3, 48], 'label': '256.372.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '8.f1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121578
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '64.261', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.c1.a1', '16.h1.a1', '16.i1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3333, -1, 7373, -1, 3315, -1, 7411, -1], 'generators': [1, 200], 'label': '256.372.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.g1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121579
{'ambient': '256.372', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.7529826', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6304, 7569, 3795, 6468, 6270, 7432, 3815, 6659], 'generators': [1, 92, 64], 'label': '256.372.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121580
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.b1.a1', '16.h1.a1', '16.k1.a1', '16.k1.b1', '16.l1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5673, -1, 3094, -1, 5642, -1, 3111, -1], 'generators': [1, 136, 128], 'label': '256.372.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121581
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.254', 'aut_weyl_index': 32, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.f1.a1'], 'contains': ['16.b1.a1', '16.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4832, -1, 3881, -1, 4805, -1, 3902, -1], 'generators': [65, 136], 'label': '256.372.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.i1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121582
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.913', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.k1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9236, -1, 1312, -1, 9186, -1, 1319, -1], 'generators': [1, 220], 'label': '256.372.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.j1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121583
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.5', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.m1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8652, -1, 5983, -1, 8604, -1, 6015, -1], 'generators': [2], 'label': '256.372.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.k1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121584
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.5', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.m1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8652, -1, 5442, -1, 8604, -1, 5471, -1], 'generators': [130], 'label': '256.372.8.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.k1.b1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121585
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2097, 2511, 8509, 2314, 2086, 2464, 8554, 2383], 'generators': [48, 64], 'label': '256.372.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '32.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121586
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '16.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.h1.a1', '8.i1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6417, 5747, 3979, 5299, 6381, 5642, 4001, 5455], 'generators': [136, 128], 'label': '256.372.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.b1.a1', '32.e1.a1', '32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121587
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.g1.a1'], 'contains': ['32.b1.a1', '32.j1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4931, 3950, 6205, 3642, 4904, 3878, 6237, 3749], 'generators': [200, 128], 'label': '256.372.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121588
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.j1.a1'], 'contains': ['32.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8323, 7227, 2087, 6663, 8277, 7095, 2098, 6859], 'generators': [220], 'label': '256.372.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121589
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.d1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8901, 8389, 882, 7966, 8853, 8236, 887, 8201], 'generators': [92], 'label': '256.372.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1', '8.d1.b1', '8.d1.a1'], 'normal_contains': ['32.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121590
{'ambient': '256.372', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.7529826', 'aut_weyl_index': 4, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5391, 3581, 5652, 4774, 5361, 3515, 5681, 4915], 'generators': [3, 92], 'label': '256.372.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121591
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1558, -1, 8006, -1, 1550, -1, 8048, -1], 'generators': [1, 64], 'label': '256.372.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.f1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121592
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.5', 'aut_weyl_index': 256, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1'], 'contains': ['32.a1.a1', '32.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [842, -1, 9180, -1, 837, -1, 9228, -1], 'generators': [3, 32], 'label': '256.372.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1.a1', 'old_label': '16.g1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121593
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '32.f1.a1', '32.i1.a1', '32.k1.a1', '32.k1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4030, -1, 5363, -1, 4008, -1, 5391, -1], 'generators': [1, 48, 128], 'label': '256.372.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.h1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121594
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.11', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1', '8.i1.a1'], 'contains': ['32.b1.a1', '32.g1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3274, -1, 6906, -1, 3256, -1, 6942, -1], 'generators': [65, 48], 'label': '256.372.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.i1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121595
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.14', 'aut_weyl_index': 128, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.c1.a1', '32.f1.a1', '32.g1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2669, -1, 7471, -1, 2654, -1, 7510, -1], 'generators': [1, 112], 'label': '256.372.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '16.j1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 36121596
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.h1.a1', '8.j1.a1'], 'contains': ['32.d1.a1', '32.k1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7737, -1, 1540, -1, 7695, -1, 1548, -1], 'generators': [1, 136], 'label': '256.372.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.k1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121597
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.h1.a1', '8.j1.a1'], 'contains': ['32.d1.a1', '32.k1.b1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7737, -1, 2633, -1, 7695, -1, 2648, -1], 'generators': [129, 136], 'label': '256.372.16.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.k1.b1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121598
{'ambient': '256.372', 'aut_centralizer_order': 16, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.43', 'aut_weyl_index': 64, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1'], 'contains': ['32.e1.a1', '32.k1.a1', '32.k1.b1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5673, -1, 3285, -1, 5642, -1, 3302, -1], 'generators': [1, 8], 'label': '256.372.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '16.l1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121599
{'ambient': '256.372', 'aut_centralizer_order': 128, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 256, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.k1.a1', '8.k1.b1'], 'contains': ['32.e1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7153, -1, 4668, -1, 7113, -1, 4693, -1], 'generators': [156], 'label': '256.372.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121600
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [861, 779, 9143, 719, 856, 765, 9191, 740], 'generators': [32, 64], 'label': '256.372.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '64.c1.a1', '64.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '32.18', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.18', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121601
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.246', 'aut_weyl_index': 32, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.g1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7383, 5404, 4804, 3094, 7342, 5305, 4829, 3185], 'generators': [2, 64], 'label': '256.372.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '32.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121602
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '64.d1.a1', '64.e1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4911, 4373, 5356, 4032, 4884, 4293, 5385, 4151], 'generators': [48, 128], 'label': '256.372.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '64.d1.a1', '64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121603
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '32.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '64.f1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1755, 2577, 8307, 2375, 1746, 2529, 8350, 2445], 'generators': [112, 128], 'label': '256.372.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '64.38', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.1', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121604
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '32.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.d1.a1', '16.e1.a1', '16.k1.a1', '16.k1.b1'], 'contains': ['64.e1.a1'], 'core': '32.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7737, 6962, 2363, 6419, 7695, 6835, 2370, 6608], 'generators': [136], 'label': '256.372.32.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.d1.a1', 'normal_contained_in': ['16.b1.a1', '16.e1.a1', '16.d1.a1'], 'normal_contains': ['64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121605
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.e1.a1'], 'core': '32.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6541, 5747, 4225, 5299, 6505, 5642, 4248, 5455], 'generators': [8], 'label': '256.372.32.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.e1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.e1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.2', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121606
{'ambient': '256.372', 'aut_centralizer_order': 64, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.h1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '64.h1.a1', '64.h1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3544, -1, 6635, -1, 3524, -1, 6670, -1], 'generators': [1, 128], 'label': '256.372.32.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.f1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121607
{'ambient': '256.372', 'aut_centralizer_order': 64, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '64.g1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2649, -1, 7471, -1, 2635, -1, 7510, -1], 'generators': [65, 128], 'label': '256.372.32.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.g1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121608
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '16.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1'], 'contains': ['64.c1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [178, -1, 9782, -1, 177, -1, 9833, -1], 'generators': [3], 'label': '256.372.32.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.g1.a1', 'old_label': '32.h1.a1', 'projective_image': '64.53', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121609
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1'], 'contains': ['64.d1.a1', '64.h1.a1', '64.h1.b1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4227, -1, 4717, -1, 4204, -1, 4742, -1], 'generators': [1, 176], 'label': '256.372.32.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '32.i1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 36121610
{'ambient': '256.372', 'aut_centralizer_order': 256, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 512, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1'], 'contains': ['64.d1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5595, -1, 5996, -1, 5564, -1, 6027, -1], 'generators': [200], 'label': '256.372.32.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.j1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121611
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.k1.a1', '16.l1.a1'], 'contains': ['64.e1.a1', '64.h1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6068, -1, 3340, -1, 6034, -1, 3358, -1], 'generators': [1, 48], 'label': '256.372.32.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.k1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121612
{'ambient': '256.372', 'aut_centralizer_order': 128, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 128, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6304, 5404, 4662, 4714, 6270, 5305, 4687, 4853], 'generators': [92, 64], 'label': '256.372.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '32.18', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121613
{'ambient': '256.372', 'aut_centralizer_order': 32, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.3', 'aut_weyl_index': 256, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '16.k1.b1', '16.l1.a1'], 'contains': ['64.e1.a1', '64.h1.b1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6068, -1, 3783, -1, 6034, -1, 3803, -1], 'generators': [129, 48], 'label': '256.372.32.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '32.k1.b1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 36121614
{'ambient': '256.372', 'aut_centralizer_order': 2048, 'aut_label': '64.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.f1.a1', '32.g1.a1'], 'contains': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2288, 2748, 7367, 2534, 2275, 2698, 7405, 2608], 'generators': [32, 128], 'label': '256.372.64.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['128.b1.a1', '128.c1.a1', '128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '64.38', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.38', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121615
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '64.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1'], 'contains': ['128.a1.a1'], 'core': '64.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1308, 1730, 8724, 1595, 1301, 1699, 8770, 1643], 'generators': [96], 'label': '256.372.64.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '64.54', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.54', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121616
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '64.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.h1.a1'], 'contains': ['128.a1.a1'], 'core': '64.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [835, 779, 9167, 719, 830, 765, 9215, 740], 'generators': [64], 'label': '256.372.64.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.c1.a1', 'normal_contained_in': ['32.a1.a1'], 'normal_contains': ['128.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.c1.a1', 'projective_image': '64.53', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.53', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121617
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '64.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.i1.a1', '32.j1.a1'], 'contains': ['128.c1.a1'], 'core': '64.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4806, 4201, 5480, 3873, 4779, 3995, 5632, 3862], 'generators': [176], 'label': '256.372.64.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.d1.a1', 'normal_contained_in': ['32.b1.a1'], 'normal_contains': ['128.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.d1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.16', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121618
{'ambient': '256.372', 'aut_centralizer_order': 1024, 'aut_label': '64.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '32.d1.a1', '32.e1.a1', '32.k1.a1', '32.k1.b1'], 'contains': ['128.c1.a1'], 'core': '64.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6068, 5457, 3968, 5030, 6034, 5279, 4025, 5104], 'generators': [48], 'label': '256.372.64.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.e1.a1', 'normal_contained_in': ['32.b1.a1', '32.e1.a1', '32.d1.a1'], 'normal_contains': ['128.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.e1.a1', 'projective_image': '128.63', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.3', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121619
{'ambient': '256.372', 'aut_centralizer_order': 512, 'aut_label': '64.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1781, -1, 8282, -1, 1772, -1, 8326, -1], 'generators': [112], 'label': '256.372.64.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '64.f1.a1', 'projective_image': '128.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121620
{'ambient': '256.372', 'aut_centralizer_order': 64, 'aut_label': '64.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.g1.a1'], 'contains': ['128.b1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2794, -1, 7839, -1, 2779, -1, 7881, -1], 'generators': [65], 'label': '256.372.64.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.f1.a1', 'old_label': '64.g1.a1', 'projective_image': '128.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121621
{'ambient': '256.372', 'aut_centralizer_order': 64, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.i1.a1', '32.k1.a1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4227, -1, 4595, -1, 4204, -1, 4742, -1], 'generators': [1], 'label': '256.372.64.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '64.h1.a1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121622
{'ambient': '256.372', 'aut_centralizer_order': 64, 'aut_label': '64.h1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1024, 'centralizer': '16.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.f1.a1', '32.i1.a1', '32.k1.b1'], 'contains': ['128.c1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4227, -1, 5037, -1, 4204, -1, 5187, -1], 'generators': [129], 'label': '256.372.64.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.e1.a1', 'old_label': '64.h1.b1', 'projective_image': '128.63', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 36121623
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.26455', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1', '8.h1.a1', '8.j1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9236, 9221, 1699, 8198, 9186, 9053, 1708, 8439], 'generators': [1, 92, 128], 'label': '256.372.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.d1.b1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121624
{'ambient': '256.372', 'aut_centralizer_order': 2048, 'aut_label': '128.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.b1.a1', '64.c1.a1'], 'contains': ['256.a1.a1'], 'core': '128.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1564, 1770, 8504, 1632, 1556, 1738, 8548, 1680], 'generators': [128], 'label': '256.372.128.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.a1.a1', 'normal_contained_in': ['64.a1.a1', '64.c1.a1', '64.b1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '128.148', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.148', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121625
{'ambient': '256.372', 'aut_centralizer_order': 2048, 'aut_label': '128.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.f1.a1', '64.g1.a1'], 'contains': ['256.a1.a1'], 'core': '128.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2288, 2748, 7839, 2534, 2275, 2698, 7881, 2608], 'generators': [160], 'label': '256.372.128.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1.a1', 'normal_contained_in': ['64.a1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.b1.a1', 'projective_image': '128.149', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.149', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121626
{'ambient': '256.372', 'aut_centralizer_order': 2048, 'aut_label': '128.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 2048, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '64.d1.a1', '64.e1.a1', '64.h1.a1', '64.h1.b1'], 'contains': ['256.a1.a1'], 'core': '128.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4227, 3871, 5258, 3569, 4204, 3658, 5409, 3536], 'generators': [32], 'label': '256.372.128.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.c1.a1', 'normal_contained_in': ['64.a1.a1', '64.d1.a1', '64.e1.a1'], 'normal_contains': ['256.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '128.c1.a1', 'projective_image': '128.63', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.63', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121627
{'ambient': '256.372', 'aut_centralizer_order': None, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '128.b1.a1', '128.c1.a1'], 'contains': [], 'core': '256.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2288, 2748, 7839, 2534, 2275, 2698, 7881, 2608], 'generators': [], 'label': '256.372.256.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '256.a1.a1', 'normal_contained_in': ['128.b1.a1', '128.c1.a1', '128.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '256.372', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 36121628
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.26455', 'aut_weyl_index': 8, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.i1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7232, 7346, 3064, 6468, 7192, 7212, 3080, 6659], 'generators': [65, 92], 'label': '256.372.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '64.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.18'}
id: 36121629
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2310', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4444, -1, 6671, -1, 4420, -1, 6707, -1], 'generators': [1, 136, 64], 'label': '256.372.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}
id: 36121630
{'ambient': '256.372', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '128.2310', 'aut_weyl_index': 16, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3465, -1, 7588, -1, 3446, -1, 7628, -1], 'generators': [3, 136], 'label': '256.372.4.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.e1.a1', 'projective_image': '32.18', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.7'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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