LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-11-04T14:44:00.894033

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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 42, 'aut_gen_orders': [6, 6, 6, 6, 6, 6, 2, 6, 6, 2], 'aut_gens': [[1, 2, 8], [289, 678, 924], [389, 2, 252], [293, 230, 1208], [869, 226, 636], [97, 678, 972], [677, 678, 924], [389, 6, 1340], [1057, 450, 1116], [293, 230, 184], [1057, 454, 332]], 'aut_group': None, 'aut_hash': 9164245504634031933, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 48, 'aut_perms': [11246525781685119829918450733687831648926308978879148167563536, 9645453932098781240294462322708633146687603780249888482942259, 1381524037746308915052927690111178467771098614303855995142507, 385173634947215940349819619642442616180943187389496557898090, 715349461359179674242767098040685659296374237403910166166464, 5130394676953228356878577490845481594516588219927266798413624, 2394967304032009393294302204878958006598735829726559320264479, 1634783982347687301948662597533530603048463403539659218645645, 10960115183221379429614911624853013701297657307306834179137427, 1634783982354377815827376061364377266452546451394972218527267], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 28, 1, 1], [2, 42, 2, 1], [3, 2, 1, 1], [4, 1, 2, 2], [4, 12, 1, 2], [4, 28, 1, 1], [4, 42, 2, 1], [6, 2, 1, 3], [6, 28, 2, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 6, 4, 1], [8, 14, 4, 1], [8, 84, 2, 1], [12, 2, 2, 2], [12, 28, 2, 1], [14, 2, 3, 3], [21, 4, 3, 1], [24, 4, 4, 1], [24, 28, 4, 1], [28, 2, 6, 2], [28, 12, 6, 2], [42, 4, 3, 3], [56, 4, 12, 1], [56, 12, 12, 1], [84, 4, 6, 2], [168, 4, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7\\times S_3\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '252.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 252, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 28, 1], [2, 42, 2], [3, 2, 1], [4, 1, 4], [4, 12, 2], [4, 28, 1], [4, 42, 2], [6, 2, 3], [6, 28, 2], [7, 2, 3], [8, 4, 2], [8, 6, 4], [8, 14, 4], [8, 84, 2], [12, 2, 4], [12, 28, 2], [14, 2, 9], [21, 4, 3], [24, 4, 4], [24, 28, 4], [28, 2, 12], [28, 12, 12], [42, 4, 9], [56, 4, 12], [56, 12, 12], [84, 4, 12], [168, 4, 24]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '84.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2375, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 28, 1, 1], [2, 42, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 12, 1, 2], [4, 28, 1, 1], [4, 42, 2, 1], [6, 2, 1, 3], [6, 28, 2, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 6, 2, 2], [8, 14, 4, 1], [8, 84, 2, 1], [12, 2, 2, 2], [12, 28, 2, 1], [14, 2, 3, 3], [21, 4, 3, 1], [24, 4, 4, 1], [24, 28, 4, 1], [28, 2, 6, 2], [28, 12, 6, 2], [42, 4, 3, 3], [56, 4, 12, 1], [56, 12, 6, 2], [84, 4, 6, 2], [168, 4, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2375, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 42], 'inner_gens': [[1, 6, 108], [5, 2, 232], [1253, 1122, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 76], [4, 64]], 'label': '1344.2375', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 80, 'linQ_dim': 14, 'linQ_dim_count': 72, 'linR_count': 48, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D42:OD16', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 43, 'number_characteristic_subgroups': 70, 'number_conjugacy_classes': 156, 'number_divisions': 46, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 248, 'number_subgroups': 1908, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 115], [3, 2], [4, 140], [6, 62], [7, 6], [8, 256], [12, 64], [14, 18], [21, 12], [24, 128], [28, 168], [42, 36], [56, 192], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 904], [673, 2, 8], [1, 674, 904], [1, 678, 904], [1, 6, 684], [1, 2, 1304]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [482671464, 720, 3669864, 41064, 24, 87178291203], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 7], [6, 4], [8, 2], [12, 6], [16, 1], [24, 6], [48, 2]], 'representations': {'PC': {'code': 32639098466100982008414820012401002826149593107097499159837195, 'gens': [1, 2, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 97, 41, 3459, 3723, 91, 8324, 9292, 116, 19973, 22285, 141, 46598, 14350, 222, 73735]}, 'Perm': {'d': 22, 'gens': [2439325304683547167, 6238311970, 44725813, 95212103, 23, 132089760, 93405312000, 55969571858264064000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{42}:\\OD_{16}', 'transitive_degree': 672, '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: 115777962
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2375, 'group_order': 1344, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 115778030
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2375, 'group_order': 1344, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 672, 'size': 1}
id: 115778041
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 2375, 'group_order': 1344, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 4, 'size': 1}
id: 115778052
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 2375, 'group_order': 1344, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 676, 'size': 1}
id: 115778063
{'aut_label': '2D', 'centralizer': '28.e1.a1', 'counter': 5, 'group_counter': 2375, 'group_order': 1344, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 961, 'size': 28}
id: 115778074
{'aut_label': '2E', 'centralizer': '42.e1.a1', 'counter': 6, 'group_counter': 2375, 'group_order': 1344, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 35, 'size': 42}
id: 115778085
{'aut_label': '2E', 'centralizer': '42.e1.a1', 'counter': 7, 'group_counter': 2375, 'group_order': 1344, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 711, 'size': 42}
id: 115778096
{'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 2375, 'group_order': 1344, 'label': '3A', 'order': 3, 'powers': [8, 1, 8], 'representative': 896, 'size': 2}
id: 115778107
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 2375, 'group_order': 1344, 'label': '4A1', 'order': 4, 'powers': [2, 10, 10], 'representative': 340, 'size': 1}
id: 115777963
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 2375, 'group_order': 1344, 'label': '4A-1', 'order': 4, 'powers': [2, 9, 9], 'representative': 1012, 'size': 1}
id: 115777974
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 2375, 'group_order': 1344, 'label': '4B1', 'order': 4, 'powers': [2, 12, 12], 'representative': 336, 'size': 1}
id: 115777985
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 2375, 'group_order': 1344, 'label': '4B-1', 'order': 4, 'powers': [2, 11, 11], 'representative': 1008, 'size': 1}
id: 115777996
{'aut_label': '4C', 'centralizer': '12.h1.a1', 'counter': 13, 'group_counter': 2375, 'group_order': 1344, 'label': '4C', 'order': 4, 'powers': [3, 13, 13], 'representative': 6, 'size': 12}
id: 115778007
{'aut_label': '4D', 'centralizer': '12.h1.a1', 'counter': 14, 'group_counter': 2375, 'group_order': 1344, 'label': '4D', 'order': 4, 'powers': [4, 14, 14], 'representative': 118, 'size': 12}
id: 115778018
{'aut_label': '4E', 'centralizer': '28.e1.a1', 'counter': 15, 'group_counter': 2375, 'group_order': 1344, 'label': '4E', 'order': 4, 'powers': [2, 15, 15], 'representative': 241, 'size': 28}
id: 115778026
{'aut_label': '4F1', 'centralizer': '42.e1.a1', 'counter': 16, 'group_counter': 2375, 'group_order': 1344, 'label': '4F1', 'order': 4, 'powers': [2, 17, 17], 'representative': 823, 'size': 42}
id: 115778027
{'aut_label': '4F1', 'centralizer': '42.e1.a1', 'counter': 17, 'group_counter': 2375, 'group_order': 1344, 'label': '4F-1', 'order': 4, 'powers': [2, 16, 16], 'representative': 151, 'size': 42}
id: 115778028
{'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 18, 'group_counter': 2375, 'group_order': 1344, 'label': '6A', 'order': 6, 'powers': [8, 2, 18], 'representative': 224, 'size': 2}
id: 115778029
{'aut_label': '6B', 'centralizer': '2.b1.a1', 'counter': 19, 'group_counter': 2375, 'group_order': 1344, 'label': '6B', 'order': 6, 'powers': [8, 3, 19], 'representative': 452, 'size': 2}
id: 115778031
{'aut_label': '6C', 'centralizer': '2.b1.a1', 'counter': 20, 'group_counter': 2375, 'group_order': 1344, 'label': '6C', 'order': 6, 'powers': [8, 4, 20], 'representative': 228, 'size': 2}
id: 115778032
{'aut_label': '6D1', 'centralizer': '28.e1.a1', 'counter': 21, 'group_counter': 2375, 'group_order': 1344, 'label': '6D1', 'order': 6, 'powers': [8, 5, 21], 'representative': 65, 'size': 28}
id: 115778033
{'aut_label': '6D1', 'centralizer': '28.e1.a1', 'counter': 22, 'group_counter': 2375, 'group_order': 1344, 'label': '6D-1', 'order': 6, 'powers': [8, 5, 22], 'representative': 129, 'size': 28}
id: 115778034
{'aut_label': '7A1', 'centralizer': '2.f1.a1', 'counter': 23, 'group_counter': 2375, 'group_order': 1344, 'label': '7A1', 'order': 7, 'powers': [24, 25, 1], 'representative': 768, 'size': 2}
id: 115778035
{'aut_label': '7A1', 'centralizer': '2.f1.a1', 'counter': 24, 'group_counter': 2375, 'group_order': 1344, 'label': '7A2', 'order': 7, 'powers': [25, 23, 1], 'representative': 192, 'size': 2}
id: 115778036
{'aut_label': '7A1', 'centralizer': '2.f1.a1', 'counter': 25, 'group_counter': 2375, 'group_order': 1344, 'label': '7A3', 'order': 7, 'powers': [23, 24, 1], 'representative': 960, 'size': 2}
id: 115778037
{'aut_label': '8A1', 'centralizer': '4.g1.a1', 'counter': 26, 'group_counter': 2375, 'group_order': 1344, 'label': '8A1', 'order': 8, 'powers': [11, 27, 27], 'representative': 168, 'size': 4}
id: 115778038
{'aut_label': '8A1', 'centralizer': '4.g1.a1', 'counter': 27, 'group_counter': 2375, 'group_order': 1344, 'label': '8A-1', 'order': 8, 'powers': [12, 26, 26], 'representative': 1176, 'size': 4}
id: 115778039
{'aut_label': '8B1', 'centralizer': '6.e1.a1', 'counter': 28, 'group_counter': 2375, 'group_order': 1344, 'label': '8B1', 'order': 8, 'powers': [9, 29, 29], 'representative': 734, 'size': 6}
id: 115778040
{'aut_label': '8B1', 'centralizer': '6.e1.a1', 'counter': 29, 'group_counter': 2375, 'group_order': 1344, 'label': '8B-1', 'order': 8, 'powers': [10, 28, 28], 'representative': 394, 'size': 6}
id: 115778042
{'aut_label': '8B1', 'centralizer': '6.e1.a1', 'counter': 30, 'group_counter': 2375, 'group_order': 1344, 'label': '8C1', 'order': 8, 'powers': [10, 31, 31], 'representative': 846, 'size': 6}
id: 115778043
{'aut_label': '8B1', 'centralizer': '6.e1.a1', 'counter': 31, 'group_counter': 2375, 'group_order': 1344, 'label': '8C-1', 'order': 8, 'powers': [9, 30, 30], 'representative': 1178, 'size': 6}
id: 115778044
{'aut_label': '8D1', 'centralizer': '14.f1.a1', 'counter': 32, 'group_counter': 2375, 'group_order': 1344, 'label': '8D1', 'order': 8, 'powers': [9, 34, 33], 'representative': 125, 'size': 14}
id: 115778045
{'aut_label': '8D1', 'centralizer': '14.f1.a1', 'counter': 33, 'group_counter': 2375, 'group_order': 1344, 'label': '8D-1', 'order': 8, 'powers': [10, 35, 32], 'representative': 1129, 'size': 14}
id: 115778046
{'aut_label': '8D1', 'centralizer': '14.f1.a1', 'counter': 34, 'group_counter': 2375, 'group_order': 1344, 'label': '8D3', 'order': 8, 'powers': [10, 32, 35], 'representative': 457, 'size': 14}
id: 115778047
{'aut_label': '8D1', 'centralizer': '14.f1.a1', 'counter': 35, 'group_counter': 2375, 'group_order': 1344, 'label': '8D-3', 'order': 8, 'powers': [9, 33, 34], 'representative': 797, 'size': 14}
id: 115778048
{'aut_label': '8E1', 'centralizer': '84.j1.a1', 'counter': 36, 'group_counter': 2375, 'group_order': 1344, 'label': '8E1', 'order': 8, 'powers': [10, 37, 37], 'representative': 511, 'size': 84}
id: 115778049
{'aut_label': '8E1', 'centralizer': '84.j1.a1', 'counter': 37, 'group_counter': 2375, 'group_order': 1344, 'label': '8E-1', 'order': 8, 'powers': [9, 36, 36], 'representative': 843, 'size': 84}
id: 115778050
{'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 2375, 'group_order': 1344, 'label': '12A1', 'order': 12, 'powers': [18, 9, 39], 'representative': 116, 'size': 2}
id: 115778051
{'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 2375, 'group_order': 1344, 'label': '12A-1', 'order': 12, 'powers': [18, 10, 38], 'representative': 1236, 'size': 2}
id: 115778053
{'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 2375, 'group_order': 1344, 'label': '12B1', 'order': 12, 'powers': [18, 11, 41], 'representative': 112, 'size': 2}
id: 115778054
{'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 41, 'group_counter': 2375, 'group_order': 1344, 'label': '12B-1', 'order': 12, 'powers': [18, 12, 40], 'representative': 1232, 'size': 2}
id: 115778055
{'aut_label': '12C1', 'centralizer': '28.e1.a1', 'counter': 42, 'group_counter': 2375, 'group_order': 1344, 'label': '12C1', 'order': 12, 'powers': [18, 15, 43], 'representative': 17, 'size': 28}
id: 115778056
{'aut_label': '12C1', 'centralizer': '28.e1.a1', 'counter': 43, 'group_counter': 2375, 'group_order': 1344, 'label': '12C5', 'order': 12, 'powers': [18, 15, 42], 'representative': 81, 'size': 28}
id: 115778057
{'aut_label': '14A1', 'centralizer': '2.f1.a1', 'counter': 44, 'group_counter': 2375, 'group_order': 1344, 'label': '14A1', 'order': 14, 'powers': [23, 45, 3], 'representative': 388, 'size': 2}
id: 115778058
{'aut_label': '14A1', 'centralizer': '2.f1.a1', 'counter': 45, 'group_counter': 2375, 'group_order': 1344, 'label': '14A3', 'order': 14, 'powers': [25, 46, 3], 'representative': 1156, 'size': 2}
id: 115778059
{'aut_label': '14A1', 'centralizer': '2.f1.a1', 'counter': 46, 'group_counter': 2375, 'group_order': 1344, 'label': '14A5', 'order': 14, 'powers': [24, 44, 3], 'representative': 580, 'size': 2}
id: 115778060
{'aut_label': '14B1', 'centralizer': '2.f1.a1', 'counter': 47, 'group_counter': 2375, 'group_order': 1344, 'label': '14B1', 'order': 14, 'powers': [25, 48, 4], 'representative': 484, 'size': 2}
id: 115778061
{'aut_label': '14B1', 'centralizer': '2.f1.a1', 'counter': 48, 'group_counter': 2375, 'group_order': 1344, 'label': '14B3', 'order': 14, 'powers': [24, 49, 4], 'representative': 100, 'size': 2}
id: 115778062
{'aut_label': '14B1', 'centralizer': '2.f1.a1', 'counter': 49, 'group_counter': 2375, 'group_order': 1344, 'label': '14B5', 'order': 14, 'powers': [23, 47, 4], 'representative': 1060, 'size': 2}
id: 115778064
{'aut_label': '14C1', 'centralizer': '2.f1.a1', 'counter': 50, 'group_counter': 2375, 'group_order': 1344, 'label': '14C1', 'order': 14, 'powers': [25, 51, 2], 'representative': 480, 'size': 2}
id: 115778065
{'aut_label': '14C1', 'centralizer': '2.f1.a1', 'counter': 51, 'group_counter': 2375, 'group_order': 1344, 'label': '14C3', 'order': 14, 'powers': [24, 52, 2], 'representative': 96, 'size': 2}
id: 115778066
{'aut_label': '14C1', 'centralizer': '2.f1.a1', 'counter': 52, 'group_counter': 2375, 'group_order': 1344, 'label': '14C5', 'order': 14, 'powers': [23, 50, 2], 'representative': 1056, 'size': 2}
id: 115778067
{'aut_label': '21A1', 'centralizer': '4.g1.a1', 'counter': 53, 'group_counter': 2375, 'group_order': 1344, 'label': '21A1', 'order': 21, 'powers': [54, 25, 8], 'representative': 128, 'size': 4}
id: 115778068
{'aut_label': '21A1', 'centralizer': '4.g1.a1', 'counter': 54, 'group_counter': 2375, 'group_order': 1344, 'label': '21A2', 'order': 21, 'powers': [55, 23, 8], 'representative': 256, 'size': 4}
id: 115778069
{'aut_label': '21A1', 'centralizer': '4.g1.a1', 'counter': 55, 'group_counter': 2375, 'group_order': 1344, 'label': '21A4', 'order': 21, 'powers': [53, 24, 8], 'representative': 512, 'size': 4}
id: 115778070
{'aut_label': '24A1', 'centralizer': '4.g1.a1', 'counter': 56, 'group_counter': 2375, 'group_order': 1344, 'label': '24A1', 'order': 24, 'powers': [40, 26, 58], 'representative': 56, 'size': 4}
id: 115778071
{'aut_label': '24A1', 'centralizer': '4.g1.a1', 'counter': 57, 'group_counter': 2375, 'group_order': 1344, 'label': '24A-1', 'order': 24, 'powers': [41, 27, 59], 'representative': 1288, 'size': 4}
id: 115778072
{'aut_label': '24A1', 'centralizer': '4.g1.a1', 'counter': 58, 'group_counter': 2375, 'group_order': 1344, 'label': '24A7', 'order': 24, 'powers': [41, 27, 56], 'representative': 392, 'size': 4}
id: 115778073
{'aut_label': '24A1', 'centralizer': '4.g1.a1', 'counter': 59, 'group_counter': 2375, 'group_order': 1344, 'label': '24A-7', 'order': 24, 'powers': [40, 26, 57], 'representative': 952, 'size': 4}
id: 115778075
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 60, 'group_counter': 2375, 'group_order': 1344, 'label': '24B1', 'order': 24, 'powers': [38, 32, 61], 'representative': 9, 'size': 28}
id: 115778076
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 61, 'group_counter': 2375, 'group_order': 1344, 'label': '24B-1', 'order': 24, 'powers': [39, 33, 60], 'representative': 57, 'size': 28}
id: 115778077
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 62, 'group_counter': 2375, 'group_order': 1344, 'label': '24B5', 'order': 24, 'powers': [38, 35, 63], 'representative': 41, 'size': 28}
id: 115778078
{'aut_label': '24B1', 'centralizer': '28.i1.a1', 'counter': 63, 'group_counter': 2375, 'group_order': 1344, 'label': '24B-5', 'order': 24, 'powers': [39, 34, 62], 'representative': 89, 'size': 28}
id: 115778079
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 64, 'group_counter': 2375, 'group_order': 1344, 'label': '28A1', 'order': 28, 'powers': [50, 66, 9], 'representative': 244, 'size': 2}
id: 115778080
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 65, 'group_counter': 2375, 'group_order': 1344, 'label': '28A-1', 'order': 28, 'powers': [50, 67, 10], 'representative': 1108, 'size': 2}
id: 115778081
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 66, 'group_counter': 2375, 'group_order': 1344, 'label': '28A3', 'order': 28, 'powers': [51, 68, 10], 'representative': 724, 'size': 2}
id: 115778082
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 67, 'group_counter': 2375, 'group_order': 1344, 'label': '28A-3', 'order': 28, 'powers': [51, 69, 9], 'representative': 628, 'size': 2}
id: 115778083
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 68, 'group_counter': 2375, 'group_order': 1344, 'label': '28A5', 'order': 28, 'powers': [52, 65, 9], 'representative': 1204, 'size': 2}
id: 115778084
{'aut_label': '28A1', 'centralizer': '2.f1.a1', 'counter': 69, 'group_counter': 2375, 'group_order': 1344, 'label': '28A-5', 'order': 28, 'powers': [52, 64, 10], 'representative': 148, 'size': 2}
id: 115778086
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 70, 'group_counter': 2375, 'group_order': 1344, 'label': '28B1', 'order': 28, 'powers': [51, 72, 11], 'representative': 48, 'size': 2}
id: 115778087
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 71, 'group_counter': 2375, 'group_order': 1344, 'label': '28B-1', 'order': 28, 'powers': [51, 73, 12], 'representative': 1296, 'size': 2}
id: 115778088
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 72, 'group_counter': 2375, 'group_order': 1344, 'label': '28B3', 'order': 28, 'powers': [52, 74, 12], 'representative': 144, 'size': 2}
id: 115778089
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 73, 'group_counter': 2375, 'group_order': 1344, 'label': '28B-3', 'order': 28, 'powers': [52, 75, 11], 'representative': 1200, 'size': 2}
id: 115778090
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 74, 'group_counter': 2375, 'group_order': 1344, 'label': '28B5', 'order': 28, 'powers': [50, 71, 11], 'representative': 240, 'size': 2}
id: 115778091
{'aut_label': '28B1', 'centralizer': '2.f1.a1', 'counter': 75, 'group_counter': 2375, 'group_order': 1344, 'label': '28B-5', 'order': 28, 'powers': [50, 70, 12], 'representative': 1104, 'size': 2}
id: 115778092
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 76, 'group_counter': 2375, 'group_order': 1344, 'label': '28C1', 'order': 28, 'powers': [44, 77, 13], 'representative': 194, 'size': 12}
id: 115778093
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 77, 'group_counter': 2375, 'group_order': 1344, 'label': '28C3', 'order': 28, 'powers': [45, 79, 13], 'representative': 770, 'size': 12}
id: 115778094
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 78, 'group_counter': 2375, 'group_order': 1344, 'label': '28C5', 'order': 28, 'powers': [46, 81, 13], 'representative': 66, 'size': 12}
id: 115778095
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 79, 'group_counter': 2375, 'group_order': 1344, 'label': '28C9', 'order': 28, 'powers': [46, 76, 13], 'representative': 386, 'size': 12}
id: 115778097
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 80, 'group_counter': 2375, 'group_order': 1344, 'label': '28C11', 'order': 28, 'powers': [45, 78, 13], 'representative': 130, 'size': 12}
id: 115778098
{'aut_label': '28C1', 'centralizer': '12.h1.a1', 'counter': 81, 'group_counter': 2375, 'group_order': 1344, 'label': '28C13', 'order': 28, 'powers': [44, 80, 13], 'representative': 34, 'size': 12}
id: 115778099
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 82, 'group_counter': 2375, 'group_order': 1344, 'label': '28D1', 'order': 28, 'powers': [47, 83, 14], 'representative': 18, 'size': 12}
id: 115778100
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 83, 'group_counter': 2375, 'group_order': 1344, 'label': '28D3', 'order': 28, 'powers': [48, 85, 14], 'representative': 402, 'size': 12}
id: 115778101
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 84, 'group_counter': 2375, 'group_order': 1344, 'label': '28D5', 'order': 28, 'powers': [49, 87, 14], 'representative': 82, 'size': 12}
id: 115778102
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 85, 'group_counter': 2375, 'group_order': 1344, 'label': '28D9', 'order': 28, 'powers': [49, 82, 14], 'representative': 146, 'size': 12}
id: 115778103
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 86, 'group_counter': 2375, 'group_order': 1344, 'label': '28D11', 'order': 28, 'powers': [48, 84, 14], 'representative': 50, 'size': 12}
id: 115778104
{'aut_label': '28D1', 'centralizer': '12.h1.a1', 'counter': 87, 'group_counter': 2375, 'group_order': 1344, 'label': '28D13', 'order': 28, 'powers': [47, 86, 14], 'representative': 210, 'size': 12}
id: 115778105
{'aut_label': '42A1', 'centralizer': '4.g1.a1', 'counter': 88, 'group_counter': 2375, 'group_order': 1344, 'label': '42A1', 'order': 42, 'powers': [53, 45, 19], 'representative': 68, 'size': 4}
id: 115778106
{'aut_label': '42A1', 'centralizer': '4.g1.a1', 'counter': 89, 'group_counter': 2375, 'group_order': 1344, 'label': '42A5', 'order': 42, 'powers': [54, 44, 19], 'representative': 132, 'size': 4}
id: 115778108
{'aut_label': '42A1', 'centralizer': '4.g1.a1', 'counter': 90, 'group_counter': 2375, 'group_order': 1344, 'label': '42A11', 'order': 42, 'powers': [55, 46, 19], 'representative': 260, 'size': 4}
id: 115778109
{'aut_label': '42B1', 'centralizer': '4.g1.a1', 'counter': 91, 'group_counter': 2375, 'group_order': 1344, 'label': '42B1', 'order': 42, 'powers': [55, 48, 20], 'representative': 36, 'size': 4}
id: 115778110
{'aut_label': '42B1', 'centralizer': '4.g1.a1', 'counter': 92, 'group_counter': 2375, 'group_order': 1344, 'label': '42B5', 'order': 42, 'powers': [53, 47, 20], 'representative': 164, 'size': 4}
id: 115778111
{'aut_label': '42B1', 'centralizer': '4.g1.a1', 'counter': 93, 'group_counter': 2375, 'group_order': 1344, 'label': '42B11', 'order': 42, 'powers': [54, 49, 20], 'representative': 804, 'size': 4}
id: 115778112
{'aut_label': '42C1', 'centralizer': '4.g1.a1', 'counter': 94, 'group_counter': 2375, 'group_order': 1344, 'label': '42C1', 'order': 42, 'powers': [55, 51, 18], 'representative': 32, 'size': 4}
id: 115778113
{'aut_label': '42C1', 'centralizer': '4.g1.a1', 'counter': 95, 'group_counter': 2375, 'group_order': 1344, 'label': '42C5', 'order': 42, 'powers': [53, 50, 18], 'representative': 160, 'size': 4}
id: 115778114
{'aut_label': '42C1', 'centralizer': '4.g1.a1', 'counter': 96, 'group_counter': 2375, 'group_order': 1344, 'label': '42C11', 'order': 42, 'powers': [54, 52, 18], 'representative': 352, 'size': 4}
id: 115778115
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 97, 'group_counter': 2375, 'group_order': 1344, 'label': '56A1', 'order': 56, 'powers': [70, 99, 26], 'representative': 24, 'size': 4}
id: 115778116
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 98, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-1', 'order': 56, 'powers': [71, 100, 27], 'representative': 1320, 'size': 4}
id: 115778117
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 99, 'group_counter': 2375, 'group_order': 1344, 'label': '56A3', 'order': 56, 'powers': [72, 103, 27], 'representative': 72, 'size': 4}
id: 115777964
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 100, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-3', 'order': 56, 'powers': [73, 104, 26], 'representative': 1272, 'size': 4}
id: 115777965
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 101, 'group_counter': 2375, 'group_order': 1344, 'label': '56A5', 'order': 56, 'powers': [74, 108, 26], 'representative': 120, 'size': 4}
id: 115777966
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 102, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-5', 'order': 56, 'powers': [75, 107, 27], 'representative': 1224, 'size': 4}
id: 115777967
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 103, 'group_counter': 2375, 'group_order': 1344, 'label': '56A9', 'order': 56, 'powers': [74, 98, 26], 'representative': 216, 'size': 4}
id: 115777968
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 104, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-9', 'order': 56, 'powers': [75, 97, 27], 'representative': 1128, 'size': 4}
id: 115777969
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 105, 'group_counter': 2375, 'group_order': 1344, 'label': '56A11', 'order': 56, 'powers': [72, 101, 27], 'representative': 264, 'size': 4}
id: 115777970
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 106, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-11', 'order': 56, 'powers': [73, 102, 26], 'representative': 1080, 'size': 4}
id: 115777971
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 107, 'group_counter': 2375, 'group_order': 1344, 'label': '56A13', 'order': 56, 'powers': [70, 105, 26], 'representative': 312, 'size': 4}
id: 115777972
{'aut_label': '56A1', 'centralizer': '4.g1.a1', 'counter': 108, 'group_counter': 2375, 'group_order': 1344, 'label': '56A-13', 'order': 56, 'powers': [71, 106, 27], 'representative': 1032, 'size': 4}
id: 115777973
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 109, 'group_counter': 2375, 'group_order': 1344, 'label': '56B1', 'order': 56, 'powers': [64, 111, 28], 'representative': 10, 'size': 12}
id: 115777975
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 110, 'group_counter': 2375, 'group_order': 1344, 'label': '56B-1', 'order': 56, 'powers': [65, 112, 29], 'representative': 222, 'size': 12}
id: 115777976
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 111, 'group_counter': 2375, 'group_order': 1344, 'label': '56B3', 'order': 56, 'powers': [66, 113, 29], 'representative': 30, 'size': 12}
id: 115777977
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 112, 'group_counter': 2375, 'group_order': 1344, 'label': '56B-3', 'order': 56, 'powers': [67, 114, 28], 'representative': 202, 'size': 12}
id: 115777978
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 113, 'group_counter': 2375, 'group_order': 1344, 'label': '56B5', 'order': 56, 'powers': [68, 110, 28], 'representative': 74, 'size': 12}
id: 115777979
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 114, 'group_counter': 2375, 'group_order': 1344, 'label': '56B-5', 'order': 56, 'powers': [69, 109, 29], 'representative': 414, 'size': 12}
id: 115777980
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 115, 'group_counter': 2375, 'group_order': 1344, 'label': '56C1', 'order': 56, 'powers': [66, 117, 30], 'representative': 26, 'size': 12}
id: 115777981
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 116, 'group_counter': 2375, 'group_order': 1344, 'label': '56C-1', 'order': 56, 'powers': [67, 118, 31], 'representative': 206, 'size': 12}
id: 115777982
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 117, 'group_counter': 2375, 'group_order': 1344, 'label': '56C3', 'order': 56, 'powers': [68, 119, 31], 'representative': 78, 'size': 12}
id: 115777983
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 118, 'group_counter': 2375, 'group_order': 1344, 'label': '56C-3', 'order': 56, 'powers': [69, 120, 30], 'representative': 410, 'size': 12}
id: 115777984
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 119, 'group_counter': 2375, 'group_order': 1344, 'label': '56C5', 'order': 56, 'powers': [65, 116, 30], 'representative': 218, 'size': 12}
id: 115777986
{'aut_label': '56B1', 'centralizer': '12.i1.a1', 'counter': 120, 'group_counter': 2375, 'group_order': 1344, 'label': '56C-5', 'order': 56, 'powers': [64, 115, 31], 'representative': 14, 'size': 12}
id: 115777987
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 121, 'group_counter': 2375, 'group_order': 1344, 'label': '84A1', 'order': 84, 'powers': [94, 67, 38], 'representative': 20, 'size': 4}
id: 115777988
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 122, 'group_counter': 2375, 'group_order': 1344, 'label': '84A-1', 'order': 84, 'powers': [94, 66, 39], 'representative': 692, 'size': 4}
id: 115777989
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 123, 'group_counter': 2375, 'group_order': 1344, 'label': '84A5', 'order': 84, 'powers': [95, 64, 38], 'representative': 84, 'size': 4}
id: 115777990
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 124, 'group_counter': 2375, 'group_order': 1344, 'label': '84A-5', 'order': 84, 'powers': [95, 65, 39], 'representative': 308, 'size': 4}
id: 115777991
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 125, 'group_counter': 2375, 'group_order': 1344, 'label': '84A11', 'order': 84, 'powers': [96, 69, 39], 'representative': 180, 'size': 4}
id: 115777992
{'aut_label': '84A1', 'centralizer': '4.g1.a1', 'counter': 126, 'group_counter': 2375, 'group_order': 1344, 'label': '84A-11', 'order': 84, 'powers': [96, 68, 38], 'representative': 404, 'size': 4}
id: 115777993
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 127, 'group_counter': 2375, 'group_order': 1344, 'label': '84B1', 'order': 84, 'powers': [94, 70, 40], 'representative': 16, 'size': 4}
id: 115777994
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 128, 'group_counter': 2375, 'group_order': 1344, 'label': '84B-1', 'order': 84, 'powers': [94, 71, 41], 'representative': 1328, 'size': 4}
id: 115777995
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 129, 'group_counter': 2375, 'group_order': 1344, 'label': '84B5', 'order': 84, 'powers': [95, 74, 40], 'representative': 80, 'size': 4}
id: 115777997
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 130, 'group_counter': 2375, 'group_order': 1344, 'label': '84B-5', 'order': 84, 'powers': [95, 75, 41], 'representative': 1264, 'size': 4}
id: 115777998
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 131, 'group_counter': 2375, 'group_order': 1344, 'label': '84B11', 'order': 84, 'powers': [96, 72, 41], 'representative': 176, 'size': 4}
id: 115777999
{'aut_label': '84B1', 'centralizer': '4.g1.a1', 'counter': 132, 'group_counter': 2375, 'group_order': 1344, 'label': '84B-11', 'order': 84, 'powers': [96, 73, 40], 'representative': 1168, 'size': 4}
id: 115778000
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 133, 'group_counter': 2375, 'group_order': 1344, 'label': '168A1', 'order': 168, 'powers': [127, 97, 56], 'representative': 8, 'size': 4}
id: 115778001
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 134, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-1', 'order': 168, 'powers': [128, 98, 57], 'representative': 1112, 'size': 4}
id: 115778002
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 135, 'group_counter': 2375, 'group_order': 1344, 'label': '168A5', 'order': 168, 'powers': [129, 101, 56], 'representative': 40, 'size': 4}
id: 115778003
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 136, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-5', 'order': 168, 'powers': [130, 102, 57], 'representative': 184, 'size': 4}
id: 115778004
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 137, 'group_counter': 2375, 'group_order': 1344, 'label': '168A11', 'order': 168, 'powers': [131, 105, 58], 'representative': 88, 'size': 4}
id: 115778005
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 138, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-11', 'order': 168, 'powers': [132, 106, 59], 'representative': 136, 'size': 4}
id: 115778006
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 139, 'group_counter': 2375, 'group_order': 1344, 'label': '168A13', 'order': 168, 'powers': [127, 107, 59], 'representative': 12, 'size': 4}
id: 115778008
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 140, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-13', 'order': 168, 'powers': [128, 108, 58], 'representative': 1016, 'size': 4}
id: 115778009
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 141, 'group_counter': 2375, 'group_order': 1344, 'label': '168A19', 'order': 168, 'powers': [130, 104, 57], 'representative': 152, 'size': 4}
id: 115778010
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 142, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-19', 'order': 168, 'powers': [129, 103, 56], 'representative': 968, 'size': 4}
id: 115778011
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 143, 'group_counter': 2375, 'group_order': 1344, 'label': '168A25', 'order': 168, 'powers': [132, 100, 56], 'representative': 200, 'size': 4}
id: 115778012
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 144, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-25', 'order': 168, 'powers': [131, 99, 57], 'representative': 92, 'size': 4}
id: 115778013
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 145, 'group_counter': 2375, 'group_order': 1344, 'label': '168A31', 'order': 168, 'powers': [131, 99, 58], 'representative': 248, 'size': 4}
id: 115778014
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 146, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-31', 'order': 168, 'powers': [132, 100, 59], 'representative': 588, 'size': 4}
id: 115778015
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 147, 'group_counter': 2375, 'group_order': 1344, 'label': '168A37', 'order': 168, 'powers': [129, 103, 59], 'representative': 44, 'size': 4}
id: 115778016
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 148, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-37', 'order': 168, 'powers': [130, 104, 58], 'representative': 824, 'size': 4}
id: 115778017
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 149, 'group_counter': 2375, 'group_order': 1344, 'label': '168A43', 'order': 168, 'powers': [128, 108, 57], 'representative': 344, 'size': 4}
id: 115778019
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 150, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-43', 'order': 168, 'powers': [127, 107, 56], 'representative': 776, 'size': 4}
id: 115778020
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 151, 'group_counter': 2375, 'group_order': 1344, 'label': '168A55', 'order': 168, 'powers': [128, 98, 58], 'representative': 440, 'size': 4}
id: 115778021
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 152, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-55', 'order': 168, 'powers': [127, 97, 59], 'representative': 780, 'size': 4}
id: 115778022
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 153, 'group_counter': 2375, 'group_order': 1344, 'label': '168A61', 'order': 168, 'powers': [129, 101, 59], 'representative': 712, 'size': 4}
id: 115778023
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 154, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-61', 'order': 168, 'powers': [130, 102, 58], 'representative': 156, 'size': 4}
id: 115778024
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 155, 'group_counter': 2375, 'group_order': 1344, 'label': '168A67', 'order': 168, 'powers': [131, 105, 57], 'representative': 536, 'size': 4}
id: 115778025
{'aut_label': '168A1', 'centralizer': '4.g1.a1', 'counter': 156, 'group_counter': 2375, 'group_order': 1344, 'label': '168A-67', 'order': 168, 'powers': [132, 106, 56], 'representative': 584, 'size': 4}

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

gps_qchar • Show schema

id: 5707102
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 5707113
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 5707124
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1c', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5707135
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1d', '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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5707143
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5707144
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5707145
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5707146
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -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: 5707147
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 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, 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, 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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707103
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, 2, 2, -2, -2, 2, 2, 2, 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, 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, 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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707104
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1k', '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, 2, 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, 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, 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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707105
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.1l', '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, 2, 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, 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, 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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707106
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 0, 0, 2, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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], 'schur_index': 1}
id: 5707107
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707108
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707109
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, -1, 2, 2, 2, 2, 0, 0, -2, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 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], 'schur_index': 1}
id: 5707110
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 0, 0, -1, 2, 2, 2, 2, 0, 0, -2, 0, 0, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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], 'schur_index': 1}
id: 5707111
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, 2, 0, 0, 2, 0, 0, -1, -1, -1, -1, -1, 2, 2, 2, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 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], 'schur_index': 1}
id: 5707112
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2g', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707114
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2h', 'multiplicity': 2, 'nt': [8, 7], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707115
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, 0, 0, -4, 4, -4, -4, -4, 4, -4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707116
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2j', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, 0, 0, -2, -4, -4, -4, -4, 0, 0, 4, 0, 0, -2, -2, -2, 2, 2, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707117
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2k', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 0, 0, -2, -4, -4, -4, -4, 0, 0, -4, 0, 0, -2, -2, -2, -2, -2, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707130
{'cdim': 4, 'counter': 35, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -2, -4, -4, 4, 4, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, -4, 4, -4, -4, -4, 4, -4, 4, -4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707131
{'cdim': 4, 'counter': 36, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4b', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, -2, 4, 4, -4, -4, 0, 0, 0, 0, 0, 2, 2, -2, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, -4, 4, -4, -4, -4, 4, -4, 4, -4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5707118
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2l', 'multiplicity': 3, 'nt': [7, 2], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 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], 'schur_index': 1}
id: 5707119
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2m', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, -6, -6, 0, 0, 0, 6, 6, 6, 0, 0, -1, -1, -1, -6, -6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, 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], 'schur_index': 1}
id: 5707120
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2n', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, -6, -6, 0, 0, 0, 6, 6, 6, 0, 0, -1, -1, -1, 6, 6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 6, 6, 6, 6, 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], 'schur_index': 1}
id: 5707121
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2o', 'multiplicity': 3, 'nt': [14, 3], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 6, 6, 6, 0, 0, -1, -1, -1, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 6, 6, 6, 6, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, 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], 'schur_index': 1}
id: 5707122
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2p', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
id: 5707132
{'cdim': 4, 'counter': 37, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4c', 'multiplicity': 2, 'nt': [24, 104], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, 8, -8, 8, -8, 8, -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, 4, -4, 4, -4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707123
{'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2q', 'multiplicity': 6, 'nt': [28, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, 12, -12, -12, -12, -12, -12, 12, 0, 0, 0, 12, 12, 12, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -12, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707125
{'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2r', 'multiplicity': 6, 'nt': [28, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, 12, -12, -12, -12, -12, 12, -12, 0, 0, 0, 12, 12, 12, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -12, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707126
{'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2s', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 12, -12, -12, 12, 12, 0, 0, 0, 0, 0, -12, -12, 12, 0, 0, -2, -2, -2, 0, 0, -12, -12, 12, 12, 0, 0, 0, 0, 0, 0, 12, 12, -12, -12, 0, 0, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707127
{'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2t', 'multiplicity': 6, 'nt': [28, 10], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 0, 0, 0, 12, -12, -12, 12, 12, 0, 0, 0, 0, 0, -12, -12, 12, 0, 0, -2, -2, -2, 0, 0, 12, 12, -12, -12, 0, 0, 0, 0, 0, 0, 12, 12, -12, -12, 0, 0, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, -2, 2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, -2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707133
{'cdim': 4, 'counter': 38, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4d', 'multiplicity': 3, 'nt': [21, 8], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, -6, 12, 12, 12, 12, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, -2, -2, -2, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, -6, -6, -6, -6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 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], 'schur_index': 1}
id: 5707134
{'cdim': 4, 'counter': 39, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4e', 'multiplicity': 3, 'nt': [42, 36], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 0, 0, 0, -6, 12, 12, 12, 12, 0, 0, 0, 0, 0, -6, -6, -6, 0, 0, -2, -2, -2, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 6, 6, 6, 6, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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], 'schur_index': 1}
id: 5707128
{'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2u', 'multiplicity': 8, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, 0, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -16, 16, 16, -16, -16, -16, -16, -16, -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, -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], 'schur_index': 1}
id: 5707129
{'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.2v', 'multiplicity': 12, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, 24, 24, 24, -24, -24, 0, 0, 0, 0, 0, -24, -24, 24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, -24, 24, 24, 0, 0, 4, -4, 4, 4, 4, -4, 4, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707136
{'cdim': 4, 'counter': 40, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4f', 'multiplicity': 6, 'nt': [56, 0], 'qdim': 24, 'qvalues': [24, -24, -24, 24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -24, -24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -4, 4, -4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707137
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4g', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, -12, -24, -24, 24, 24, 0, 0, 0, 0, 0, 12, 12, -12, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 12, 12, 0, 0, 4, -4, 4, 4, 4, -4, 4, -4, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, -4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707138
{'cdim': 4, 'counter': 42, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4h', 'multiplicity': 6, 'nt': [84, 0], 'qdim': 24, 'qvalues': [24, 24, 24, 24, 0, 0, 0, -12, -24, -24, -24, -24, 0, 0, 0, 0, 0, -12, -12, -12, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707139
{'cdim': 4, 'counter': 43, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4i', 'multiplicity': 6, 'nt': [112, 0], 'qdim': 24, 'qvalues': [24, 24, -24, -24, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 24, -24, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, -4, 4, 4, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707140
{'cdim': 4, 'counter': 44, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4j', 'multiplicity': 6, 'nt': [168, 0], 'qdim': 24, 'qvalues': [24, -24, 24, -24, 0, 0, 0, -12, 24, 24, -24, -24, 0, 0, 0, 0, 0, 12, 12, -12, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -12, -12, 0, 0, 4, -4, 4, 4, 4, -4, 4, -4, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5707141
{'cdim': 4, 'counter': 45, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4k', 'multiplicity': 12, 'nt': [168, 0], 'qdim': 48, 'qvalues': [48, -48, -48, 48, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24, 24, 24, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, -8, 8, -8, 8, -8, 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, -4, 4, -4, 4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5707142
{'cdim': 4, 'counter': 46, 'faithful': False, 'group': '1344.2375', 'group_order': 1344, 'image': None, 'label': '1344.2375.4l', 'multiplicity': 12, 'nt': [336, 0], 'qdim': 48, 'qvalues': [48, 48, -48, -48, 0, 0, 0, -24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, -24, 24, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, -8, 8, 8, 8, 8, 8, 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, 4, -4, -4, -4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 11438618
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id: 11438686
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id: 11438697
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id: 11438708
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 672, 'label': '1344.2375.1d', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 11438719
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1344, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 672, 'label': '1344.2375.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 11438730
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id: 11438741
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id: 11438752
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id: 11438763
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id: 11438619
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id: 11438630
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id: 11438641
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id: 11438652
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id: 11438663
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id: 11438674
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id: 11438682
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id: 11438683
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id: 11438684
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id: 11438685
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id: 11438687
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id: 11438688
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id: 11438689
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id: 11438690
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id: 11438691
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id: 11438692
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id: 11438693
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id: 11438694
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id: 11438695
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id: 11438696
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id: 11438698
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id: 11438699
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id: 11438700
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id: 11438701
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id: 11438702
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id: 11438703
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id: 11438704
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id: 11438705
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id: 11438706
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id: 11438707
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id: 11438709
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id: 11438710
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id: 11438711
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id: 11438712
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id: 11438713
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id: 11438714
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id: 11438715
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id: 11438716
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id: 11438717
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id: 11438718
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id: 11438720
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id: 11438721
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id: 11438722
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id: 11438723
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id: 11438724
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id: 11438725
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id: 11438726
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id: 11438727
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id: 11438728
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id: 11438729
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id: 11438731
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id: 11438732
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id: 11438733
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id: 11438734
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id: 11438735
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id: 11438736
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id: 11438737
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id: 11438738
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id: 11438739
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id: 11438740
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id: 11438742
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id: 11438743
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id: 11438744
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id: 11438745
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id: 11438746
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id: 11438747
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id: 11438748
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id: 11438749
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id: 11438750
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id: 11438751
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id: 11438753
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id: 11438754
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id: 11438764
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id: 11438765
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id: 11438766
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id: 11438755
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id: 11438756
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id: 11438757
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id: 11438758
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id: 11438759
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id: 11438760
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id: 11438761
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id: 11438762
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id: 11438767
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id: 11438768
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id: 11438769
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id: 11438770
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id: 11438771
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id: 11438772
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id: 11438773
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id: 11438620
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id: 11438621
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id: 11438622
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id: 11438623
{'center': '56.a1.a1', 'center_index': 56, 'center_order': 24, 'counter': 103, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 6, 0, 5, 0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '224.101', 'image_order': 224, 'indicator': 0, 'kernel': '224.b1.a1', 'kernel_order': 6, 'label': '1344.2375.4f1', 'nt': [56, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 7]], [[4, 7]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 7]], [[4, 7]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 4], [2, -4]], [[2, 2], [2, -2]], [[-2, 6], [-2, -6]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5], [2, 9]], [[-2, 3], [-2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 5], [-2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[2, 3], [2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 5], [2, 9]], [[-2, 3], [-2, 11]], [[-2, 5], [-2, 9]], [[2, 3], [2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, -4]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 6], [-2, -6]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 4], [2, -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]], [[2, 5], [2, 9]], [[-2, 3], [-2, 11]], [[2, 3], [2, 11]], [[-2, 5], [-2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 5], [-2, 9]], [[2, 3], [2, 11]], [[2, 5], [2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[-2, 3], [-2, 11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 11438624
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id: 11438625
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id: 11438626
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id: 11438627
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id: 11438628
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id: 11438629
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id: 11438631
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id: 11438632
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id: 11438633
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id: 11438634
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id: 11438635
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id: 11438636
{'center': '84.a1.a1', 'center_index': 84, 'center_order': 16, 'counter': 115, 'cyclotomic_n': 28, 'dim': 4, 'faithful': False, 'field': [1, 0, 6, 0, 5, 0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '336.147', 'image_order': 336, 'indicator': 0, 'kernel': '336.a1.a1', 'kernel_order': 4, 'label': '1344.2375.4h1', 'nt': [84, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[-2, 6], [-2, -6]], [[-4, 7]], [[4, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 6], [-2, -6]], [[-2, 6], [-2, -6]], [[-2, 2], [-2, -2]], [[2, 4], [2, -4]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[-2, 6], [-2, -6]], [[2, 4], [2, -4]], [[-2, 2], [-2, -2]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[-2, 7]], [[2, 7]], [[-2, 7]], [[2, 7]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[2, 6], [2, -6]], [[-2, 4], [-2, -4]], [[2, 6], [2, -6]], [[2, 2], [2, -2]], [[-2, 4], [-2, -4]], [[2, 2], [2, -2]], [[-2, 4], [-2, -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]], [[-1, 4], [-1, -4]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 6], [1, -6]], [[1, 6], [1, -6]], [[1, 2], [1, -2]], [[-1, 4], [-1, -4]], [[1, 6], [1, -6]], [[-1, 4], [-1, -4]], [[-2, 5], [-2, 9]], [[2, 5], [2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[2, 3], [2, 11]], [[2, 5], [2, 9]], [[-2, 3], [2, 5], [-2, 7], [2, 9], [-2, 11]], [[-2, 3], [-2, 11]], [[2, 3], [2, 11]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 5], [-2, 9]], [[2, 3], [-2, 5], [2, 7], [-2, 9], [2, 11]], [[-2, 3], [-2, 11]], [[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, 2], [-1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 6], [-1, -6]], [[-1, 2], [-1, -2]], [[1, 4], [1, -4]], [[-1, 2], [-1, -2]], [[-1, 6], [-1, -6]], [[1, 4], [1, -4]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 3], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 5], [-1, 9]], [[-1, 5], [-1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 3], [-1, 11]], [[-1, 3], [-1, 11]], [[1, 3], [1, 11]], [[1, 3], [1, 11]], [[1, 5], [1, 9]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [-1, 11]], [[1, 5], [1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[-1, 3], [-1, 11]], [[-1, 5], [-1, 9]], [[1, 3], [1, 11]], [[-1, 3], [1, 5], [-1, 7], [1, 9], [-1, 11]], [[1, 5], [1, 9]], [[1, 3], [-1, 5], [1, 7], [-1, 9], [1, 11]], [[1, 5], [1, 9]]]}
id: 11438637
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id: 11438638
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id: 11438639
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id: 11438640
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id: 11438642
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id: 11438643
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id: 11438644
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id: 11438645
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id: 11438646
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id: 11438647
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id: 11438648
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id: 11438649
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id: 11438650
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id: 11438651
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id: 11438653
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id: 11438654
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id: 11438655
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id: 11438656
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id: 11438666
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id: 11438667
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id: 11438668
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id: 11438657
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id: 11438658
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id: 11438659
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id: 11438660
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id: 11438661
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id: 11438662
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id: 11438664
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id: 11438665
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id: 11438669
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id: 11438679
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id: 11438680
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id: 11438681
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id: 11438670
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id: 11438671
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id: 11438672
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id: 11438673
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id: 11438675
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id: 11438676
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id: 11438677
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 152, 'cyclotomic_n': 168, 'dim': 4, 'faithful': False, 'field': [2017, -780, -1860, 1296, 451, -276, -46, -24, 64, -12, 10, 0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '672.410', 'image_order': 672, 'indicator': 0, 'kernel': '672.c1.a1', 'kernel_order': 2, 'label': '1344.2375.4l8', 'nt': [336, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 42]], [[-4, 42]], [[-4, 42]], [[4, 42]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 36], [-2, -36]], [[-2, 12], [-2, -12]], [[2, 24], [2, -24]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 42]], [[-2, 42]], [[-2, 42]], [[2, 42]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 24], [-2, -24]], [[-2, 36], [-2, -36]], [[-2, 12], [-2, -12]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-1, 24], [-1, -24]], [[1, 36], [1, -36]], [[1, 12], [1, -12]], [[4, 1], [4, 5], [-4, 13], [-4, 17], [2, 21], [4, 25], [-4, 33], [-4, 37], [4, 45]], [[-2, 7], [-2, 35]], [[-4, 1], [-4, 5], [4, 13], [4, 17], [-2, 21], [-4, 25], [4, 33], [4, 37], [-4, 45]], [[2, 7], [2, 35]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, 14], [2, 18], [-2, 22], [-2, 26], [2, 34], [2, 38], [-2, 46]], [[-2, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [-2, 42], [-2, 46]], [[-2, 10], [2, 18], [2, 38]], [[-2, 10], [2, 18], [2, 38]], [[-2, 2], [2, 14], [2, 18], [-2, 22], [-2, 26], [2, 34], [2, 38], [-2, 46]], [[2, 10], [-2, 18], [-2, 38]], [[2, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [2, 42], [2, 46]], [[2, 10], [-2, 18], [-2, 38]], [[2, 2], [-2, 14], [-2, 18], [2, 22], [2, 26], [-2, 34], [-2, 38], [2, 46]], [[2, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [2, 42], [2, 46]], [[2, 2], [-2, 14], [-2, 18], [2, 22], [2, 26], [-2, 34], [-2, 38], [2, 46]], [[-2, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [-2, 42], [-2, 46]], [[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, 12], [1, -12]], [[-1, 36], [-1, -36]], [[-1, 36], [-1, -36]], [[1, 24], [1, -24]], [[-1, 24], [-1, -24]], [[1, 36], [1, -36]], [[-1, 12], [-1, -12]], [[1, 24], [1, -24]], [[-1, 12], [-1, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [-1, 14], [-1, 18], [1, 22], [1, 26], [-1, 34], [-1, 38], [1, 46]], [[-1, 2], [1, 10], [1, 14], [-1, 22], [-1, 26], [1, 34], [-1, 42], [-1, 46]], [[1, 2], [-1, 10], [-1, 14], [1, 22], [1, 26], [-1, 34], [1, 42], [1, 46]], [[-1, 2], [1, 14], [1, 18], [-1, 22], [-1, 26], [1, 34], [1, 38], [-1, 46]], [[-1, 10], [1, 18], [1, 38]], [[1, 10], [-1, 18], [-1, 38]], [[1, 10], [-1, 18], [-1, 38]], [[1, 2], [-1, 14], [-1, 18], [1, 22], [1, 26], [-1, 34], [-1, 38], [1, 46]], [[-1, 2], [1, 10], [1, 14], [-1, 22], [-1, 26], [1, 34], [-1, 42], [-1, 46]], [[-1, 2], [1, 14], [1, 18], [-1, 22], [-1, 26], [1, 34], [1, 38], [-1, 46]], [[-1, 10], [1, 18], [1, 38]], [[1, 2], [-1, 10], [-1, 14], [1, 22], [1, 26], [-1, 34], [1, 42], [1, 46]], [[1, 1], [-1, 9], [-1, 13], [-2, 17], [1, 21], [2, 25], [-1, 29], [-1, 33], [1, 41], [2, 45]], [[-1, 3], [-1, 7], [1, 15], [-2, 23], [-1, 27], [1, 35], [1, 39], [-2, 47]], [[-1, 3], [2, 11], [2, 31], [-1, 39]], [[2, 3], [-2, 11], [-1, 15], [2, 23], [1, 27], [-2, 31], [-2, 35], [2, 47]], [[2, 3], [-2, 11], [-1, 15], [2, 23], [1, 27], [-2, 31], [-2, 35], [2, 47]], [[1, 3], [-2, 11], [-2, 31], [1, 39]], [[-2, 5], [-1, 9], [1, 33], [2, 37]], [[2, 5], [1, 9], [-1, 33], [-2, 37]], [[1, 3], [1, 7], [-1, 15], [2, 23], [1, 27], [-1, 35], [-1, 39], [2, 47]], [[-1, 3], [-1, 7], [1, 15], [-2, 23], [-1, 27], [1, 35], [1, 39], [-2, 47]], [[-1, 1], [1, 13], [-1, 29], [1, 41]], [[1, 3], [-2, 11], [-2, 31], [1, 39]], [[-2, 3], [2, 11], [1, 15], [-2, 23], [-1, 27], [2, 31], [2, 35], [-2, 47]], [[-1, 1], [1, 9], [1, 13], [2, 17], [-1, 21], [-2, 25], [1, 29], [1, 33], [-1, 41], [-2, 45]], [[2, 5], [1, 9], [-1, 33], [-2, 37]], [[1, 1], [-1, 13], [1, 29], [-1, 41]], [[-1, 1], [1, 9], [1, 13], [2, 17], [-1, 21], [-2, 25], [1, 29], [1, 33], [-1, 41], [-2, 45]], [[-2, 5], [-1, 9], [1, 33], [2, 37]], [[-2, 3], [2, 11], [1, 15], [-2, 23], [-1, 27], [2, 31], [2, 35], [-2, 47]], [[1, 3], [1, 7], [-1, 15], [2, 23], [1, 27], [-1, 35], [-1, 39], [2, 47]], [[-1, 3], [2, 11], [2, 31], [-1, 39]], [[1, 1], [-1, 13], [1, 29], [-1, 41]], [[1, 1], [-1, 9], [-1, 13], [-2, 17], [1, 21], [2, 25], [-1, 29], [-1, 33], [1, 41], [2, 45]], [[-1, 1], [1, 13], [-1, 29], [1, 41]]]}
id: 11438678
{'center': '168.a1.a1', 'center_index': 168, 'center_order': 8, 'counter': 153, 'cyclotomic_n': 168, 'dim': 4, 'faithful': False, 'field': [2017, -780, -1860, 1296, 451, -276, -46, -24, 64, -12, 10, 0, 1], 'group': '1344.2375', 'group_counter': 2375, 'group_order': 1344, 'image': None, 'image_isoclass': '672.410', 'image_order': 672, 'indicator': 0, 'kernel': '672.c1.a1', 'kernel_order': 2, 'label': '1344.2375.4l9', 'nt': [336, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 42]], [[4, 42]], [[4, 42]], [[-4, 42]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 24], [2, -24]], [[-2, 36], [-2, -36]], [[-2, 12], [-2, -12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 42]], [[2, 42]], [[2, 42]], [[-2, 42]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 12], [2, -12]], [[2, 24], [2, -24]], [[-2, 36], [-2, -36]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-2, 24], [-2, -24]], [[1, 12], [1, -12]], [[-1, 24], [-1, -24]], [[1, 36], [1, -36]], [[-2, 7], [-2, 35]], [[4, 1], [4, 5], [-4, 13], [-4, 17], [2, 21], [4, 25], [-4, 33], [-4, 37], [4, 45]], [[2, 7], [2, 35]], [[-4, 1], [-4, 5], [4, 13], [4, 17], [-2, 21], [-4, 25], [4, 33], [4, 37], [-4, 45]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 10], [2, 18], [2, 38]], [[-2, 2], [2, 14], [2, 18], [-2, 22], [-2, 26], [2, 34], [2, 38], [-2, 46]], [[2, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [2, 42], [2, 46]], [[2, 2], [-2, 10], [-2, 14], [2, 22], [2, 26], [-2, 34], [2, 42], [2, 46]], [[-2, 10], [2, 18], [2, 38]], [[-2, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [-2, 42], [-2, 46]], [[2, 2], [-2, 14], [-2, 18], [2, 22], [2, 26], [-2, 34], [-2, 38], [2, 46]], [[-2, 2], [2, 10], [2, 14], [-2, 22], [-2, 26], [2, 34], [-2, 42], [-2, 46]], [[2, 10], [-2, 18], [-2, 38]], [[2, 2], [-2, 14], [-2, 18], [2, 22], [2, 26], [-2, 34], [-2, 38], [2, 46]], [[2, 10], [-2, 18], [-2, 38]], [[-2, 2], [2, 14], [2, 18], [-2, 22], [-2, 26], [2, 34], [2, 38], [-2, 46]], [[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, 36], [1, -36]], [[1, 24], [1, -24]], [[1, 24], [1, -24]], [[-1, 12], [-1, -12]], [[1, 12], [1, -12]], [[-1, 24], [-1, -24]], [[-1, 36], [-1, -36]], [[-1, 12], [-1, -12]], [[-1, 36], [-1, -36]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 10], [-1, 18], [-1, 38]], [[-1, 2], [1, 14], [1, 18], [-1, 22], [-1, 26], [1, 34], [1, 38], [-1, 46]], [[1, 2], [-1, 14], [-1, 18], [1, 22], [1, 26], [-1, 34], [-1, 38], [1, 46]], [[-1, 10], [1, 18], [1, 38]], [[1, 2], [-1, 10], [-1, 14], [1, 22], [1, 26], [-1, 34], [1, 42], [1, 46]], [[-1, 2], [1, 10], [1, 14], [-1, 22], [-1, 26], [1, 34], [-1, 42], [-1, 46]], [[-1, 2], [1, 10], [1, 14], [-1, 22], [-1, 26], [1, 34], [-1, 42], [-1, 46]], [[1, 10], [-1, 18], [-1, 38]], [[-1, 2], [1, 14], [1, 18], [-1, 22], [-1, 26], [1, 34], [1, 38], [-1, 46]], [[-1, 10], [1, 18], [1, 38]], [[1, 2], [-1, 10], [-1, 14], [1, 22], [1, 26], [-1, 34], [1, 42], [1, 46]], [[1, 2], [-1, 14], [-1, 18], [1, 22], [1, 26], [-1, 34], [-1, 38], [1, 46]], [[-1, 3], [-1, 7], [1, 15], [-2, 23], [-1, 27], [1, 35], [1, 39], [-2, 47]], [[1, 1], [-1, 13], [1, 29], [-1, 41]], [[2, 5], [1, 9], [-1, 33], [-2, 37]], [[1, 1], [-1, 9], [-1, 13], [-2, 17], [1, 21], [2, 25], [-1, 29], [-1, 33], [1, 41], [2, 45]], [[1, 1], [-1, 9], [-1, 13], [-2, 17], [1, 21], [2, 25], [-1, 29], [-1, 33], [1, 41], [2, 45]], [[-2, 5], [-1, 9], [1, 33], [2, 37]], [[-2, 3], [2, 11], [1, 15], [-2, 23], [-1, 27], [2, 31], [2, 35], [-2, 47]], [[2, 3], [-2, 11], [-1, 15], [2, 23], [1, 27], [-2, 31], [-2, 35], [2, 47]], [[-1, 1], [1, 13], [-1, 29], [1, 41]], [[1, 1], [-1, 13], [1, 29], [-1, 41]], [[1, 3], [-2, 11], [-2, 31], [1, 39]], [[-2, 5], [-1, 9], [1, 33], [2, 37]], [[-1, 1], [1, 9], [1, 13], [2, 17], [-1, 21], [-2, 25], [1, 29], [1, 33], [-1, 41], [-2, 45]], [[1, 3], [1, 7], [-1, 15], [2, 23], [1, 27], [-1, 35], [-1, 39], [2, 47]], [[2, 3], [-2, 11], [-1, 15], [2, 23], [1, 27], [-2, 31], [-2, 35], [2, 47]], [[-1, 3], [2, 11], [2, 31], [-1, 39]], [[1, 3], [1, 7], [-1, 15], [2, 23], [1, 27], [-1, 35], [-1, 39], [2, 47]], [[-2, 3], [2, 11], [1, 15], [-2, 23], [-1, 27], [2, 31], [2, 35], [-2, 47]], [[-1, 1], [1, 9], [1, 13], [2, 17], [-1, 21], [-2, 25], [1, 29], [1, 33], [-1, 41], [-2, 45]], [[-1, 1], [1, 13], [-1, 29], [1, 41]], [[2, 5], [1, 9], [-1, 33], [-2, 37]], [[-1, 3], [2, 11], [2, 31], [-1, 39]], [[-1, 3], [-1, 7], [1, 15], [-2, 23], [-1, 27], [1, 35], [1, 39], [-2, 47]], [[1, 3], [-2, 11], [-2, 31], [1, 39]]]}

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: 72062586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.2375.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.2375', 'subgroup_hash': 2375, 'subgroup_order': 1344, 'subgroup_tex': 'D_{42}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062697
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 672, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.587', 'subgroup_hash': 587, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}:D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062757
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.159', 'subgroup_hash': 159, 'subgroup_order': 672, 'subgroup_tex': 'D_{14}:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062768
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 672, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.437', 'subgroup_hash': 437, 'subgroup_order': 672, 'subgroup_tex': 'C_{42}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062779
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 672, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.241', 'subgroup_hash': 241, 'subgroup_order': 672, 'subgroup_tex': 'D_{42}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062790
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 672, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.433', 'subgroup_hash': 433, 'subgroup_order': 672, 'subgroup_tex': 'D_{42}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062801
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 672, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.195', 'subgroup_hash': 195, 'subgroup_order': 672, 'subgroup_tex': 'C_{24}:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062812
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.101', 'subgroup_hash': 101, 'subgroup_order': 672, 'subgroup_tex': 'C_{12}.D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062823
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 224, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '1344.2375.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, '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': '448.240', 'subgroup_hash': 240, 'subgroup_order': 448, 'subgroup_tex': 'C_8:D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.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': '336.158', 'subgroup_hash': 158, 'subgroup_order': 336, 'subgroup_tex': 'C_6:D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062598
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 336, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.175', 'subgroup_hash': 175, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062609
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '336.42', 'subgroup_hash': 42, 'subgroup_order': 336, 'subgroup_tex': 'C_6.D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062620
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.195', 'subgroup_hash': 195, 'subgroup_order': 336, 'subgroup_tex': 'C_4\\times D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.44', 'subgroup_hash': 44, 'subgroup_order': 336, 'subgroup_tex': 'D_{42}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062642
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.81', 'subgroup_hash': 81, 'subgroup_order': 336, 'subgroup_tex': 'C_{12}:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 336, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.g1.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': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.109', 'subgroup_hash': 109, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times C_{168}', 'supersolvable': True, 'sylow': 0}
id: 72062664
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 336, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.79', 'subgroup_hash': 79, 'subgroup_order': 336, 'subgroup_tex': 'C_6:C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062675
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 336, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.63', 'subgroup_hash': 63, 'subgroup_order': 336, 'subgroup_tex': 'C_{14}:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062686
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.95', 'subgroup_hash': 95, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062698
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 336, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.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': '336.47', 'subgroup_hash': 47, 'subgroup_order': 336, 'subgroup_tex': 'C_6.D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062709
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '336.26', 'subgroup_hash': 26, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062720
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.l1.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': 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': '336.26', 'subgroup_hash': 26, 'subgroup_order': 336, 'subgroup_tex': 'C_{21}:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062731
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '336.25', 'subgroup_hash': 25, 'subgroup_order': 336, 'subgroup_tex': 'D_{21}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062742
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 168, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.4.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.m1.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': 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': '336.25', 'subgroup_hash': 25, 'subgroup_order': 336, 'subgroup_tex': 'D_{21}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062752
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 224, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.26', 'subgroup_hash': 26, 'subgroup_order': 224, 'subgroup_tex': 'D_{14}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062753
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '224.68', 'subgroup_hash': 68, 'subgroup_order': 224, 'subgroup_tex': 'C_4\\times D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062754
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, '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': '224.95', 'subgroup_hash': 95, 'subgroup_order': 224, 'subgroup_tex': 'C_8:D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062755
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, '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': '224.26', 'subgroup_hash': 26, 'subgroup_order': 224, 'subgroup_tex': 'D_{14}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062756
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 112, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, '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': '224.94', 'subgroup_hash': 94, 'subgroup_order': 224, 'subgroup_tex': 'C_8\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062758
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 112, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 6, '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': '224.46', 'subgroup_hash': 46, 'subgroup_order': 224, 'subgroup_tex': 'C_8:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062759
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 112, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, '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': '224.10', 'subgroup_hash': 10, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062760
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 96, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1344.2375.7.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.287', 'subgroup_hash': 287, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062761
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 168, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.54', 'subgroup_hash': 54, 'subgroup_order': 168, 'subgroup_tex': 'C_6\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062762
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 168, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '168.56', 'subgroup_hash': 56, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 168, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.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': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
id: 72062764
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.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': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062765
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 168, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.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': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062766
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 168, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.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': '168.27', 'subgroup_hash': 27, 'subgroup_order': 168, 'subgroup_tex': 'C_{14}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062767
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 168, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.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': '168.37', 'subgroup_hash': 37, 'subgroup_order': 168, 'subgroup_tex': 'C_{42}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062769
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062770
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 168, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.3', 'subgroup_hash': 3, 'subgroup_order': 168, 'subgroup_tex': 'C_3:C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062771
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062772
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '168.25', 'subgroup_hash': 25, 'subgroup_order': 168, 'subgroup_tex': 'C_{12}\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062773
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
id: 72062774
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '168.35', 'subgroup_hash': 35, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times D_{21}', 'supersolvable': True, 'sylow': 0}
id: 72062775
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 84, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '168.4', 'subgroup_hash': 4, 'subgroup_order': 168, 'subgroup_tex': 'C_7:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062776
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.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': '168.5', 'subgroup_hash': 5, 'subgroup_order': 168, 'subgroup_tex': 'C_{21}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062777
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 84, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.o1.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': '168.6', 'subgroup_hash': 6, 'subgroup_order': 168, 'subgroup_tex': 'C_{168}', 'supersolvable': True, 'sylow': 0}
id: 72062778
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.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': '168.16', 'subgroup_hash': 16, 'subgroup_order': 168, 'subgroup_tex': 'C_3:D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062780
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.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': '168.16', 'subgroup_hash': 16, 'subgroup_order': 168, 'subgroup_tex': 'C_3:D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062781
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 112, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062782
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 112, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062783
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 112, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '112.8', 'subgroup_hash': 8, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062784
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.29', 'subgroup_hash': 29, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062785
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.13', 'subgroup_hash': 13, 'subgroup_order': 112, 'subgroup_tex': 'D_{14}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062786
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 56, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.28', 'subgroup_hash': 28, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062787
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.13', 'subgroup_hash': 13, 'subgroup_order': 112, 'subgroup_tex': 'D_{14}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062788
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.19', 'subgroup_hash': 19, 'subgroup_order': 112, 'subgroup_tex': 'C_4\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062789
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 56, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.22', 'subgroup_hash': 22, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062791
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.8', 'subgroup_hash': 8, 'subgroup_order': 112, 'subgroup_tex': 'C_{14}:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 56, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.12', 'subgroup_hash': 12, 'subgroup_order': 112, 'subgroup_tex': 'C_{28}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062793
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.4', 'subgroup_hash': 4, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
id: 72062794
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.4', 'subgroup_hash': 4, 'subgroup_order': 112, 'subgroup_tex': 'C_{56}:C_2', 'supersolvable': True, 'sylow': 0}
id: 72062795
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.3', 'subgroup_hash': 3, 'subgroup_order': 112, 'subgroup_tex': 'C_8\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.3', 'subgroup_hash': 3, 'subgroup_order': 112, 'subgroup_tex': 'C_8\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062797
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 96, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.14.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.22', 'subgroup_hash': 22, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062798
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 72062799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 48, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.48', 'subgroup_hash': 48, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062800
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.128', 'subgroup_hash': 128, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062802
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062803
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.106', 'subgroup_hash': 106, 'subgroup_order': 96, 'subgroup_tex': 'C_8\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 72062804
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.14.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.21', 'subgroup_hash': 21, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
id: 72062805
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.16.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': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062806
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 74, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.16.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': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
id: 72062807
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 84, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.16.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': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
id: 72062808
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062809
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 84, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062810
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062811
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062813
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.4', 'subgroup_hash': 4, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062814
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.5', 'subgroup_hash': 5, 'subgroup_order': 84, 'subgroup_tex': 'C_{21}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062815
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062816
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 42, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062817
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 42, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.12', 'subgroup_hash': 12, 'subgroup_order': 84, 'subgroup_tex': 'C_3\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062818
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 42, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.14', 'subgroup_hash': 14, 'subgroup_order': 84, 'subgroup_tex': 'D_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062819
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 42, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1344.2375.21.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, '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': '64.116', 'subgroup_hash': 116, 'subgroup_order': 64, 'subgroup_tex': 'C_8:D_4', 'supersolvable': True, 'sylow': 2}
id: 72062821
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062822
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 56, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062824
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 56, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062825
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062826
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062827
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062828
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.6', 'subgroup_hash': 6, 'subgroup_order': 56, 'subgroup_tex': 'C_{14}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062829
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062830
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 28, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062831
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062832
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 28, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062833
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062588
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 28, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062589
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 28, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062590
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 28, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.1', 'subgroup_hash': 1, 'subgroup_order': 56, 'subgroup_tex': 'C_7:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062591
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 28, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.2', 'subgroup_hash': 2, 'subgroup_order': 56, 'subgroup_tex': 'C_{56}', 'supersolvable': True, 'sylow': 0}
id: 72062592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 14, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.p1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062594
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 48, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.28.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062595
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 48, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.28.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062596
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 48, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.28.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '28.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 72062599
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 72062601
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 72062602
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062603
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062604
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 72062606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.10', 'subgroup_hash': 10, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062608
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.28.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.4', 'subgroup_hash': 4, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062611
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 121, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.32.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': '32.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062612
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 122, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.32.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': '32.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062613
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 123, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.32.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': '32.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
id: 72062614
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 21, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '42.4', 'subgroup_hash': 4, 'subgroup_order': 42, 'subgroup_tex': 'C_3\\times D_7', 'supersolvable': True, 'sylow': 0}
id: 72062615
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 21, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.32.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.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': 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': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
id: 72062616
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 21, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.32.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '42.5', 'subgroup_hash': 5, 'subgroup_order': 42, 'subgroup_tex': 'D_{21}', 'supersolvable': True, 'sylow': 0}
id: 72062617
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 72062618
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 16, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062619
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062622
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 16, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.4', 'subgroup_hash': 4, 'subgroup_order': 32, 'subgroup_tex': 'C_8:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062624
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.42.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.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': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062625
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 134, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062626
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 135, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062627
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 28, 'counter': 136, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062628
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062629
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062630
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062632
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062633
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062634
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062635
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.i1.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062636
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062637
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 14, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062638
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 14, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062639
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 14, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
id: 72062640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 24, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062641
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062643
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': True, 'core_order': 24, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062644
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062645
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.56.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '56.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062646
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 72062647
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 72062648
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062649
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062652
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 72062654
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 72062655
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 161, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.56.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062656
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 72062657
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 163, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.56.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 72062658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 72062659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.56.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.p1.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 72062660
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 166, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '1344.2375.64.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': '64.116', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 116, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
id: 72062661
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 16, 'counter': 167, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '84.8', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_7', 'simple': False, 'solvable': True, 'special_labels': ['U0'], '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: 72062662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 72062663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062666
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 8, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 72062669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 8, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062670
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 8, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062671
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062672
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062673
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062674
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.l1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 72062676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062677
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.84.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.m1.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 72062678
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 182, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.88', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 88, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062679
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 183, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.113', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 113, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062680
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 184, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.108', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 108, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 72062681
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 7, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 72062682
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 7, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.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': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 72062683
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 7, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 72062684
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 12, 'counter': 188, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.28', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 72062685
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 12, 'counter': 189, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062687
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 12, 'counter': 190, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '112.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{28}:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 72062689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 72062690
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 193, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 72062691
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 72062693
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 72062694
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.i1.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 72062695
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062696
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 72062699
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 72062700
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 6, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.112.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 72062701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 8, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '168.50', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{14}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], '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: 72062702
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 72062703
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 72062704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 4, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062706
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062710
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062711
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062712
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 72062713
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 213, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.168.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 72062714
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.168.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.l1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 72062715
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.168.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 72062716
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.168.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 72062717
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.168.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 72062718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 72062719
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.168.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.p1.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 72062721
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 220, 'cyclic': True, 'direct': False, 'hall': 7, 'label': '1344.2375.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.287', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 287, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:\\OD_{16}', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
id: 72062722
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 221, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.68', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 68, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 72062723
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 222, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.101', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 101, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_7\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 72062724
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 6, 'counter': 223, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '224.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8.D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 72062725
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 72062726
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.224.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 72062727
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 3, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.224.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 72062728
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 4, 'counter': 227, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2375.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.147', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 147, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062729
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 4, 'counter': 228, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.149', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 149, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{28}', '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: 72062730
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 4, 'counter': 229, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '336.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '336.152', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 152, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{14}.D_6', '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: 72062732
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062733
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062734
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 72062735
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 72062736
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062737
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062738
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.i1.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062739
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 237, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 72062740
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062741
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1344.2375.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 72062743
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 2, 'counter': 240, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 72062744
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 3, 'counter': 241, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '1344.2375.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '448.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '448.240', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 240, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 448, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_{28}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 72062745
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 242, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.539', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 539, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:(C_4\\times D_{28})', 'simple': True, 'solvable': True, 'special_labels': [], '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: 72062746
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 243, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.390', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 390, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], '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: 72062747
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 2, 'counter': 244, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.2375.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '672.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '672.410', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 410, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}.D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], '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: 72062748
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 72062749
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 72062750
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1344.2375.672.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 72062751
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.2375', 'ambient_counter': 2375, 'ambient_order': 1344, 'ambient_tex': 'D_{42}:\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1344, 'characteristic': True, 'core_order': 1, 'counter': 248, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1344.2375.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1344.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1344.2375', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2375, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1344, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{42}:\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', '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: 72062586
{'ambient': '1344.2375', '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': '168.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7695, 3034, 6965, 6505, 6799, 4115, 7117, 4238], 'generators': [1, 336, 448, 168, 672, 192, 2, 4], 'label': '1344.2375.1.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', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '168.50', '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': '168.50'}
id: 72062587
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.d1.a1', '8.p1.a1', '8.p1.b1', '12.d1.a1', '28.d1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1884, 6215, 1935, 2690, 1765, 8244, 1675, 7982], 'generators': [1, 192, 672, 4, 2, 448], 'label': '1344.2375.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062588
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.i1.a1', '12.l1.b1', '12.m1.b1'], 'contains': ['48.b1.a1', '168.l1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9140, -1, 9357, -1, 8575, -1, 8128, -1], 'generators': [846, 1012, 672, 192], 'label': '1344.2375.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062589
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '28.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.c1.a1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.b1.a1', '168.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8975, -1, 8588, -1, 7766, -1, 8887, -1], 'generators': [125, 672, 192, 340], 'label': '1344.2375.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062590
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.j1.a1', '12.l1.a1', '12.l1.b1'], 'contains': ['48.b1.a1', '168.n1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8566, -1, 9831, -1, 9233, -1, 6836, -1], 'generators': [971, 672, 192, 340], 'label': '1344.2375.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.n1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062591
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.b1.a1'], 'contains': ['48.c1.a1', '168.o1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7147, -1, 5409, -1, 6949, -1, 5702, -1], 'generators': [168, 336, 672, 192], 'label': '1344.2375.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '24.o1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062592
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.d1.a1'], 'contains': ['48.h1.a1', '48.i1.a1', '48.j1.a1', '168.p1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [667, -1, 618, -1, 869, -1, 37, -1], 'generators': [97, 4, 192, 2], 'label': '1344.2375.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062593
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.d1.a1'], 'contains': ['48.h1.a1', '48.i1.b1', '48.j1.a1', '168.p1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [667, -1, 747, -1, 869, -1, 400, -1], 'generators': [1, 4, 192, 2], 'label': '1344.2375.24.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.p1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062594
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '28.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '14.a1.a1', '14.b1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.b1.a1', '56.c1.a1', '84.g1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4266, 4653, 4509, 5083, 3797, 3610, 3930, 4624], 'generators': [2, 448, 336, 4, 672], 'label': '1344.2375.28.a1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.a1.a1', 'normal_contained_in': ['4.f1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.c1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062595
{'ambient': '1344.2375', 'aut_centralizer_order': 2016, 'aut_label': '28.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '14.a1.a1', '14.c1.a1', '14.e1.a1'], 'contains': ['56.a1.a1', '56.o1.a1', '84.a1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7250, 847, 5816, 7934, 6358, 1628, 5930, 2154], 'generators': [4, 672, 168, 448, 336], 'label': '1344.2375.28.b1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.b1.a1', 'normal_contained_in': ['4.g1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '28.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062596
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '28.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '14.a1.a1', '14.d1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.d1.a1', '56.d1.b1', '84.h1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8556, 2987, 7758, 8827, 8237, 967, 8309, 1534], 'generators': [734, 448, 336, 340, 672], 'label': '1344.2375.28.c1.a1', 'mobius_quo': 0, 'mobius_sub': -14, 'normal_closure': '28.c1.a1', 'normal_contained_in': ['4.h1.a1', '14.a1.a1'], 'normal_contains': ['56.a1.a1', '56.d1.b1', '56.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '28.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062597
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.230', 'aut_weyl_index': 336, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '14.b1.a1'], 'contains': ['56.b1.a1', '56.e1.a1', '56.f1.a1', '56.p1.a1', '56.p1.b1', '84.b1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1736, -1, 2161, -1, 1341, -1, 2186, -1], 'generators': [1, 448, 2, 672, 4], 'label': '1344.2375.28.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062598
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.f1.a1', '8.i1.a1', '8.j1.a1', '12.a1.a1', '28.e1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5233, 5198, 6081, 5545, 4954, 5705, 5027, 5601], 'generators': [1, 192, 336, 448, 4, 672], 'label': '1344.2375.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.f1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '168.50', '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': '56.12'}
id: 72062599
{'ambient': '1344.2375', 'aut_centralizer_order': 288, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1'], 'contains': ['56.a1.a1', '56.e1.a1', '56.g1.a1', '56.i1.a1', '56.j1.a1', '84.c1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4736, -1, 6499, -1, 4733, -1, 5128, -1], 'generators': [1, 672, 4, 336, 448], 'label': '1344.2375.28.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062600
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.230', 'aut_weyl_index': 336, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.e1.a1', '56.h1.a1', '84.d1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3230, -1, 2767, -1, 2702, -1, 2778, -1], 'generators': [1, 448, 118, 4, 672], 'label': '1344.2375.28.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.f1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062601
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '28.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '14.b1.a1', '14.e1.a1', '14.f1.a1'], 'contains': ['56.a1.a1', '56.f1.a1', '56.h1.a1', '56.k1.a1', '56.l1.a1', '84.e1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5457, -1, 5120, -1, 4962, -1, 4921, -1], 'generators': [3, 448, 4, 336, 672], 'label': '1344.2375.28.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.g1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062602
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '28.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.230', 'aut_weyl_index': 336, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '14.b1.a1'], 'contains': ['56.c1.a1', '56.f1.a1', '56.g1.a1', '84.f1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3642, -1, 3079, -1, 2595, -1, 2875, -1], 'generators': [49, 448, 118, 4, 672], 'label': '1344.2375.28.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.h1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062603
{'ambient': '1344.2375', 'aut_centralizer_order': 288, 'aut_label': '28.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '14.c1.a1', '14.f1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.m1.a1', '84.i1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7773, -1, 8651, -1, 7317, -1, 9176, -1], 'generators': [125, 672, 336, 448, 340], 'label': '1344.2375.28.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.i1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062604
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '28.j1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '14.d1.a1', '14.e1.a1', '14.g1.a1'], 'contains': ['56.a1.a1', '56.n1.a1', '84.j1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7511, -1, 9059, -1, 9040, -1, 6587, -1], 'generators': [971, 448, 336, 340, 672], 'label': '1344.2375.28.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.j1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062605
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '28.k1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '96.230', 'aut_weyl_index': 336, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '14.b1.a1'], 'contains': ['56.b1.a1', '56.g1.a1', '56.h1.a1', '84.k1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3783, -1, 3521, -1, 3088, -1, 3302, -1], 'generators': [49, 448, 2, 4, 672], 'label': '1344.2375.28.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '28.k1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062606
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '14.d1.a1'], 'contains': ['56.d1.a1', '56.i1.a1', '56.n1.a1', '84.l1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8238, -1, 9652, -1, 9630, -1, 7552, -1], 'generators': [1, 448, 734, 340, 672], 'label': '1344.2375.28.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062607
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '28.l1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '14.d1.a1'], 'contains': ['56.d1.b1', '56.i1.a1', '56.n1.a1', '84.l1.b1'], 'core': '56.d1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [8238, -1, 9901, -1, 9630, -1, 7739, -1], 'generators': [1, 448, 846, 1012, 672], 'label': '1344.2375.28.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '28.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062608
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '14.f1.a1'], 'contains': ['56.d1.a1', '56.k1.a1', '56.m1.a1', '84.m1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8898, -1, 7446, -1, 8062, -1, 9796, -1], 'generators': [125, 448, 734, 340, 672], 'label': '1344.2375.28.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '28.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062609
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1', '12.e1.a1', '28.f1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3171, 8961, 2701, 1168, 2866, 7499, 2585, 7283], 'generators': [1, 192, 4, 672, 118, 448], 'label': '1344.2375.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '336.147', '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': '168.50'}
id: 72062610
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '28.m1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '48.51', 'aut_weyl_index': 672, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '14.f1.a1'], 'contains': ['56.d1.b1', '56.k1.a1', '56.m1.a1', '84.m1.b1'], 'core': '56.d1.b1', 'coset_action_label': None, 'count': 14, 'diagramx': [8898, -1, 8128, -1, 8062, -1, 9939, -1], 'generators': [125, 448, 846, 340, 672], 'label': '1344.2375.28.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '28.m1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062611
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '32.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.e1.a1', '16.f1.a1', '16.g1.a1', '16.h1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2588, 4358, 4685, 5391, 4490, 4656, 3371, 4617], 'generators': [672, 192, 448], 'label': '1344.2375.32.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1', '224.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '672.539', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062612
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '32.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.i1.a1', '16.j1.a1'], 'contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [479, 7971, 278, 1982, 986, 6618, 613, 6900], 'generators': [4, 192, 448], 'label': '1344.2375.32.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1'], 'normal_contains': ['64.a1.a1', '96.b1.a1', '224.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '672.390', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062613
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '32.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.k1.a1', '16.l1.a1', '16.m1.a1'], 'contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1164, 7436, 1547, 2597, 1249, 6209, 1319, 6074], 'generators': [676, 192, 448], 'label': '1344.2375.32.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.c1.a1', '224.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '672.410', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062614
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.i1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.d1.a1', '224.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [298, -1, 1081, -1, 1117, -1, 826, -1], 'generators': [1, 192, 448], 'label': '1344.2375.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '32.d1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062615
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '252.26', 'aut_weyl_index': 128, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '16.f1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.e1.a1', '224.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [915, -1, 1210, -1, 533, -1, 1038, -1], 'generators': [995, 192, 448], 'label': '1344.2375.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.e1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062616
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '252.26', 'aut_weyl_index': 128, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '16.f1.a1', '16.l1.a1'], 'contains': ['64.a1.a1', '96.e1.b1', '224.e1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [915, -1, 1314, -1, 533, -1, 1132, -1], 'generators': [3, 192, 448], 'label': '1344.2375.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '32.e1.b1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062617
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '14.b1.a1', '21.a1.a1'], 'contains': ['84.b1.a1', '84.c1.a1', '84.d1.a1', '84.e1.a1', '84.f1.a1', '84.g1.a1', '84.k1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5589, -1, 4788, -1, 3974, -1, 3770, -1], 'generators': [1, 2, 336], 'label': '1344.2375.42.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062618
{'ambient': '1344.2375', 'aut_centralizer_order': 144, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '14.c1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.c1.a1', '84.i1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8637, -1, 7108, -1, 6708, -1, 7893, -1], 'generators': [1, 168], 'label': '1344.2375.42.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '42.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062619
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '14.d1.a1', '21.a1.a1'], 'contains': ['84.c1.a1', '84.h1.a1', '84.j1.a1', '84.l1.a1', '84.l1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9298, -1, 9246, -1, 8813, -1, 7215, -1], 'generators': [1, 734, 336], 'label': '1344.2375.42.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062620
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.g1.a1', '8.k1.a1', '8.l1.a1', '12.f1.a1', '28.g1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5811, 7229, 5132, 3641, 5344, 6662, 4575, 6498], 'generators': [3, 192, 336, 672, 4, 448], 'label': '1344.2375.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '168.50', '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': '168.50'}
id: 72062621
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '14.e1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.e1.a1', '84.j1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8148, -1, 6846, -1, 7048, -1, 6075, -1], 'generators': [3, 168], 'label': '1344.2375.42.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062622
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '14.f1.a1', '21.a1.a1'], 'contains': ['84.e1.a1', '84.h1.a1', '84.i1.a1', '84.m1.a1', '84.m1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9689, -1, 7527, -1, 7697, -1, 9007, -1], 'generators': [125, 734, 336], 'label': '1344.2375.42.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062623
{'ambient': '1344.2375', 'aut_centralizer_order': 336, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '14.a1.a1', '21.a1.a1'], 'contains': ['84.a1.a1', '84.g1.a1', '84.h1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8825, -1, 6590, -1, 6878, -1, 6229, -1], 'generators': [2, 168], 'label': '1344.2375.42.f1.a1', 'mobius_quo': None, 'mobius_sub': -7, 'normal_closure': '14.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '42.f1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062624
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '42.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '32.51', 'aut_weyl_index': 1008, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '14.g1.a1', '21.a1.a1'], 'contains': ['84.g1.a1', '84.i1.a1', '84.j1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9048, -1, 8934, -1, 7168, -1, 8001, -1], 'generators': [125, 2], 'label': '1344.2375.42.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '42.g1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.g1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062625
{'ambient': '1344.2375', 'aut_centralizer_order': 5376, 'aut_label': '48.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '336.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3483, 6385, 3213, 3957, 2873, 5705, 2403, 5601], 'generators': [4, 192, 672], 'label': '1344.2375.48.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['96.c1.a1', '96.a1.a1', '96.b1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '336.147', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062626
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '48.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.b1.a1', '24.h1.a1', '24.j1.a1', '24.l1.a1', '24.l1.b1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.a1.a1', '336.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7137, 3269, 8552, 7974, 7096, 3054, 7040, 3115], 'generators': [340, 672, 192], 'label': '1344.2375.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '336.149', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062627
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '48.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.b1.a1', '24.i1.a1', '24.k1.a1', '24.o1.a1'], 'contains': ['96.a1.a1', '336.c1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6386, 1795, 5471, 6143, 5540, 4303, 5008, 4286], 'generators': [336, 672, 192], 'label': '1344.2375.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.b1.a1'], 'normal_contains': ['96.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '336.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.7', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062628
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1', '24.h1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '336.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3122, -1, 5792, -1, 4386, -1, 3278, -1], 'generators': [1, 192, 672], 'label': '1344.2375.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.d1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062629
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.d1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.e1.b1', '336.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4004, -1, 4089, -1, 4594, -1, 2766, -1], 'generators': [3, 192, 672], 'label': '1344.2375.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.e1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062630
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.c1.a1', '24.h1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '336.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6194, -1, 6079, -1, 4802, -1, 4375, -1], 'generators': [49, 192, 672], 'label': '1344.2375.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.f1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062631
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.f1.a1', '12.g1.a1', '28.h1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3390, 9659, 3018, 512, 2644, 9513, 2830, 9172], 'generators': [49, 192, 4, 672, 118, 448], 'label': '1344.2375.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '336.147', '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': '168.50'}
id: 72062632
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.g1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.a1.a1', '336.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5244, -1, 4498, -1, 5174, -1, 4279, -1], 'generators': [595, 192, 672], 'label': '1344.2375.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.g1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062633
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.a1.a1', '24.p1.a1', '24.p1.b1'], 'contains': ['96.b1.a1', '96.d1.a1', '336.h1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [430, -1, 679, -1, 1905, -1, 519, -1], 'generators': [1, 192, 4], 'label': '1344.2375.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062634
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1', '24.p1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '336.i1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1312, -1, 577, -1, 1594, -1, 332, -1], 'generators': [995, 192, 4], 'label': '1344.2375.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062635
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.d1.a1', '24.p1.b1'], 'contains': ['96.b1.a1', '96.e1.b1', '336.i1.b1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1312, -1, 940, -1, 1594, -1, 707, -1], 'generators': [3, 192, 4], 'label': '1344.2375.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062636
{'ambient': '1344.2375', 'aut_centralizer_order': 448, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.e1.a1', '24.p1.a1', '24.p1.b1'], 'contains': ['96.b1.a1', '336.j1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [789, -1, 431, -1, 1802, -1, 426, -1], 'generators': [2, 4, 192], 'label': '1344.2375.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.j1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062637
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.a1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '336.k1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1197, -1, 1563, -1, 2009, -1, 945, -1], 'generators': [1, 192, 676], 'label': '1344.2375.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062638
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '84.7', 'aut_weyl_index': 384, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.d1.a1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.e1.b1', '336.l1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2845, -1, 2082, -1, 1698, -1, 1226, -1], 'generators': [3, 192, 676], 'label': '1344.2375.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.l1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062639
{'ambient': '1344.2375', 'aut_centralizer_order': 448, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.f1.a1'], 'contains': ['96.c1.a1', '336.m1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2959, -1, 2184, -1, 2219, -1, 2174, -1], 'generators': [118, 676, 192], 'label': '1344.2375.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '48.m1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062640
{'ambient': '1344.2375', 'aut_centralizer_order': 8064, 'aut_label': '56.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1', '28.e1.a1', '28.g1.a1', '28.i1.a1', '28.j1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.a1', '168.a1.a1'], 'core': '56.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6257, 2579, 6000, 7146, 6484, 2998, 6099, 3062], 'generators': [4, 336, 448, 672], 'label': '1344.2375.56.a1.a1', 'mobius_quo': 0, 'mobius_sub': 56, 'normal_closure': '56.a1.a1', 'normal_contained_in': ['8.c1.a1', '28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normal_contains': ['112.a1.a1', '112.c1.a1', '112.b1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.3', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062641
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '56.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '28.a1.a1', '28.d1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.j1.a1', '168.d1.a1'], 'core': '56.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2042, 5076, 2685, 4916, 1395, 5332, 2367, 5252], 'generators': [2, 672, 4, 448], 'label': '1344.2375.56.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': ['8.d1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062695
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '112.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '56.b1.a1', '56.p1.a1', '56.p1.b1'], 'contains': ['224.b1.a1', '336.j1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [271, -1, 278, -1, 723, -1, 1566, -1], 'generators': [2, 4, 448], 'label': '1344.2375.112.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '112.j1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062642
{'ambient': '1344.2375', 'aut_centralizer_order': 112, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1043', 'aut_weyl_index': 112, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.e1.a1', '12.h1.a1', '28.a1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4134, 4183, 4854, 4595, 3870, 4063, 3701, 4790], 'generators': [2, 448, 192, 4, 336, 672], 'label': '1344.2375.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.c1.a1', '8.e1.a1', '8.d1.a1', '28.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '168.50', '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': '24.14'}
id: 72062643
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '56.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '28.a1.a1', '28.f1.a1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.m1.a1', '168.e1.a1'], 'core': '56.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2598, 5859, 3008, 3183, 2681, 4664, 2974, 4624], 'generators': [118, 672, 676, 448], 'label': '1344.2375.56.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': ['8.e1.a1', '28.a1.a1'], 'normal_contains': ['112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062644
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '56.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '12.c1.a1', 'complements': ['24.p1.b1', '24.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '28.c1.a1', '28.l1.a1', '28.m1.a1'], 'contains': ['112.b1.a1', '168.l1.a1'], 'core': '56.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8392, 3935, 7935, 9254, 8441, 967, 8222, 1635], 'generators': [734, 340, 672, 448], 'label': '1344.2375.56.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.d1.a1', 'normal_contained_in': ['8.h1.a1', '28.c1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.d1.a1', 'projective_image': '336.149', 'quotient_action_image': '4.2', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062645
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '56.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '12.c1.a1', 'complements': ['24.p1.b1', '24.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '28.c1.a1', '28.l1.b1', '28.m1.b1'], 'contains': ['112.b1.a1', '168.l1.b1'], 'core': '56.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8392, 3935, 9195, 8827, 8441, 967, 8319, 1290], 'generators': [846, 1012, 672, 448], 'label': '1344.2375.56.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.d1.b1', 'normal_contained_in': ['8.h1.b1', '28.c1.a1'], 'normal_contains': ['112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '56.d1.b1', 'projective_image': '336.149', 'quotient_action_image': '4.2', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '56.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062646
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '28.d1.a1', '28.e1.a1', '28.f1.a1'], 'contains': ['112.a1.a1', '112.d1.a1', '112.h1.a1', '112.k1.a1', '168.b1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1638, -1, 1837, -1, 1584, -1, 2803, -1], 'generators': [1, 4, 672, 448], 'label': '1344.2375.56.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.e1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062647
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '28.d1.a1', '28.g1.a1', '28.h1.a1'], 'contains': ['112.a1.a1', '112.e1.a1', '112.i1.a1', '112.i1.b1', '112.l1.a1', '168.c1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [1435, -1, 2456, -1, 1207, -1, 2197, -1], 'generators': [3, 4, 672, 448], 'label': '1344.2375.56.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.f1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062648
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '28.e1.a1', '28.h1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.f1.a1', '168.f1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3855, -1, 3871, -1, 3326, -1, 4154, -1], 'generators': [49, 4, 448, 672], 'label': '1344.2375.56.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.g1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062649
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '56.h1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '28.f1.a1', '28.g1.a1', '28.k1.a1'], 'contains': ['112.a1.a1', '112.g1.a1', '168.g1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [3644, -1, 3505, -1, 3626, -1, 3981, -1], 'generators': [595, 4, 672, 448], 'label': '1344.2375.56.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '56.h1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062650
{'ambient': '1344.2375', 'aut_centralizer_order': 288, 'aut_label': '56.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '28.e1.a1', '28.l1.a1', '28.l1.b1'], 'contains': ['112.b1.a1', '112.d1.a1', '112.f1.a1', '168.h1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5040, -1, 9388, -1, 6033, -1, 6415, -1], 'generators': [1, 340, 448, 672], 'label': '1344.2375.56.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.i1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062651
{'ambient': '1344.2375', 'aut_centralizer_order': 288, 'aut_label': '56.j1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '28.e1.a1'], 'contains': ['112.c1.a1', '112.d1.a1', '112.f1.a1', '168.i1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4731, -1, 6232, -1, 4760, -1, 5145, -1], 'generators': [1, 336, 448, 672], 'label': '1344.2375.56.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.j1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062652
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '56.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '28.g1.a1', '28.m1.a1', '28.m1.b1'], 'contains': ['112.b1.a1', '112.e1.a1', '112.g1.a1', '168.j1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5477, -1, 7227, -1, 6207, -1, 7395, -1], 'generators': [3, 340, 672, 448], 'label': '1344.2375.56.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '56.k1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062653
{'ambient': '1344.2375', 'aut_centralizer_order': 336, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.231', 'aut_weyl_index': 336, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.c1.a1', '8.o1.a1', '12.b1.a1', '28.b1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6705, 547, 5843, 8202, 5781, 2185, 5664, 2300], 'generators': [4, 672, 448, 192, 168, 336], 'label': '1344.2375.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.c1.a1', '12.b1.a1', '28.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062654
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '56.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '28.g1.a1'], 'contains': ['112.c1.a1', '112.e1.a1', '112.g1.a1', '168.k1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4489, -1, 4613, -1, 5231, -1, 4988, -1], 'generators': [3, 336, 672, 448], 'label': '1344.2375.56.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '56.l1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062655
{'ambient': '1344.2375', 'aut_centralizer_order': 288, 'aut_label': '56.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '28.i1.a1', '28.m1.a1', '28.m1.b1'], 'contains': ['112.b1.a1', '168.m1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7903, -1, 8378, -1, 7661, -1, 9454, -1], 'generators': [125, 448, 340, 672], 'label': '1344.2375.56.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '56.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062656
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '56.n1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '28.j1.a1', '28.l1.a1', '28.l1.b1'], 'contains': ['112.b1.a1', '168.n1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7787, -1, 9827, -1, 9040, -1, 7038, -1], 'generators': [971, 340, 672, 448], 'label': '1344.2375.56.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '56.n1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062657
{'ambient': '1344.2375', 'aut_centralizer_order': 2016, 'aut_label': '56.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '28.b1.a1'], 'contains': ['112.c1.a1', '168.o1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6901, -1, 5268, -1, 6337, -1, 5967, -1], 'generators': [168, 448, 336, 672], 'label': '1344.2375.56.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '56.o1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062658
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '28.d1.a1'], 'contains': ['112.h1.a1', '112.i1.a1', '112.j1.a1', '168.p1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [249, -1, 112, -1, 43, -1, 972, -1], 'generators': [97, 2, 4, 448], 'label': '1344.2375.56.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.p1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062659
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '56.p1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '24.14', 'aut_weyl_index': 1344, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '28.d1.a1'], 'contains': ['112.h1.a1', '112.i1.b1', '112.j1.a1', '168.p1.b1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [249, -1, 734, -1, 43, -1, 1069, -1], 'generators': [1, 2, 4, 448], 'label': '1344.2375.56.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '56.p1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.p1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062660
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.g1.a1', 'complements': ['21.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.e1.a1', '32.e1.b1'], 'contains': ['192.a1.a1', '448.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [773, 7525, 1269, 1956, 1196, 5977, 1146, 5913], 'generators': [448, 192], 'label': '1344.2375.64.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.c1.a1', '32.a1.a1', '32.b1.a1'], 'normal_contains': ['192.a1.a1', '448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '1344.2375', 'quotient_action_image': '4.2', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062661
{'ambient': '1344.2375', 'aut_centralizer_order': 4032, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '28.b1.a1', '42.b1.a1', '42.d1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.o1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8050, 847, 6564, 7591, 7270, 2397, 6573, 2499], 'generators': [4, 168], 'label': '1344.2375.84.a1.a1', 'mobius_quo': 0, 'mobius_sub': 42, 'normal_closure': '84.a1.a1', 'normal_contained_in': ['12.b1.a1', '28.b1.a1'], 'normal_contains': ['168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '21.2', 'quotient_action_kernel_order': 21, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062662
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '28.d1.a1', '42.a1.a1'], 'contains': ['168.b1.a1', '168.c1.a1', '168.d1.a1', '168.p1.a1', '168.p1.b1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [2647, -1, 2580, -1, 1755, -1, 1871, -1], 'generators': [1, 2, 672], 'label': '1344.2375.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062663
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '28.e1.a1', '42.a1.a1', '42.b1.a1', '42.c1.a1'], 'contains': ['168.a1.a1', '168.b1.a1', '168.f1.a1', '168.h1.a1', '168.i1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6896, -1, 6864, -1, 5664, -1, 5572, -1], 'generators': [1, 4, 336], 'label': '1344.2375.84.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062664
{'ambient': '1344.2375', 'aut_centralizer_order': 112, 'aut_label': '4.h1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1043', 'aut_weyl_index': 112, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.c1.a1', '8.h1.a1', '8.h1.b1', '12.i1.a1', '28.c1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8810, 3273, 7994, 9007, 8375, 971, 8294, 1162], 'generators': [734, 448, 192, 340, 336, 672], 'label': '1344.2375.4.h1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.c1.a1', '8.h1.b1', '8.h1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062665
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '28.f1.a1', '42.a1.a1'], 'contains': ['168.b1.a1', '168.e1.a1', '168.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3914, -1, 3470, -1, 3166, -1, 3121, -1], 'generators': [1, 118], 'label': '1344.2375.84.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062666
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '28.g1.a1', '42.a1.a1', '42.d1.a1', '42.e1.a1'], 'contains': ['168.a1.a1', '168.c1.a1', '168.g1.a1', '168.j1.a1', '168.k1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6506, -1, 5483, -1, 5847, -1, 5407, -1], 'generators': [3, 4, 336], 'label': '1344.2375.84.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062667
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '28.h1.a1', '42.a1.a1'], 'contains': ['168.c1.a1', '168.e1.a1', '168.f1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [4843, -1, 3645, -1, 3034, -1, 3240, -1], 'generators': [49, 118], 'label': '1344.2375.84.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.f1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062668
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '28.a1.a1', '42.a1.a1', '42.f1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.d1.a1', '168.e1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5724, -1, 5177, -1, 4424, -1, 4284, -1], 'generators': [2, 336], 'label': '1344.2375.84.g1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.g1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062669
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '28.c1.a1', '42.c1.a1', '42.e1.a1', '42.f1.a1'], 'contains': ['168.a1.a1', '168.l1.a1', '168.l1.b1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9468, -1, 7706, -1, 8150, -1, 7917, -1], 'generators': [734, 336], 'label': '1344.2375.84.h1.a1', 'mobius_quo': None, 'mobius_sub': 14, 'normal_closure': '28.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '84.h1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062670
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '14.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '28.i1.a1', '42.b1.a1', '42.e1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.m1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8969, -1, 8073, -1, 7531, -1, 8767, -1], 'generators': [125, 336], 'label': '1344.2375.84.i1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '84.i1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062671
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '84.j1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '84.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '28.j1.a1', '42.c1.a1', '42.d1.a1', '42.g1.a1'], 'contains': ['168.a1.a1', '168.n1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8561, -1, 9065, -1, 8308, -1, 6716, -1], 'generators': [971, 336], 'label': '1344.2375.84.j1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.j1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062672
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '84.k1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '16.14', 'aut_weyl_index': 2016, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '28.k1.a1', '42.a1.a1'], 'contains': ['168.d1.a1', '168.f1.a1', '168.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5611, -1, 4028, -1, 3475, -1, 3668, -1], 'generators': [49, 2], 'label': '1344.2375.84.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '84.k1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062673
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '28.l1.a1', '42.c1.a1'], 'contains': ['168.h1.a1', '168.l1.a1', '168.n1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9224, -1, 9634, -1, 8813, -1, 6937, -1], 'generators': [1, 734], 'label': '1344.2375.84.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '84.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062674
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '84.l1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.b1', '28.l1.b1', '42.c1.a1'], 'contains': ['168.h1.a1', '168.l1.b1', '168.n1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9224, -1, 9959, -1, 8813, -1, 7519, -1], 'generators': [1, 846], 'label': '1344.2375.84.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '84.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.l1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062675
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '4.i1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.c1.a1', '8.m1.a1', '12.c1.a1', '28.i1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7537, 1518, 8201, 6605, 7533, 3342, 8808, 3385], 'generators': [125, 192, 448, 340, 336, 672], 'label': '1344.2375.4.i1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.c1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062676
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '28.m1.a1', '42.e1.a1'], 'contains': ['168.j1.a1', '168.l1.a1', '168.m1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9713, -1, 7527, -1, 7956, -1, 9007, -1], 'generators': [125, 734], 'label': '1344.2375.84.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '84.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062677
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '84.m1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '8.5', 'aut_weyl_index': 4032, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '28.m1.b1', '42.e1.a1'], 'contains': ['168.j1.a1', '168.l1.b1', '168.m1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [9713, -1, 8230, -1, 7956, -1, 9151, -1], 'generators': [125, 846], 'label': '1344.2375.84.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '84.m1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062678
{'ambient': '1344.2375', 'aut_centralizer_order': 5376, 'aut_label': '96.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1'], 'contains': ['192.a1.a1', '672.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4664, 4193, 4851, 5673, 4678, 4656, 3366, 4636], 'generators': [672, 192], 'label': '1344.2375.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.b1.a1'], 'normal_contains': ['192.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '672.539', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.11', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062679
{'ambient': '1344.2375', 'aut_centralizer_order': 5376, 'aut_label': '96.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.h1.a1', '48.i1.a1', '48.i1.b1', '48.j1.a1'], 'contains': ['192.a1.a1', '672.b1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1229, 8149, 516, 2721, 1920, 6618, 660, 6513], 'generators': [4, 192], 'label': '1344.2375.96.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '672.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '672.390', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.5', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062680
{'ambient': '1344.2375', 'aut_centralizer_order': 5376, 'aut_label': '96.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1'], 'contains': ['192.a1.a1', '672.c1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2890, 7168, 2105, 3130, 2107, 5625, 1319, 5582], 'generators': [676, 192], 'label': '1344.2375.96.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['32.c1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': '672.410', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.5', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062681
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.d1.a1', '48.h1.a1', '48.k1.a1'], 'contains': ['192.a1.a1', '672.d1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [648, -1, 1178, -1, 2013, -1, 965, -1], 'generators': [1, 192], 'label': '1344.2375.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '96.d1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062682
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '48.e1.a1', '48.i1.a1', '48.l1.a1'], 'contains': ['192.a1.a1', '672.e1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2105, -1, 1414, -1, 1553, -1, 1061, -1], 'generators': [995, 192], 'label': '1344.2375.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.e1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062683
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '42.1', 'aut_weyl_index': 768, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '48.e1.a1', '48.i1.b1', '48.l1.a1'], 'contains': ['192.a1.a1', '672.e1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2105, -1, 1623, -1, 1553, -1, 1230, -1], 'generators': [3, 192], 'label': '1344.2375.96.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.e1.b1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062684
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '112.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '56.a1.a1', '56.b1.a1', '56.c1.a1', '56.e1.a1', '56.f1.a1', '56.g1.a1', '56.h1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '224.c1.a1', '336.a1.a1'], 'core': '112.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1744, 6267, 2860, 3913, 2350, 5104, 2972, 5038], 'generators': [4, 672, 448], 'label': '1344.2375.112.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '112.a1.a1', 'normal_contained_in': ['16.a1.a1', '56.a1.a1', '56.c1.a1', '56.b1.a1'], 'normal_contains': ['224.c1.a1', '224.a1.a1', '224.b1.a1', '336.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '336.147', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.4', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062685
{'ambient': '1344.2375', 'aut_centralizer_order': 8064, 'aut_label': '112.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '56.a1.a1', '56.d1.a1', '56.d1.b1', '56.i1.a1', '56.k1.a1', '56.m1.a1', '56.n1.a1'], 'contains': ['224.a1.a1', '336.b1.a1'], 'core': '112.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6017, 3179, 8500, 8506, 6898, 2701, 7133, 2503], 'generators': [340, 448, 672], 'label': '1344.2375.112.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.b1.a1', 'normal_contained_in': ['16.b1.a1', '56.a1.a1', '56.d1.b1', '56.d1.a1'], 'normal_contains': ['224.a1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '336.149', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.5', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062686
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.c1.a1', '8.n1.a1', '12.j1.a1', '28.j1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7094, 2363, 9519, 7397, 9122, 4840, 6472, 4061], 'generators': [971, 192, 340, 672, 336, 448], 'label': '1344.2375.4.j1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062687
{'ambient': '1344.2375', 'aut_centralizer_order': 8064, 'aut_label': '112.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '56.a1.a1', '56.j1.a1', '56.l1.a1', '56.o1.a1'], 'contains': ['224.a1.a1', '336.c1.a1'], 'core': '112.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5104, 2527, 5304, 6179, 5437, 3951, 5145, 3956], 'generators': [336, 448, 672], 'label': '1344.2375.112.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.c1.a1', 'normal_contained_in': ['16.c1.a1', '56.a1.a1'], 'normal_contains': ['224.a1.a1', '336.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '336.152', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.7', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062688
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '56.e1.a1', '56.i1.a1', '56.j1.a1'], 'contains': ['224.a1.a1', '224.d1.a1', '336.d1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2761, -1, 5758, -1, 4171, -1, 3565, -1], 'generators': [1, 672, 448], 'label': '1344.2375.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '112.d1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062689
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '56.f1.a1', '56.k1.a1', '56.l1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '224.e1.b1', '336.e1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [2225, -1, 4058, -1, 4292, -1, 3456, -1], 'generators': [3, 672, 448], 'label': '1344.2375.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '112.e1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062690
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '56.g1.a1', '56.i1.a1', '56.j1.a1'], 'contains': ['224.a1.a1', '336.f1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [4099, -1, 6159, -1, 4697, -1, 4567, -1], 'generators': [49, 448, 672], 'label': '1344.2375.112.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '112.f1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062691
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '56.h1.a1', '56.k1.a1', '56.l1.a1'], 'contains': ['224.a1.a1', '336.g1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3813, -1, 4463, -1, 5067, -1, 4472, -1], 'generators': [595, 672, 448], 'label': '1344.2375.112.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '112.g1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062692
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '112.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '56.e1.a1', '56.p1.a1', '56.p1.b1'], 'contains': ['224.b1.a1', '224.d1.a1', '336.h1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [76, -1, 509, -1, 855, -1, 1761, -1], 'generators': [1, 4, 448], 'label': '1344.2375.112.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '112.h1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062693
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '56.f1.a1', '56.p1.a1'], 'contains': ['224.b1.a1', '224.e1.a1', '336.i1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [378, -1, 157, -1, 439, -1, 1479, -1], 'generators': [995, 4, 448], 'label': '1344.2375.112.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.i1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062694
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '112.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '56.f1.a1', '56.p1.b1'], 'contains': ['224.b1.a1', '224.e1.b1', '336.i1.b1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [378, -1, 852, -1, 439, -1, 1871, -1], 'generators': [3, 4, 448], 'label': '1344.2375.112.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '112.i1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062696
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '112.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '56.e1.a1'], 'contains': ['224.c1.a1', '224.d1.a1', '336.k1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [928, -1, 1190, -1, 1379, -1, 1980, -1], 'generators': [1, 676, 448], 'label': '1344.2375.112.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '112.k1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062697
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '168.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.e1.a1', '4.f1.a1', '4.k1.a1', '6.b1.a1', '14.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4035, 6783, 4288, 3165, 3765, 7106, 3607, 6889], 'generators': [1, 448, 336, 4, 2, 192, 672], 'label': '1344.2375.2.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', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '168.50', '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': '168.50'}
id: 72062698
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '4.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.d1.a1', '8.f1.a1', '8.g1.a1', '12.k1.a1', '28.k1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3634, 8168, 3476, 1911, 3322, 8953, 3227, 8646], 'generators': [49, 192, 4, 672, 2, 448], 'label': '1344.2375.4.k1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.d1.a1', '8.f1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062699
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '112.l1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '56.f1.a1'], 'contains': ['224.c1.a1', '224.e1.a1', '224.e1.b1', '336.l1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1111, -1, 1866, -1, 627, -1, 2090, -1], 'generators': [3, 676, 448], 'label': '1344.2375.112.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '112.l1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062700
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '112.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 2688, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '56.c1.a1'], 'contains': ['224.c1.a1', '336.m1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1900, -1, 2192, -1, 2115, -1, 2269, -1], 'generators': [118, 676, 448], 'label': '1344.2375.112.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '112.m1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062701
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '168.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '56.a1.a1', '84.a1.a1', '84.c1.a1', '84.e1.a1', '84.g1.a1', '84.h1.a1', '84.i1.a1', '84.j1.a1'], 'contains': ['336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '168.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7289, 2204, 6675, 6874, 6578, 3502, 5967, 3535], 'generators': [4, 336], 'label': '1344.2375.168.a1.a1', 'mobius_quo': 0, 'mobius_sub': -168, 'normal_closure': '168.a1.a1', 'normal_contained_in': ['24.b1.a1', '56.a1.a1', '84.a1.a1'], 'normal_contains': ['336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.50', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062702
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '56.e1.a1', '84.b1.a1', '84.c1.a1', '84.d1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.h1.a1', '336.k1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2464, -1, 2954, -1, 2730, -1, 2857, -1], 'generators': [1, 4, 672], 'label': '1344.2375.168.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062703
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '56.f1.a1', '84.b1.a1', '84.e1.a1', '84.f1.a1'], 'contains': ['336.a1.a1', '336.e1.a1', '336.i1.a1', '336.i1.b1', '336.l1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3396, -1, 3049, -1, 2477, -1, 2533, -1], 'generators': [3, 4, 672], 'label': '1344.2375.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.c1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062704
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '56.b1.a1', '84.b1.a1', '84.g1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.j1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3054, -1, 3708, -1, 2603, -1, 2647, -1], 'generators': [2, 672], 'label': '1344.2375.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062705
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '56.c1.a1', '84.d1.a1', '84.f1.a1', '84.g1.a1'], 'contains': ['336.a1.a1', '336.m1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4640, -1, 3551, -1, 3048, -1, 3115, -1], 'generators': [118, 672], 'label': '1344.2375.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.e1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062706
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '56.g1.a1', '84.c1.a1', '84.f1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.f1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [5405, -1, 3865, -1, 3472, -1, 3851, -1], 'generators': [49, 4], 'label': '1344.2375.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '168.f1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062707
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '56.h1.a1', '84.d1.a1', '84.e1.a1', '84.k1.a1'], 'contains': ['336.a1.a1', '336.g1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [5122, -1, 4197, -1, 3630, -1, 3708, -1], 'generators': [595, 4], 'label': '1344.2375.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '168.g1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062708
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '56.i1.a1', '84.c1.a1', '84.l1.a1', '84.l1.b1'], 'contains': ['336.b1.a1', '336.d1.a1', '336.f1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6863, -1, 9395, -1, 6033, -1, 6336, -1], 'generators': [1, 340], 'label': '1344.2375.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '168.h1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062709
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.h1.a1', '8.i1.a1', '8.n1.a1', '12.l1.a1', '28.l1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8130, -1, 9315, -1, 9528, -1, 6862, -1], 'generators': [1, 192, 340, 672, 734, 448], 'label': '1344.2375.4.l1.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.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062710
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '56.j1.a1', '84.c1.a1'], 'contains': ['336.c1.a1', '336.d1.a1', '336.f1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [6610, -1, 6254, -1, 4935, -1, 4879, -1], 'generators': [1, 336], 'label': '1344.2375.168.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '168.i1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062711
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '56.k1.a1', '84.e1.a1', '84.m1.a1', '84.m1.b1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.g1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6436, -1, 7342, -1, 6207, -1, 7252, -1], 'generators': [3, 340], 'label': '1344.2375.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '168.j1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062712
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '56.l1.a1', '84.e1.a1'], 'contains': ['336.c1.a1', '336.e1.a1', '336.g1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5678, -1, 4623, -1, 5307, -1, 4712, -1], 'generators': [3, 336], 'label': '1344.2375.168.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '168.k1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062713
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '56.d1.a1', '84.h1.a1', '84.l1.a1', '84.m1.a1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9496, -1, 7883, -1, 8296, -1, 7976, -1], 'generators': [734], 'label': '1344.2375.168.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062714
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '168.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '56.d1.b1', '84.h1.a1', '84.l1.b1', '84.m1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9496, -1, 8938, -1, 8296, -1, 8119, -1], 'generators': [846], 'label': '1344.2375.168.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '168.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062715
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '168.m1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '14.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '56.m1.a1', '84.i1.a1', '84.m1.a1', '84.m1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [8969, -1, 8258, -1, 7661, -1, 8947, -1], 'generators': [125], 'label': '1344.2375.168.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '168.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062716
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '168.n1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '84.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '56.n1.a1', '84.j1.a1', '84.l1.a1', '84.l1.b1'], 'contains': ['336.b1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8000, -1, 9859, -1, 8813, -1, 6947, -1], 'generators': [971], 'label': '1344.2375.168.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.c1.a1', 'old_label': '168.n1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062717
{'ambient': '1344.2375', 'aut_centralizer_order': 4032, 'aut_label': '168.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '56.o1.a1', '84.a1.a1'], 'contains': ['336.c1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7020, -1, 5721, -1, 6396, -1, 5779, -1], 'generators': [168], 'label': '1344.2375.168.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '84.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '168.o1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062718
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '56.p1.a1', '84.b1.a1'], 'contains': ['336.h1.a1', '336.i1.a1', '336.j1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [817, -1, 38, -1, 1500, -1, 1403, -1], 'generators': [97, 2], 'label': '1344.2375.168.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.p1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062719
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '168.p1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '4.2', 'aut_weyl_index': 8064, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.b1', '56.p1.b1', '84.b1.a1'], 'contains': ['336.h1.a1', '336.i1.b1', '336.j1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [817, -1, 769, -1, 1500, -1, 1652, -1], 'generators': [1, 2], 'label': '1344.2375.168.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.a1.a1', 'old_label': '168.p1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.p1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062720
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.h1.b1', '8.i1.a1', '8.n1.a1', '12.l1.b1', '28.l1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8130, -1, 9723, -1, 9528, -1, 7298, -1], 'generators': [1, 192, 1012, 672, 846, 448], 'label': '1344.2375.4.l1.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': '4.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062721
{'ambient': '1344.2375', 'aut_centralizer_order': 5376, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 5376, 'centralizer': '2.f1.a1', 'complements': ['7.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.e1.b1'], 'contains': ['1344.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1878, 7562, 1501, 2708, 1923, 5881, 1188, 5822], 'generators': [192], 'label': '1344.2375.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.c1.a1', '96.a1.a1', '96.b1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '1344.2375', 'quotient_action_image': '2.1', 'quotient_action_kernel': '96.22', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062722
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '224.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.b1.a1', '112.c1.a1', '112.d1.a1', '112.e1.a1', '112.f1.a1', '112.g1.a1'], 'contains': ['448.a1.a1', '672.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2974, 4596, 4764, 5518, 4490, 4335, 3623, 4335], 'generators': [672, 448], 'label': '1344.2375.224.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1', '112.c1.a1', '112.b1.a1'], 'normal_contains': ['448.a1.a1', '672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '672.539', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.13', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062723
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '224.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '112.a1.a1', '112.h1.a1', '112.i1.a1', '112.i1.b1', '112.j1.a1'], 'contains': ['448.a1.a1', '672.b1.a1'], 'core': '224.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [258, 7375, 358, 2980, 986, 6297, 1671, 6213], 'generators': [4, 448], 'label': '1344.2375.224.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.b1.a1', 'normal_contained_in': ['32.b1.a1', '112.a1.a1'], 'normal_contains': ['448.a1.a1', '672.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.b1.a1', 'projective_image': '672.390', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.4', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062724
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '224.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '112.a1.a1', '112.k1.a1', '112.l1.a1', '112.m1.a1'], 'contains': ['448.a1.a1', '672.c1.a1'], 'core': '224.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1089, 6520, 1936, 3619, 1373, 5304, 2233, 5282], 'generators': [676, 448], 'label': '1344.2375.224.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '224.c1.a1', 'normal_contained_in': ['32.c1.a1', '112.a1.a1'], 'normal_contains': ['448.a1.a1', '672.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.c1.a1', 'projective_image': '672.410', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.3', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062725
{'ambient': '1344.2375', 'aut_centralizer_order': 576, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '112.d1.a1', '112.h1.a1', '112.k1.a1'], 'contains': ['448.a1.a1', '672.d1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [73, -1, 949, -1, 1290, -1, 1833, -1], 'generators': [1, 448], 'label': '1344.2375.224.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.e1.a1', 'old_label': '224.d1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062726
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5376, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.a1', '112.e1.a1', '112.i1.a1', '112.l1.a1'], 'contains': ['448.a1.a1', '672.e1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [661, -1, 1253, -1, 765, -1, 1995, -1], 'generators': [995, 448], 'label': '1344.2375.224.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '224.e1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062727
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.1', 'aut_weyl_index': 5376, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.e1.b1', '112.e1.a1', '112.i1.b1', '112.l1.a1'], 'contains': ['448.a1.a1', '672.e1.b1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [661, -1, 1629, -1, 765, -1, 2071, -1], 'generators': [3, 448], 'label': '1344.2375.224.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.f1.a1', 'old_label': '224.e1.b1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 72062728
{'ambient': '1344.2375', 'aut_centralizer_order': 32256, 'aut_label': '336.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1', '168.b1.a1', '168.c1.a1', '168.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1'], 'contains': ['672.a1.a1', '672.b1.a1', '672.c1.a1'], 'core': '336.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3636, 5878, 3545, 4252, 2801, 4996, 2915, 4992], 'generators': [4, 672], 'label': '1344.2375.336.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '336.a1.a1', 'normal_contained_in': ['48.a1.a1', '112.a1.a1', '168.a1.a1'], 'normal_contains': ['672.c1.a1', '672.a1.a1', '672.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '336.147', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.147', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062729
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '336.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1', '168.h1.a1', '168.j1.a1', '168.l1.a1', '168.l1.b1', '168.m1.a1', '168.n1.a1'], 'contains': ['672.a1.a1'], 'core': '336.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7289, 2926, 8528, 7569, 6898, 3278, 7087, 3325], 'generators': [340], 'label': '1344.2375.336.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.b1.a1', 'normal_contained_in': ['48.b1.a1', '112.b1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '336.149', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.149', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062730
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '336.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1', '168.i1.a1', '168.k1.a1', '168.o1.a1'], 'contains': ['672.a1.a1'], 'core': '336.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6610, 2527, 5657, 6447, 5437, 3999, 5008, 4009], 'generators': [336], 'label': '1344.2375.336.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '336.c1.a1', 'normal_contained_in': ['48.c1.a1', '112.c1.a1', '168.a1.a1'], 'normal_contains': ['672.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '336.c1.a1', 'projective_image': '336.152', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.152', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062731
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.h1.a1', '8.k1.a1', '8.m1.a1', '12.m1.a1', '28.m1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8510, -1, 7576, -1, 8192, -1, 9257, -1], 'generators': [125, 192, 340, 672, 734, 448], 'label': '1344.2375.4.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062732
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '112.d1.a1', '168.b1.a1', '168.h1.a1', '168.i1.a1'], 'contains': ['672.a1.a1', '672.d1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [3384, -1, 5789, -1, 4386, -1, 3542, -1], 'generators': [1, 672], 'label': '1344.2375.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '336.d1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062733
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '112.e1.a1', '168.c1.a1', '168.j1.a1', '168.k1.a1'], 'contains': ['672.a1.a1', '672.e1.a1', '672.e1.b1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3530, -1, 4102, -1, 4580, -1, 3456, -1], 'generators': [3, 672], 'label': '1344.2375.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '336.e1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062734
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '112.f1.a1', '168.f1.a1', '168.h1.a1', '168.i1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [5493, -1, 6190, -1, 4787, -1, 4471, -1], 'generators': [49], 'label': '1344.2375.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.d1.a1', 'old_label': '336.f1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062735
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '112.g1.a1', '168.g1.a1', '168.j1.a1', '168.k1.a1'], 'contains': ['672.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [5196, -1, 4516, -1, 5121, -1, 4289, -1], 'generators': [595], 'label': '1344.2375.336.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '336.g1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062736
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '112.h1.a1', '168.b1.a1', '168.p1.a1', '168.p1.b1'], 'contains': ['672.b1.a1', '672.d1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [747, -1, 509, -1, 1821, -1, 1590, -1], 'generators': [1, 4], 'label': '1344.2375.336.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1.a1', 'old_label': '336.h1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062737
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '112.i1.a1', '168.c1.a1', '168.p1.a1'], 'contains': ['672.b1.a1', '672.e1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1470, -1, 37, -1, 1463, -1, 1428, -1], 'generators': [995, 4], 'label': '1344.2375.336.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '336.i1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062738
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '112.i1.b1', '168.c1.a1', '168.p1.b1'], 'contains': ['672.b1.a1', '672.e1.b1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1470, -1, 1099, -1, 1463, -1, 1752, -1], 'generators': [3, 4], 'label': '1344.2375.336.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '336.i1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062739
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '112.j1.a1', '168.d1.a1', '168.p1.a1', '168.p1.b1'], 'contains': ['672.b1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [905, -1, 201, -1, 1732, -1, 1509, -1], 'generators': [2], 'label': '1344.2375.336.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '336.j1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062740
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '112.k1.a1', '168.b1.a1'], 'contains': ['672.c1.a1', '672.d1.a1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [1236, -1, 1786, -1, 2205, -1, 1914, -1], 'generators': [1, 676], 'label': '1344.2375.336.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.c1.a1', 'old_label': '336.k1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062741
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '112.l1.a1', '168.c1.a1'], 'contains': ['672.c1.a1', '672.e1.a1', '672.e1.b1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2221, -1, 2023, -1, 1642, -1, 2152, -1], 'generators': [3, 676], 'label': '1344.2375.336.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '336.l1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062742
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['8.h1.b1', '8.k1.a1', '8.m1.a1', '12.m1.b1', '28.m1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8510, -1, 8431, -1, 8192, -1, 9429, -1], 'generators': [125, 192, 340, 672, 846, 448], 'label': '1344.2375.4.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '4.m1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062743
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '112.m1.a1', '168.e1.a1'], 'contains': ['672.c1.a1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2501, -1, 2418, -1, 2295, -1, 2308, -1], 'generators': [118], 'label': '1344.2375.336.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '336.m1.a1', 'projective_image': '672.410', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062744
{'ambient': '1344.2375', 'aut_centralizer_order': 16128, 'aut_label': '448.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 16128, 'centralizer': '2.b1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '224.a1.a1', '224.b1.a1', '224.c1.a1', '224.d1.a1', '224.e1.a1', '224.e1.b1'], 'contains': ['1344.a1.a1'], 'core': '448.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [285, 7032, 1339, 2915, 1290, 5593, 1995, 5552], 'generators': [448], 'label': '1344.2375.448.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '448.a1.a1', 'normal_contained_in': ['64.a1.a1', '224.c1.a1', '224.a1.a1', '224.b1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '448.a1.a1', 'projective_image': '1344.2375', 'quotient_action_image': '2.1', 'quotient_action_kernel': '224.26', 'quotient_action_kernel_order': 224, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062745
{'ambient': '1344.2375', 'aut_centralizer_order': 32256, 'aut_label': '672.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1', '336.d1.a1', '336.e1.a1', '336.f1.a1', '336.g1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4351, 4263, 4832, 5915, 4628, 4495, 3582, 4485], 'generators': [672], 'label': '1344.2375.672.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.a1.a1', 'normal_contained_in': ['96.a1.a1', '224.a1.a1', '336.a1.a1', '336.c1.a1', '336.b1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '672.539', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.539', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062746
{'ambient': '1344.2375', 'aut_centralizer_order': 32256, 'aut_label': '672.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1', '336.h1.a1', '336.i1.a1', '336.i1.b1', '336.j1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1383, 7351, 442, 3376, 1821, 6233, 1630, 6153], 'generators': [4], 'label': '1344.2375.672.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.b1.a1', 'normal_contained_in': ['96.b1.a1', '224.b1.a1', '336.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.b1.a1', 'projective_image': '672.390', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.390', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062747
{'ambient': '1344.2375', 'aut_centralizer_order': 32256, 'aut_label': '672.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '224.c1.a1', '336.a1.a1', '336.k1.a1', '336.l1.a1', '336.m1.a1'], 'contains': ['1344.a1.a1'], 'core': '672.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2269, 6727, 2023, 3785, 2107, 5304, 2152, 5282], 'generators': [676], 'label': '1344.2375.672.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '672.c1.a1', 'normal_contained_in': ['96.c1.a1', '224.c1.a1', '336.a1.a1'], 'normal_contains': ['1344.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '672.c1.a1', 'projective_image': '672.410', 'quotient_action_image': '1.1', 'quotient_action_kernel': '672.410', 'quotient_action_kernel_order': 672, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062748
{'ambient': '1344.2375', 'aut_centralizer_order': 1152, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '28.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '224.d1.a1', '336.d1.a1', '336.h1.a1', '336.k1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [547, -1, 1035, -1, 2011, -1, 1838, -1], 'generators': [1], 'label': '1344.2375.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.e1.a1', 'old_label': '672.d1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062749
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '224.e1.a1', '336.e1.a1', '336.i1.a1', '336.l1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [1986, -1, 1298, -1, 1597, -1, 1919, -1], 'generators': [995], 'label': '1344.2375.672.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '672.e1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062750
{'ambient': '1344.2375', 'aut_centralizer_order': 384, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '1.1', 'aut_weyl_index': 32256, 'centralizer': '42.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.b1', '224.e1.b1', '336.e1.a1', '336.i1.b1', '336.l1.a1'], 'contains': ['1344.a1.a1'], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [1986, -1, 1673, -1, 1597, -1, 2071, -1], 'generators': [3], 'label': '1344.2375.672.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1.a1', 'old_label': '672.e1.b1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062751
{'ambient': '1344.2375', 'aut_centralizer_order': None, 'aut_label': '1344.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': ['192.a1.a1', '448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1', '672.d1.a1', '672.e1.a1', '672.e1.b1'], 'contains': [], 'core': '1344.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1878, 7032, 1511, 3376, 1923, 5593, 1957, 5552], 'generators': [], 'label': '1344.2375.1344.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1344.a1.a1', 'normal_contained_in': ['192.a1.a1', '448.a1.a1', '672.c1.a1', '672.a1.a1', '672.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': '1344.2375', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 72062752
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '56.a1.a1', 'complements': ['224.e1.b1', '224.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '42.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8719, 749, 6893, 5854, 6308, 2769, 7445, 2848], 'generators': [1, 192, 676, 336, 168, 672], 'label': '1344.2375.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062753
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.k1.a1', '42.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5457, -1, 4632, -1, 4078, -1, 3512, -1], 'generators': [1, 192, 336, 4, 2, 672], 'label': '1344.2375.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062754
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.i1.a1', '12.j1.a1', '12.l1.a1', '12.l1.b1', '42.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9616, -1, 9027, -1, 8896, -1, 6676, -1], 'generators': [1, 192, 336, 340, 734, 672], 'label': '1344.2375.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062755
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.f1.a1', '12.j1.a1', '42.d1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7639, -1, 6711, -1, 6849, -1, 5817, -1], 'generators': [3, 192, 4, 336, 168, 672], 'label': '1344.2375.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062756
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.i1.a1', '12.m1.a1', '12.m1.b1', '42.e1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9927, -1, 7806, -1, 7999, -1, 8610, -1], 'generators': [125, 192, 336, 340, 734, 672], 'label': '1344.2375.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062757
{'ambient': '1344.2375', 'aut_centralizer_order': 12, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2688.ei', 'aut_weyl_index': 12, 'centralizer': '56.a1.a1', 'complements': ['672.e1.b1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.g1.a1', '4.i1.a1', '6.a1.a1', '14.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7193, 490, 6816, 5581, 6030, 2501, 7117, 2480], 'generators': [1, 672, 448, 676, 168, 192, 336], 'label': '1344.2375.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.g1.a1', '4.i1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062758
{'ambient': '1344.2375', 'aut_centralizer_order': 56, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1543', 'aut_weyl_index': 168, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.h1.a1', '12.i1.a1', '42.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9328, -1, 6497, -1, 6524, -1, 6111, -1], 'generators': [2, 672, 192, 4, 168, 336], 'label': '1344.2375.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062759
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1344.11704', 'aut_weyl_index': 24, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.h1.a1', '12.j1.a1', '42.g1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8931, -1, 8838, -1, 7359, -1, 7964, -1], 'generators': [125, 192, 340, 336, 2, 672], 'label': '1344.2375.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062760
{'ambient': '1344.2375', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '768.1083472', 'aut_weyl_index': 42, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '14.d1.a1', '14.e1.a1', '14.f1.a1', '14.g1.a1', '21.a1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7971, -1, 6927, -1, 6799, -1, 7529, -1], 'generators': [1, 672, 336, 2, 448, 168, 4], 'label': '1344.2375.7.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062761
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '16.i1.a1', '16.k1.a1', '24.a1.a1', '56.e1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1629, 5859, 1897, 4529, 2002, 6650, 1987, 6859], 'generators': [1, 672, 448, 4, 192], 'label': '1344.2375.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062762
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '8.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.f1.a1', '16.l1.a1', '24.d1.a1', '56.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1884, 8482, 2170, 368, 1546, 9666, 1575, 9686], 'generators': [3, 672, 448, 4, 192], 'label': '1344.2375.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1', '4.d1.a1', '4.e1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062763
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '8.c1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.b1.a1', '56.a1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6300, 2574, 5673, 6829, 6168, 4271, 5413, 4005], 'generators': [4, 448, 192, 336, 672], 'label': '1344.2375.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '4.g1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.b1.a1', '24.b1.a1', '56.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062764
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '8.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.f1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '24.e1.a1', '56.b1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2128, 4906, 2611, 3635, 1765, 7463, 1774, 7621], 'generators': [2, 192, 4, 672, 448], 'label': '1344.2375.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.a1', '4.f1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '56.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062765
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '8.e1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '24.f1.a1', '56.c1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2427, 6811, 2387, 1199, 2429, 5837, 2376, 6097], 'generators': [118, 192, 676, 672, 448], 'label': '1344.2375.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.c1.a1', '4.e1.a1', '4.f1.a1'], 'normal_contains': ['16.a1.a1', '56.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': '336.147', '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': '24.14'}
id: 72062766
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '8.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '24.c1.a1', '56.g1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3879, 7657, 3543, 2844, 3239, 8961, 3439, 9026], 'generators': [49, 448, 672, 4, 192], 'label': '1344.2375.8.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.b1.a1', '4.e1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': '336.147', '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': '56.12'}
id: 72062767
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '8.g1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.d1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '24.g1.a1', '56.h1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3351, 9369, 3291, 2053, 3588, 8240, 3151, 8350], 'generators': [595, 672, 448, 4, 192], 'label': '1344.2375.8.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.a1', '4.d1.a1', '4.k1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': '336.147', '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': '168.50'}
id: 72062768
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['672.e1.b1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.h1.a1', '4.j1.a1', '4.l1.a1', '4.l1.b1', '6.c1.a1', '14.d1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8155, 5198, 9032, 8435, 8636, 5016, 6862, 4238], 'generators': [1, 448, 336, 340, 734, 192, 672], 'label': '1344.2375.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.h1.a1', '4.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '168.50', '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': '168.50'}
id: 72062769
{'ambient': '1344.2375', 'aut_centralizer_order': 112, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '24.b1.a1', 'complements': ['168.p1.b1', '168.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.a1', '4.m1.a1'], 'contains': ['16.b1.a1', '24.l1.a1', '56.d1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8700, 3527, 8016, 9632, 9428, 298, 8485, 907], 'generators': [734, 340, 672, 192, 448], 'label': '1344.2375.8.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.b1.a1', '56.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': '336.149', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062770
{'ambient': '1344.2375', 'aut_centralizer_order': 112, 'aut_label': '8.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.195', 'aut_weyl_index': 224, 'centralizer': '24.b1.a1', 'complements': ['168.p1.b1', '168.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.l1.b1', '4.m1.b1'], 'contains': ['16.b1.a1', '24.l1.b1', '56.d1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8700, 3527, 8813, 8734, 9428, 298, 8661, 280], 'generators': [846, 1012, 672, 192, 448], 'label': '1344.2375.8.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.h1.a1'], 'normal_contains': ['16.b1.a1', '56.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': '336.149', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062771
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.l1.a1', '4.l1.b1'], 'contains': ['16.b1.a1', '16.e1.a1', '16.g1.a1', '24.h1.a1', '56.i1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5367, -1, 9396, -1, 5674, -1, 5586, -1], 'generators': [1, 448, 672, 340, 192], 'label': '1344.2375.8.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.i1.a1', 'projective_image': '336.149', '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': '28.3'}
id: 72062772
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.c1.a1', '16.e1.a1', '16.g1.a1', '24.i1.a1', '56.j1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5058, -1, 6037, -1, 4340, -1, 4278, -1], 'generators': [1, 448, 672, 336, 192], 'label': '1344.2375.8.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.j1.a1', 'projective_image': '336.152', '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': '28.3'}
id: 72062773
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.m1.a1', '4.m1.b1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.h1.a1', '24.j1.a1', '56.k1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5779, -1, 7300, -1, 5864, -1, 7012, -1], 'generators': [3, 672, 448, 340, 192], 'label': '1344.2375.8.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.k1.a1', 'projective_image': '336.149', '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': '84.8'}
id: 72062774
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.h1.a1', '24.k1.a1', '56.l1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4533, -1, 4507, -1, 4531, -1, 4105, -1], 'generators': [3, 672, 448, 336, 192], 'label': '1344.2375.8.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.l1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062775
{'ambient': '1344.2375', 'aut_centralizer_order': 48, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '4.m1.a1', '4.m1.b1'], 'contains': ['16.b1.a1', '24.m1.a1', '56.m1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7571, -1, 8383, -1, 7886, -1, 9638, -1], 'generators': [125, 340, 672, 448, 192], 'label': '1344.2375.8.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062776
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.l1.a1', '4.l1.b1'], 'contains': ['16.b1.a1', '24.n1.a1', '56.n1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7150, -1, 9685, -1, 9941, -1, 6862, -1], 'generators': [971, 672, 448, 340, 192], 'label': '1344.2375.8.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.n1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062777
{'ambient': '1344.2375', 'aut_centralizer_order': 336, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.52', 'aut_weyl_index': 672, 'centralizer': '4.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.c1.a1', '24.o1.a1', '56.o1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6716, -1, 4866, -1, 6017, -1, 5276, -1], 'generators': [168, 192, 336, 448, 672], 'label': '1344.2375.8.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '8.o1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062778
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.d1.a1', '16.i1.a1', '16.j1.a1', '24.p1.a1', '56.p1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [594, -1, 424, -1, 490, -1, 330, -1], 'generators': [97, 4, 448, 2, 192], 'label': '1344.2375.8.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.p1.a1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062779
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.g1.a1', '4.j1.a1', '6.d1.a1', '14.e1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6876, 3034, 6413, 7397, 6589, 5961, 5873, 5124], 'generators': [3, 448, 4, 336, 168, 192, 672], 'label': '1344.2375.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.g1.a1', '4.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062780
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1008.906', 'aut_weyl_index': 32, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.d1.b1', '16.i1.a1', '16.j1.a1', '24.p1.b1', '56.p1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [594, -1, 612, -1, 490, -1, 578, -1], 'generators': [1, 4, 448, 2, 192], 'label': '1344.2375.8.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.p1.b1', 'projective_image': '672.390', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': '84.8'}
id: 72062781
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.h1.a1', '24.i1.a1', '84.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6427, 4770, 6749, 5373, 5208, 5024, 4699, 5334], 'generators': [1, 336, 672, 4, 192], 'label': '1344.2375.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062782
{'ambient': '1344.2375', 'aut_centralizer_order': 672, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.52', 'aut_weyl_index': 672, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.a1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '24.o1.a1', '84.a1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7493, 341, 6357, 7266, 6548, 2281, 5758, 2766], 'generators': [4, 192, 336, 168, 672], 'label': '1344.2375.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.g1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '84.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062783
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '28.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.a1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.m1.a1', '84.i1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9121, 1114, 8277, 6205, 7509, 2941, 8837, 3385], 'generators': [125, 340, 672, 336, 192], 'label': '1344.2375.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.i1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062784
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '24.p1.a1', '24.p1.b1', '84.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2626, -1, 2735, -1, 2221, -1, 1391, -1], 'generators': [1, 672, 4, 2, 192], 'label': '1344.2375.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062785
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '84.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3540, -1, 3079, -1, 2964, -1, 2541, -1], 'generators': [1, 4, 672, 118, 192], 'label': '1344.2375.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062786
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.b1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.g1.a1', '24.j1.a1', '24.k1.a1', '84.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6007, -1, 5296, -1, 5455, -1, 4475, -1], 'generators': [3, 336, 672, 4, 192], 'label': '1344.2375.12.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062787
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '84.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3980, -1, 3217, -1, 2826, -1, 2666, -1], 'generators': [49, 4, 672, 118, 192], 'label': '1344.2375.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062788
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.52', 'aut_weyl_index': 672, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.f1.a1', '84.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4810, -1, 5036, -1, 4149, -1, 3612, -1], 'generators': [2, 192, 4, 336, 672], 'label': '1344.2375.12.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062789
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.52', 'aut_weyl_index': 672, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '24.l1.a1', '24.l1.b1', '84.h1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9634, -1, 7955, -1, 8589, -1, 8136, -1], 'generators': [734, 192, 340, 336, 672], 'label': '1344.2375.12.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062790
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['672.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.h1.a1', '4.i1.a1', '4.m1.a1', '4.m1.b1', '6.e1.a1', '14.f1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8487, 3987, 7691, 6505, 7753, 3342, 8708, 3269], 'generators': [125, 448, 336, 340, 734, 192, 672], 'label': '1344.2375.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.h1.a1', '4.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062791
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.n1.a1', '84.j1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8439, -1, 9031, -1, 9233, -1, 6411, -1], 'generators': [971, 340, 672, 336, 192], 'label': '1344.2375.12.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062792
{'ambient': '1344.2375', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '672.1266', 'aut_weyl_index': 48, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.g1.a1', '84.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5335, -1, 4071, -1, 3405, -1, 2986, -1], 'generators': [49, 4, 672, 2, 192], 'label': '1344.2375.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062793
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.c1.a1'], 'contains': ['24.h1.a1', '24.l1.a1', '24.n1.a1', '84.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9403, -1, 9779, -1, 9803, -1, 6737, -1], 'generators': [1, 340, 672, 734, 192], 'label': '1344.2375.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062794
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '6.c1.a1'], 'contains': ['24.h1.a1', '24.l1.b1', '24.n1.a1', '84.l1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9403, -1, 9962, -1, 9803, -1, 7395, -1], 'generators': [1, 1012, 672, 846, 192], 'label': '1344.2375.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.l1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062795
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.l1.a1', '24.m1.a1', '84.m1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9828, -1, 7519, -1, 8415, -1, 9333, -1], 'generators': [125, 340, 672, 734, 192], 'label': '1344.2375.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '12.m1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062796
{'ambient': '1344.2375', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '336.216', 'aut_weyl_index': 96, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.b1', '6.e1.a1'], 'contains': ['24.j1.a1', '24.l1.b1', '24.m1.a1', '84.m1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9828, -1, 8671, -1, 8415, -1, 9478, -1], 'generators': [125, 340, 672, 846, 192], 'label': '1344.2375.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '12.m1.b1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062797
{'ambient': '1344.2375', 'aut_centralizer_order': 168, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '24.b1.a1', 'complements': ['96.d1.a1', '96.e1.b1', '96.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1', '42.f1.a1'], 'core': '14.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7927, 2320, 5887, 7793, 6169, 1600, 6307, 1752], 'generators': [2, 448, 672, 168, 4, 336], 'label': '1344.2375.14.a1.a1', 'mobius_quo': 0, 'mobius_sub': 7, 'normal_closure': '14.a1.a1', 'normal_contained_in': ['2.f1.a1'], 'normal_contains': ['28.a1.a1', '28.b1.a1', '28.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14.a1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062798
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.d1.a1', '28.e1.a1', '28.f1.a1', '28.g1.a1', '28.h1.a1', '28.k1.a1', '42.a1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [4254, -1, 4277, -1, 3660, -1, 3890, -1], 'generators': [1, 448, 672, 2, 336, 4], 'label': '1344.2375.14.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.b1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062799
{'ambient': '1344.2375', 'aut_centralizer_order': 72, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '64.267', 'aut_weyl_index': 504, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.e1.a1', '28.i1.a1', '42.b1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7263, -1, 6868, -1, 5990, -1, 7608, -1], 'generators': [1, 672, 336, 168, 448, 676], 'label': '1344.2375.14.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.c1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062800
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '14.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.e1.a1', '28.j1.a1', '28.l1.a1', '28.l1.b1', '42.c1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8363, -1, 8943, -1, 8636, -1, 7080, -1], 'generators': [1, 448, 672, 734, 336, 340], 'label': '1344.2375.14.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.d1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062801
{'ambient': '1344.2375', 'aut_centralizer_order': 28, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.153311', 'aut_weyl_index': 28, 'centralizer': '24.b1.a1', 'complements': ['672.d1.a1', '672.e1.b1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.f1.a1', '4.g1.a1', '4.h1.a1', '6.f1.a1', '14.a1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7843, 1400, 6064, 9501, 6332, 1724, 6217, 1752], 'generators': [2, 672, 192, 4, 168, 448, 336], 'label': '1344.2375.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.f1.a1', '4.g1.a1', '4.h1.a1', '14.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062802
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '14.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '7.a1.a1'], 'contains': ['28.b1.a1', '28.g1.a1', '28.j1.a1', '42.d1.a1'], 'core': '28.b1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6936, -1, 6228, -1, 6726, -1, 5929, -1], 'generators': [3, 448, 672, 168, 4, 336], 'label': '1344.2375.14.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.e1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062803
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '14.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '84.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '7.a1.a1'], 'contains': ['28.c1.a1', '28.g1.a1', '28.i1.a1', '28.m1.a1', '28.m1.b1', '42.e1.a1'], 'core': '28.c1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8761, -1, 7491, -1, 7753, -1, 9007, -1], 'generators': [125, 448, 672, 734, 336, 340], 'label': '1344.2375.14.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.f1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 72062804
{'ambient': '1344.2375', 'aut_centralizer_order': 24, 'aut_label': '14.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1542', 'aut_weyl_index': 168, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '7.a1.a1'], 'contains': ['28.a1.a1', '28.i1.a1', '28.j1.a1', '42.g1.a1'], 'core': '28.a1.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7519, -1, 9166, -1, 7204, -1, 8104, -1], 'generators': [125, 448, 672, 2, 340, 336], 'label': '1344.2375.14.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1.a1', 'old_label': '14.g1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 72062805
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '16.a1', 'aut_quo_index': 96, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '112.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1851, 7116, 2390, 3103, 1930, 7299, 2029, 7095], 'generators': [4, 448, 192, 672], 'label': '1344.2375.16.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.e1.a1', '8.d1.a1', '8.f1.a1', '8.g1.a1'], 'normal_contains': ['32.c1.a1', '32.a1.a1', '32.b1.a1', '48.a1.a1', '112.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '336.147', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062806
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '16.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1', '8.k1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '112.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6291, 3527, 8319, 8611, 7401, 1948, 7133, 2078], 'generators': [340, 192, 672, 448], 'label': '1344.2375.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.c1.a1', '8.h1.b1', '8.h1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1', '112.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '336.149', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062807
{'ambient': '1344.2375', 'aut_centralizer_order': 1344, 'aut_label': '16.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '4.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.j1.a1', '8.l1.a1', '8.o1.a1'], 'contains': ['32.a1.a1', '48.c1.a1', '112.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5265, 2217, 4992, 5717, 5521, 4155, 5277, 4148], 'generators': [336, 192, 672, 448], 'label': '1344.2375.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '112.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '336.152', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062808
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': ['84.l1.a1', '84.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.p1.a1'], 'contains': ['32.b1.a1', '32.e1.a1', '48.i1.a1', '112.i1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [826, 8196, 510, 623, 149, 8792, 131, 8459], 'generators': [995, 448, 192, 4], 'label': '1344.2375.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '672.390', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062809
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '16.d1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': ['84.l1.a1', '84.l1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.p1.b1'], 'contains': ['32.b1.a1', '32.e1.b1', '48.i1.b1', '112.i1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [826, 8196, 892, 1300, 149, 8792, 638, 9240], 'generators': [3, 448, 192, 4], 'label': '1344.2375.16.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.b1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '672.390', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062810
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.d1.a1', '112.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2632, -1, 5341, -1, 4192, -1, 3371, -1], 'generators': [1, 448, 192, 672], 'label': '1344.2375.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.e1.a1', 'projective_image': '672.539', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062811
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.e1.b1', '48.e1.a1', '112.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2300, -1, 3667, -1, 4324, -1, 2674, -1], 'generators': [3, 448, 192, 672], 'label': '1344.2375.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.f1.a1', 'projective_image': '672.539', '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': '84.8'}
id: 72062812
{'ambient': '1344.2375', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '168.a1.a1', 'complements': ['672.d1.a1', '672.e1.b1', '672.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.f1.a1', '4.i1.a1', '4.j1.a1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7546, 2232, 9291, 4802, 7297, 4115, 7836, 5766], 'generators': [125, 448, 340, 336, 2, 192, 672], 'label': '1344.2375.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.f1.a1', '4.i1.a1', '4.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '168.50'}
id: 72062813
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.i1.a1', '8.j1.a1'], 'contains': ['32.a1.a1', '48.f1.a1', '112.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4711, -1, 5647, -1, 4568, -1, 4541, -1], 'generators': [49, 672, 192, 448], 'label': '1344.2375.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.g1.a1', 'projective_image': '672.539', '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': '28.3'}
id: 72062814
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.k1.a1', '8.l1.a1'], 'contains': ['32.a1.a1', '48.g1.a1', '112.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3499, -1, 4532, -1, 5084, -1, 4390, -1], 'generators': [595, 448, 192, 672], 'label': '1344.2375.16.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.h1.a1', 'projective_image': '672.539', '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': '84.8'}
id: 72062815
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.b1.a1', '32.d1.a1', '48.h1.a1', '112.h1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [260, -1, 380, -1, 578, -1, 519, -1], 'generators': [1, 448, 192, 4], 'label': '1344.2375.16.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '672.390', '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': '28.3'}
id: 72062816
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.48', 'aut_weyl_index': 448, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.b1.a1', '48.j1.a1', '112.j1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [660, -1, 183, -1, 402, -1, 266, -1], 'generators': [2, 4, 448, 192], 'label': '1344.2375.16.j1.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.j1.a1', 'projective_image': '672.390', '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': '12.4'}
id: 72062817
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['32.c1.a1', '32.d1.a1', '48.k1.a1', '112.k1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1021, -1, 1343, -1, 738, -1, 757, -1], 'generators': [1, 448, 192, 676], 'label': '1344.2375.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.k1.a1', 'projective_image': '672.410', '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': '28.3'}
id: 72062818
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '504.162', 'aut_weyl_index': 64, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.c1.a1', '32.e1.a1', '32.e1.b1', '48.l1.a1', '112.l1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1277, -1, 1541, -1, 253, -1, 876, -1], 'generators': [3, 448, 192, 676], 'label': '1344.2375.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.l1.a1', 'projective_image': '672.410', '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': '84.8'}
id: 72062819
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.48', 'aut_weyl_index': 448, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1'], 'contains': ['32.c1.a1', '48.m1.a1', '112.m1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2064, -1, 1767, -1, 1018, -1, 1372, -1], 'generators': [118, 676, 448, 192], 'label': '1344.2375.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '16.m1.a1', 'projective_image': '672.410', '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': '12.4'}
id: 72062820
{'ambient': '1344.2375', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '128.2328', 'aut_weyl_index': 252, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '7.a1.a1'], 'contains': ['42.a1.a1', '42.b1.a1', '42.c1.a1', '42.d1.a1', '42.e1.a1', '42.f1.a1', '42.g1.a1'], 'core': '84.a1.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9424, -1, 7115, -1, 7022, -1, 7800, -1], 'generators': [1, 2, 168], 'label': '1344.2375.21.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1.a1', 'old_label': '21.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 72062821
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.d1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.h1.a1', '48.k1.a1', '168.b1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2237, 5432, 2590, 4767, 2492, 5985, 1715, 5864], 'generators': [1, 672, 192, 4], 'label': '1344.2375.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062822
{'ambient': '1344.2375', 'aut_centralizer_order': 2688, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 2688, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.f1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '168.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6936, 1321, 6527, 6311, 7096, 3650, 5834, 3674], 'generators': [4, 192, 672, 336], 'label': '1344.2375.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.b1.a1', '168.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '168.50', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 72062823
{'ambient': '1344.2375', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '21.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9164, -1, 7105, -1, 7022, -1, 7327, -1], 'generators': [1, 672, 168, 4, 2, 192, 336], 'label': '1344.2375.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '168.50', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062824
{'ambient': '1344.2375', 'aut_centralizer_order': 192, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.a1.a1', '12.g1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '168.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5232, 6370, 3585, 3887, 3821, 6638, 3805, 6476], 'generators': [49, 672, 192, 4], 'label': '1344.2375.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.f1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '56.12'}
id: 72062825
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '48.i1.a1', '48.i1.b1', '48.l1.a1', '168.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3214, -1, 2772, -1, 2117, -1, 1200, -1], 'generators': [3, 672, 192, 4], 'label': '1344.2375.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062826
{'ambient': '1344.2375', 'aut_centralizer_order': 448, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.a1', '12.h1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.j1.a1', '168.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2860, -1, 3907, -1, 2304, -1, 1546, -1], 'generators': [2, 192, 4, 672], 'label': '1344.2375.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062827
{'ambient': '1344.2375', 'aut_centralizer_order': 448, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.e1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.m1.a1', '168.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3618, -1, 3132, -1, 2873, -1, 2541, -1], 'generators': [118, 192, 676, 672], 'label': '1344.2375.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 72062828
{'ambient': '1344.2375', 'aut_centralizer_order': 64, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.e1.a1', '12.f1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.g1.a1', '168.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4872, -1, 4141, -1, 4015, -1, 3531, -1], 'generators': [595, 672, 192, 4], 'label': '1344.2375.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '336.147', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062829
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.a1.a1', '12.l1.a1', '12.l1.b1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.f1.a1', '168.h1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6595, -1, 9963, -1, 6658, -1, 6257, -1], 'generators': [1, 672, 192, 340], 'label': '1344.2375.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.h1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062830
{'ambient': '1344.2375', 'aut_centralizer_order': 96, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '56.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.a1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.f1.a1', '168.i1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6143, -1, 6046, -1, 4935, -1, 4845, -1], 'generators': [1, 672, 192, 336], 'label': '1344.2375.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.i1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '28.3'}
id: 72062831
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.f1.a1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.g1.a1', '168.j1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6319, -1, 7357, -1, 6818, -1, 7252, -1], 'generators': [3, 672, 192, 340], 'label': '1344.2375.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.j1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062832
{'ambient': '1344.2375', 'aut_centralizer_order': 32, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '168.47', 'aut_weyl_index': 192, 'centralizer': '84.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.f1.a1'], 'contains': ['48.c1.a1', '48.e1.a1', '48.g1.a1', '168.k1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5721, -1, 4753, -1, 5390, -1, 4701, -1], 'generators': [3, 672, 192, 336], 'label': '1344.2375.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.k1.a1', 'projective_image': '336.152', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '14.1'}
id: 72062833
{'ambient': '1344.2375', 'aut_centralizer_order': 224, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.15', 'aut_weyl_index': 1344, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.i1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.b1.a1', '168.l1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9140, -1, 8120, -1, 8575, -1, 8034, -1], 'generators': [734, 340, 672, 192], 'label': '1344.2375.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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