LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-11-23T21:32:25.569647

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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 10, 10, 20, 10, 10], 'aut_gens': [[1, 2, 4], [481, 266, 916], [385, 794, 980], [865, 2, 580], [577, 2, 604], [193, 794, 916], [481, 530, 140], [1009, 530, 164]], 'aut_group': None, 'aut_hash': 7590525614158771080, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7040, 'aut_permdeg': 32, 'aut_perms': [87646255760768156228336013070246293, 158165816995166706727577525569056736, 255215826280229786484301380205678187, 125407501289921654614209707562396823, 1787059005648788702591613118682988, 199207148969919270019957330271220890, 79207701880375659609180549650192591], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 22, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 22, 1, 1], [4, 44, 1, 1], [6, 1, 2, 1], [6, 4, 2, 2], [6, 22, 2, 1], [6, 44, 2, 1], [8, 4, 1, 1], [8, 44, 1, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 22, 2, 1], [12, 44, 2, 1], [22, 2, 5, 1], [22, 8, 5, 2], [24, 4, 2, 1], [24, 44, 2, 1], [33, 2, 10, 1], [44, 4, 5, 1], [66, 2, 10, 1], [66, 8, 10, 2], [88, 4, 10, 1], [132, 4, 10, 1], [264, 4, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.(C_2^5\\times C_{10})', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '440.42', 'autcentquo_hash': 42, 'autcentquo_nilpotent': False, 'autcentquo_order': 440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [2, 22, 1], [2, 44, 1], [3, 1, 2], [4, 2, 1], [4, 22, 1], [4, 44, 1], [6, 1, 2], [6, 4, 4], [6, 22, 2], [6, 44, 2], [8, 4, 1], [8, 44, 1], [11, 2, 5], [12, 2, 2], [12, 22, 2], [12, 44, 2], [22, 2, 5], [22, 8, 10], [24, 4, 2], [24, 44, 2], [33, 2, 10], [44, 4, 5], [66, 2, 10], [66, 8, 20], [88, 4, 10], [132, 4, 10], [264, 4, 20]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '176.31', 'commutator_count': 1, 'commutator_label': '44.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 615, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['352.106', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 22, 1, 1], [2, 44, 1, 1], [3, 1, 2, 1], [4, 2, 1, 1], [4, 22, 1, 1], [4, 44, 1, 1], [6, 1, 2, 1], [6, 4, 2, 2], [6, 22, 2, 1], [6, 44, 2, 1], [8, 4, 1, 1], [8, 44, 1, 1], [11, 2, 5, 1], [12, 2, 2, 1], [12, 22, 2, 1], [12, 44, 2, 1], [22, 2, 5, 1], [22, 8, 5, 2], [24, 4, 2, 1], [24, 44, 2, 1], [33, 2, 10, 1], [44, 4, 5, 1], [66, 2, 10, 1], [66, 8, 10, 2], [88, 4, 10, 1], [132, 4, 10, 1], [264, 4, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 52416, 'exponent': 264, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[4, 0, 20]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '264.36', 'hash': 615, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 44, 'inner_gen_orders': [2, 2, 44], 'inner_gens': [[1, 530, 436], [529, 2, 796], [625, 266, 4]], 'inner_hash': 31, 'inner_nilpotent': False, 'inner_order': 176, 'inner_split': True, 'inner_tex': 'D_4\\times D_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 66], [4, 48]], 'label': '1056.615', 'linC_count': 20, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 32, 'linQ_dim': 16, 'linQ_dim_count': 32, 'linR_count': 190, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C24:D22', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 34, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 138, 'number_divisions': 34, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 132, 'number_subgroup_classes': 136, 'number_subgroups': 1012, 'old_label': None, 'order': 1056, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 75], [3, 2], [4, 68], [6, 150], [8, 48], [11, 10], [12, 136], [22, 90], [24, 96], [33, 20], [44, 20], [66, 180], [88, 40], [132, 40], [264, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 10], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[529, 2, 964], [1, 530, 964], [1, 530, 164]], 'outer_group': '40.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [3628800, 720, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 3], [8, 1], [10, 4], [20, 5], [40, 2], [80, 1]], 'representations': {'PC': {'code': 120006915383935325500681169650575812497407960000019, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -11, 7421, 9158, 8367, 58, 24419, 7514, 80, 24084, 102, 13445, 166, 47046]}, 'Perm': {'d': 22, 'gens': [2439325392329553894, 572, 12341, 3991680, 18523, 5329, 55969592955889536000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{24}:D_{22}', 'transitive_degree': 264, '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: 111692697
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 615, 'group_order': 1056, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
id: 111692747
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 615, 'group_order': 1056, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 528, 'size': 1}
id: 111692758
{'aut_label': '2B', 'centralizer': '4.i1.a1', 'counter': 3, 'group_counter': 615, 'group_order': 1056, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 2, 'size': 4}
id: 111692769
{'aut_label': '2C', 'centralizer': '4.j1.a1', 'counter': 4, 'group_counter': 615, 'group_order': 1056, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 134, 'size': 4}
id: 111692780
{'aut_label': '2D', 'centralizer': '22.d1.a1', 'counter': 5, 'group_counter': 615, 'group_order': 1056, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 385, 'size': 22}
id: 111692791
{'aut_label': '2E', 'centralizer': '44.f1.a1', 'counter': 6, 'group_counter': 615, 'group_order': 1056, 'label': '2E', 'order': 2, 'powers': [1, 6, 6, 6], 'representative': 183, 'size': 44}
id: 111692802
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 615, 'group_order': 1056, 'label': '3A1', 'order': 3, 'powers': [8, 1, 8, 8], 'representative': 352, 'size': 1}
id: 111692813
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 615, 'group_order': 1056, 'label': '3A-1', 'order': 3, 'powers': [7, 1, 7, 7], 'representative': 704, 'size': 1}
id: 111692824
{'aut_label': '4A', 'centralizer': '2.f1.a1', 'counter': 9, 'group_counter': 615, 'group_order': 1056, 'label': '4A', 'order': 4, 'powers': [2, 9, 9, 9], 'representative': 264, 'size': 2}
id: 111692698
{'aut_label': '4B', 'centralizer': '22.b1.a1', 'counter': 10, 'group_counter': 615, 'group_order': 1056, 'label': '4B', 'order': 4, 'powers': [2, 10, 10, 10], 'representative': 889, 'size': 22}
id: 111692709
{'aut_label': '4C', 'centralizer': '44.e1.a1', 'counter': 11, 'group_counter': 615, 'group_order': 1056, 'label': '4C', 'order': 4, 'powers': [2, 11, 11, 11], 'representative': 627, 'size': 44}
id: 111692720
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 615, 'group_order': 1056, 'label': '6A1', 'order': 6, 'powers': [8, 2, 13, 13], 'representative': 880, 'size': 1}
id: 111692731
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 615, 'group_order': 1056, 'label': '6A-1', 'order': 6, 'powers': [7, 2, 12, 12], 'representative': 176, 'size': 1}
id: 111692741
{'aut_label': '6B1', 'centralizer': '4.i1.a1', 'counter': 14, 'group_counter': 615, 'group_order': 1056, 'label': '6B1', 'order': 6, 'powers': [8, 3, 15, 15], 'representative': 354, 'size': 4}
id: 111692742
{'aut_label': '6B1', 'centralizer': '4.i1.a1', 'counter': 15, 'group_counter': 615, 'group_order': 1056, 'label': '6B-1', 'order': 6, 'powers': [7, 3, 14, 14], 'representative': 706, 'size': 4}
id: 111692743
{'aut_label': '6C1', 'centralizer': '4.j1.a1', 'counter': 16, 'group_counter': 615, 'group_order': 1056, 'label': '6C1', 'order': 6, 'powers': [7, 4, 17, 17], 'representative': 838, 'size': 4}
id: 111692744
{'aut_label': '6C1', 'centralizer': '4.j1.a1', 'counter': 17, 'group_counter': 615, 'group_order': 1056, 'label': '6C-1', 'order': 6, 'powers': [8, 4, 16, 16], 'representative': 486, 'size': 4}
id: 111692745
{'aut_label': '6D1', 'centralizer': '22.d1.a1', 'counter': 18, 'group_counter': 615, 'group_order': 1056, 'label': '6D1', 'order': 6, 'powers': [7, 5, 19, 19], 'representative': 33, 'size': 22}
id: 111692746
{'aut_label': '6D1', 'centralizer': '22.d1.a1', 'counter': 19, 'group_counter': 615, 'group_order': 1056, 'label': '6D-1', 'order': 6, 'powers': [8, 5, 18, 18], 'representative': 17, 'size': 22}
id: 111692748
{'aut_label': '6E1', 'centralizer': '44.f1.a1', 'counter': 20, 'group_counter': 615, 'group_order': 1056, 'label': '6E1', 'order': 6, 'powers': [8, 6, 21, 21], 'representative': 535, 'size': 44}
id: 111692749
{'aut_label': '6E1', 'centralizer': '44.f1.a1', 'counter': 21, 'group_counter': 615, 'group_order': 1056, 'label': '6E-1', 'order': 6, 'powers': [7, 6, 20, 20], 'representative': 887, 'size': 44}
id: 111692750
{'aut_label': '8A', 'centralizer': '4.f1.a1', 'counter': 22, 'group_counter': 615, 'group_order': 1056, 'label': '8A', 'order': 8, 'powers': [9, 22, 22, 22], 'representative': 132, 'size': 4}
id: 111692751
{'aut_label': '8B', 'centralizer': '44.k1.a1', 'counter': 23, 'group_counter': 615, 'group_order': 1056, 'label': '8B', 'order': 8, 'powers': [9, 23, 23, 23], 'representative': 877, 'size': 44}
id: 111692752
{'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 24, 'group_counter': 615, 'group_order': 1056, 'label': '11A1', 'order': 11, 'powers': [25, 26, 28, 1], 'representative': 192, 'size': 2}
id: 111692753
{'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 25, 'group_counter': 615, 'group_order': 1056, 'label': '11A2', 'order': 11, 'powers': [27, 28, 24, 1], 'representative': 384, 'size': 2}
id: 111692754
{'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 615, 'group_order': 1056, 'label': '11A3', 'order': 11, 'powers': [28, 25, 27, 1], 'representative': 576, 'size': 2}
id: 111692755
{'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 615, 'group_order': 1056, 'label': '11A4', 'order': 11, 'powers': [26, 24, 25, 1], 'representative': 768, 'size': 2}
id: 111692756
{'aut_label': '11A1', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 615, 'group_order': 1056, 'label': '11A5', 'order': 11, 'powers': [24, 27, 26, 1], 'representative': 960, 'size': 2}
id: 111692757
{'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 29, 'group_counter': 615, 'group_order': 1056, 'label': '12A1', 'order': 12, 'powers': [13, 9, 30, 30], 'representative': 88, 'size': 2}
id: 111692759
{'aut_label': '12A1', 'centralizer': '2.f1.a1', 'counter': 30, 'group_counter': 615, 'group_order': 1056, 'label': '12A-1', 'order': 12, 'powers': [12, 9, 29, 29], 'representative': 968, 'size': 2}
id: 111692760
{'aut_label': '12B1', 'centralizer': '22.b1.a1', 'counter': 31, 'group_counter': 615, 'group_order': 1056, 'label': '12B1', 'order': 12, 'powers': [12, 10, 32, 32], 'representative': 9, 'size': 22}
id: 111692761
{'aut_label': '12B1', 'centralizer': '22.b1.a1', 'counter': 32, 'group_counter': 615, 'group_order': 1056, 'label': '12B-1', 'order': 12, 'powers': [13, 10, 31, 31], 'representative': 41, 'size': 22}
id: 111692762
{'aut_label': '12C1', 'centralizer': '44.e1.a1', 'counter': 33, 'group_counter': 615, 'group_order': 1056, 'label': '12C1', 'order': 12, 'powers': [12, 11, 34, 34], 'representative': 803, 'size': 44}
id: 111692763
{'aut_label': '12C1', 'centralizer': '44.e1.a1', 'counter': 34, 'group_counter': 615, 'group_order': 1056, 'label': '12C-1', 'order': 12, 'powers': [13, 11, 33, 33], 'representative': 979, 'size': 44}
id: 111692764
{'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 35, 'group_counter': 615, 'group_order': 1056, 'label': '22A1', 'order': 22, 'powers': [28, 36, 37, 2], 'representative': 48, 'size': 2}
id: 111692765
{'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 36, 'group_counter': 615, 'group_order': 1056, 'label': '22A3', 'order': 22, 'powers': [27, 39, 38, 2], 'representative': 144, 'size': 2}
id: 111692766
{'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 37, 'group_counter': 615, 'group_order': 1056, 'label': '22A5', 'order': 22, 'powers': [26, 38, 36, 2], 'representative': 240, 'size': 2}
id: 111692767
{'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 38, 'group_counter': 615, 'group_order': 1056, 'label': '22A7', 'order': 22, 'powers': [25, 35, 39, 2], 'representative': 336, 'size': 2}
id: 111692768
{'aut_label': '22A1', 'centralizer': '2.a1.a1', 'counter': 39, 'group_counter': 615, 'group_order': 1056, 'label': '22A9', 'order': 22, 'powers': [24, 37, 35, 2], 'representative': 432, 'size': 2}
id: 111692770
{'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 40, 'group_counter': 615, 'group_order': 1056, 'label': '22B1', 'order': 22, 'powers': [24, 41, 42, 3], 'representative': 98, 'size': 8}
id: 111692771
{'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 41, 'group_counter': 615, 'group_order': 1056, 'label': '22B3', 'order': 22, 'powers': [26, 44, 43, 3], 'representative': 290, 'size': 8}
id: 111692772
{'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 42, 'group_counter': 615, 'group_order': 1056, 'label': '22B5', 'order': 22, 'powers': [28, 43, 41, 3], 'representative': 482, 'size': 8}
id: 111692773
{'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 43, 'group_counter': 615, 'group_order': 1056, 'label': '22B7', 'order': 22, 'powers': [27, 40, 44, 3], 'representative': 674, 'size': 8}
id: 111692774
{'aut_label': '22B1', 'centralizer': '8.d1.a1', 'counter': 44, 'group_counter': 615, 'group_order': 1056, 'label': '22B9', 'order': 22, 'powers': [25, 42, 40, 3], 'representative': 866, 'size': 8}
id: 111692775
{'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 45, 'group_counter': 615, 'group_order': 1056, 'label': '22C1', 'order': 22, 'powers': [27, 46, 47, 4], 'representative': 806, 'size': 8}
id: 111692776
{'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 46, 'group_counter': 615, 'group_order': 1056, 'label': '22C3', 'order': 22, 'powers': [24, 49, 48, 4], 'representative': 38, 'size': 8}
id: 111692777
{'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 47, 'group_counter': 615, 'group_order': 1056, 'label': '22C5', 'order': 22, 'powers': [25, 48, 46, 4], 'representative': 326, 'size': 8}
id: 111692778
{'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 48, 'group_counter': 615, 'group_order': 1056, 'label': '22C7', 'order': 22, 'powers': [28, 45, 49, 4], 'representative': 614, 'size': 8}
id: 111692779
{'aut_label': '22C1', 'centralizer': '8.e1.a1', 'counter': 49, 'group_counter': 615, 'group_order': 1056, 'label': '22C9', 'order': 22, 'powers': [26, 47, 45, 4], 'representative': 902, 'size': 8}
id: 111692781
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 50, 'group_counter': 615, 'group_order': 1056, 'label': '24A1', 'order': 24, 'powers': [29, 22, 51, 51], 'representative': 44, 'size': 4}
id: 111692782
{'aut_label': '24A1', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 615, 'group_order': 1056, 'label': '24A-1', 'order': 24, 'powers': [30, 22, 50, 50], 'representative': 1012, 'size': 4}
id: 111692783
{'aut_label': '24B1', 'centralizer': '44.k1.a1', 'counter': 52, 'group_counter': 615, 'group_order': 1056, 'label': '24B1', 'order': 24, 'powers': [30, 23, 53, 53], 'representative': 437, 'size': 44}
id: 111692784
{'aut_label': '24B1', 'centralizer': '44.k1.a1', 'counter': 53, 'group_counter': 615, 'group_order': 1056, 'label': '24B-1', 'order': 24, 'powers': [29, 23, 52, 52], 'representative': 1053, 'size': 44}
id: 111692785
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 54, 'group_counter': 615, 'group_order': 1056, 'label': '33A1', 'order': 33, 'powers': [56, 24, 60, 8], 'representative': 64, 'size': 2}
id: 111692786
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 55, 'group_counter': 615, 'group_order': 1056, 'label': '33A-1', 'order': 33, 'powers': [57, 24, 61, 7], 'representative': 992, 'size': 2}
id: 111692787
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 56, 'group_counter': 615, 'group_order': 1056, 'label': '33A2', 'order': 33, 'powers': [58, 25, 54, 7], 'representative': 128, 'size': 2}
id: 111692788
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 57, 'group_counter': 615, 'group_order': 1056, 'label': '33A-2', 'order': 33, 'powers': [59, 25, 55, 8], 'representative': 928, 'size': 2}
id: 111692789
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 58, 'group_counter': 615, 'group_order': 1056, 'label': '33A4', 'order': 33, 'powers': [62, 27, 56, 8], 'representative': 256, 'size': 2}
id: 111692790
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 59, 'group_counter': 615, 'group_order': 1056, 'label': '33A-4', 'order': 33, 'powers': [63, 27, 57, 7], 'representative': 800, 'size': 2}
id: 111692792
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 60, 'group_counter': 615, 'group_order': 1056, 'label': '33A5', 'order': 33, 'powers': [54, 28, 63, 7], 'representative': 320, 'size': 2}
id: 111692793
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 61, 'group_counter': 615, 'group_order': 1056, 'label': '33A-5', 'order': 33, 'powers': [55, 28, 62, 8], 'representative': 736, 'size': 2}
id: 111692794
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 62, 'group_counter': 615, 'group_order': 1056, 'label': '33A8', 'order': 33, 'powers': [61, 26, 58, 7], 'representative': 512, 'size': 2}
id: 111692795
{'aut_label': '33A1', 'centralizer': '2.a1.a1', 'counter': 63, 'group_counter': 615, 'group_order': 1056, 'label': '33A-8', 'order': 33, 'powers': [60, 26, 59, 8], 'representative': 544, 'size': 2}
id: 111692796
{'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 64, 'group_counter': 615, 'group_order': 1056, 'label': '44A1', 'order': 44, 'powers': [35, 65, 66, 9], 'representative': 24, 'size': 4}
id: 111692797
{'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 65, 'group_counter': 615, 'group_order': 1056, 'label': '44A3', 'order': 44, 'powers': [36, 68, 67, 9], 'representative': 72, 'size': 4}
id: 111692798
{'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 66, 'group_counter': 615, 'group_order': 1056, 'label': '44A5', 'order': 44, 'powers': [37, 67, 65, 9], 'representative': 120, 'size': 4}
id: 111692799
{'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 67, 'group_counter': 615, 'group_order': 1056, 'label': '44A7', 'order': 44, 'powers': [38, 64, 68, 9], 'representative': 168, 'size': 4}
id: 111692800
{'aut_label': '44A1', 'centralizer': '4.f1.a1', 'counter': 68, 'group_counter': 615, 'group_order': 1056, 'label': '44A9', 'order': 44, 'powers': [39, 66, 64, 9], 'representative': 216, 'size': 4}
id: 111692801
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 69, 'group_counter': 615, 'group_order': 1056, 'label': '66A1', 'order': 66, 'powers': [60, 35, 71, 13], 'representative': 16, 'size': 2}
id: 111692803
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 70, 'group_counter': 615, 'group_order': 1056, 'label': '66A-1', 'order': 66, 'powers': [61, 35, 72, 12], 'representative': 1040, 'size': 2}
id: 111692804
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 71, 'group_counter': 615, 'group_order': 1056, 'label': '66A5', 'order': 66, 'powers': [63, 37, 77, 12], 'representative': 80, 'size': 2}
id: 111692805
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 72, 'group_counter': 615, 'group_order': 1056, 'label': '66A-5', 'order': 66, 'powers': [62, 37, 78, 13], 'representative': 976, 'size': 2}
id: 111692806
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 73, 'group_counter': 615, 'group_order': 1056, 'label': '66A7', 'order': 66, 'powers': [56, 38, 76, 13], 'representative': 112, 'size': 2}
id: 111692807
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 74, 'group_counter': 615, 'group_order': 1056, 'label': '66A-7', 'order': 66, 'powers': [57, 38, 75, 12], 'representative': 944, 'size': 2}
id: 111692808
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 75, 'group_counter': 615, 'group_order': 1056, 'label': '66A13', 'order': 66, 'powers': [55, 39, 70, 13], 'representative': 208, 'size': 2}
id: 111692809
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 76, 'group_counter': 615, 'group_order': 1056, 'label': '66A-13', 'order': 66, 'powers': [54, 39, 69, 12], 'representative': 848, 'size': 2}
id: 111692810
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 77, 'group_counter': 615, 'group_order': 1056, 'label': '66A19', 'order': 66, 'powers': [59, 36, 74, 13], 'representative': 304, 'size': 2}
id: 111692811
{'aut_label': '66A1', 'centralizer': '2.a1.a1', 'counter': 78, 'group_counter': 615, 'group_order': 1056, 'label': '66A-19', 'order': 66, 'powers': [58, 36, 73, 12], 'representative': 752, 'size': 2}
id: 111692812
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 79, 'group_counter': 615, 'group_order': 1056, 'label': '66B1', 'order': 66, 'powers': [54, 40, 81, 14], 'representative': 34, 'size': 8}
id: 111692814
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 80, 'group_counter': 615, 'group_order': 1056, 'label': '66B-1', 'order': 66, 'powers': [55, 40, 82, 15], 'representative': 210, 'size': 8}
id: 111692815
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 81, 'group_counter': 615, 'group_order': 1056, 'label': '66B5', 'order': 66, 'powers': [60, 42, 87, 15], 'representative': 18, 'size': 8}
id: 111692816
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 82, 'group_counter': 615, 'group_order': 1056, 'label': '66B-5', 'order': 66, 'powers': [61, 42, 88, 14], 'representative': 106, 'size': 8}
id: 111692817
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 83, 'group_counter': 615, 'group_order': 1056, 'label': '66B7', 'order': 66, 'powers': [58, 43, 86, 14], 'representative': 130, 'size': 8}
id: 111692818
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 84, 'group_counter': 615, 'group_order': 1056, 'label': '66B-7', 'order': 66, 'powers': [59, 43, 85, 15], 'representative': 42, 'size': 8}
id: 111692819
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 85, 'group_counter': 615, 'group_order': 1056, 'label': '66B13', 'order': 66, 'powers': [57, 44, 80, 14], 'representative': 202, 'size': 8}
id: 111692820
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 86, 'group_counter': 615, 'group_order': 1056, 'label': '66B-13', 'order': 66, 'powers': [56, 44, 79, 15], 'representative': 66, 'size': 8}
id: 111692821
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 87, 'group_counter': 615, 'group_order': 1056, 'label': '66B19', 'order': 66, 'powers': [63, 41, 84, 14], 'representative': 10, 'size': 8}
id: 111692822
{'aut_label': '66B1', 'centralizer': '8.d1.a1', 'counter': 88, 'group_counter': 615, 'group_order': 1056, 'label': '66B-19', 'order': 66, 'powers': [62, 41, 83, 15], 'representative': 258, 'size': 8}
id: 111692823
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 89, 'group_counter': 615, 'group_order': 1056, 'label': '66C1', 'order': 66, 'powers': [59, 45, 91, 16], 'representative': 6, 'size': 8}
id: 111692825
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 90, 'group_counter': 615, 'group_order': 1056, 'label': '66C-1', 'order': 66, 'powers': [58, 45, 92, 17], 'representative': 262, 'size': 8}
id: 111692826
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 91, 'group_counter': 615, 'group_order': 1056, 'label': '66C5', 'order': 66, 'powers': [57, 47, 97, 17], 'representative': 22, 'size': 8}
id: 111692827
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 92, 'group_counter': 615, 'group_order': 1056, 'label': '66C-5', 'order': 66, 'powers': [56, 47, 98, 16], 'representative': 198, 'size': 8}
id: 111692828
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 93, 'group_counter': 615, 'group_order': 1056, 'label': '66C7', 'order': 66, 'powers': [60, 48, 96, 16], 'representative': 294, 'size': 8}
id: 111692829
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 94, 'group_counter': 615, 'group_order': 1056, 'label': '66C-7', 'order': 66, 'powers': [61, 48, 95, 17], 'representative': 118, 'size': 8}
id: 111692830
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 95, 'group_counter': 615, 'group_order': 1056, 'label': '66C13', 'order': 66, 'powers': [62, 49, 90, 16], 'representative': 390, 'size': 8}
id: 111692831
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 96, 'group_counter': 615, 'group_order': 1056, 'label': '66C-13', 'order': 66, 'powers': [63, 49, 89, 17], 'representative': 214, 'size': 8}
id: 111692832
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 97, 'group_counter': 615, 'group_order': 1056, 'label': '66C19', 'order': 66, 'powers': [55, 46, 94, 16], 'representative': 102, 'size': 8}
id: 111692833
{'aut_label': '66C1', 'centralizer': '8.e1.a1', 'counter': 98, 'group_counter': 615, 'group_order': 1056, 'label': '66C-19', 'order': 66, 'powers': [54, 46, 93, 17], 'representative': 166, 'size': 8}
id: 111692834
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 99, 'group_counter': 615, 'group_order': 1056, 'label': '88A1', 'order': 88, 'powers': [64, 101, 103, 22], 'representative': 12, 'size': 4}
id: 111692699
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 100, 'group_counter': 615, 'group_order': 1056, 'label': '88A-1', 'order': 88, 'powers': [64, 102, 104, 22], 'representative': 1044, 'size': 4}
id: 111692700
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 101, 'group_counter': 615, 'group_order': 1056, 'label': '88A3', 'order': 88, 'powers': [65, 107, 106, 22], 'representative': 36, 'size': 4}
id: 111692701
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 102, 'group_counter': 615, 'group_order': 1056, 'label': '88A-3', 'order': 88, 'powers': [65, 108, 105, 22], 'representative': 1020, 'size': 4}
id: 111692702
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 103, 'group_counter': 615, 'group_order': 1056, 'label': '88A5', 'order': 88, 'powers': [66, 106, 102, 22], 'representative': 60, 'size': 4}
id: 111692703
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 104, 'group_counter': 615, 'group_order': 1056, 'label': '88A-5', 'order': 88, 'powers': [66, 105, 101, 22], 'representative': 996, 'size': 4}
id: 111692704
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 105, 'group_counter': 615, 'group_order': 1056, 'label': '88A7', 'order': 88, 'powers': [67, 99, 107, 22], 'representative': 84, 'size': 4}
id: 111692705
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 106, 'group_counter': 615, 'group_order': 1056, 'label': '88A-7', 'order': 88, 'powers': [67, 100, 108, 22], 'representative': 972, 'size': 4}
id: 111692706
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 107, 'group_counter': 615, 'group_order': 1056, 'label': '88A9', 'order': 88, 'powers': [68, 103, 100, 22], 'representative': 108, 'size': 4}
id: 111692707
{'aut_label': '88A1', 'centralizer': '4.f1.a1', 'counter': 108, 'group_counter': 615, 'group_order': 1056, 'label': '88A-9', 'order': 88, 'powers': [68, 104, 99, 22], 'representative': 948, 'size': 4}
id: 111692708
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 109, 'group_counter': 615, 'group_order': 1056, 'label': '132A1', 'order': 132, 'powers': [69, 64, 111, 29], 'representative': 8, 'size': 4}
id: 111692710
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 110, 'group_counter': 615, 'group_order': 1056, 'label': '132A-1', 'order': 132, 'powers': [70, 64, 112, 30], 'representative': 1048, 'size': 4}
id: 111692711
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 111, 'group_counter': 615, 'group_order': 1056, 'label': '132A5', 'order': 132, 'powers': [71, 66, 117, 30], 'representative': 40, 'size': 4}
id: 111692712
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 112, 'group_counter': 615, 'group_order': 1056, 'label': '132A-5', 'order': 132, 'powers': [72, 66, 118, 29], 'representative': 1016, 'size': 4}
id: 111692713
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 113, 'group_counter': 615, 'group_order': 1056, 'label': '132A7', 'order': 132, 'powers': [73, 67, 116, 29], 'representative': 56, 'size': 4}
id: 111692714
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 114, 'group_counter': 615, 'group_order': 1056, 'label': '132A-7', 'order': 132, 'powers': [74, 67, 115, 30], 'representative': 1000, 'size': 4}
id: 111692715
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 115, 'group_counter': 615, 'group_order': 1056, 'label': '132A13', 'order': 132, 'powers': [75, 68, 110, 29], 'representative': 104, 'size': 4}
id: 111692716
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 116, 'group_counter': 615, 'group_order': 1056, 'label': '132A-13', 'order': 132, 'powers': [76, 68, 109, 30], 'representative': 952, 'size': 4}
id: 111692717
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 117, 'group_counter': 615, 'group_order': 1056, 'label': '132A19', 'order': 132, 'powers': [77, 65, 114, 29], 'representative': 152, 'size': 4}
id: 111692718
{'aut_label': '132A1', 'centralizer': '4.f1.a1', 'counter': 118, 'group_counter': 615, 'group_order': 1056, 'label': '132A-19', 'order': 132, 'powers': [78, 65, 113, 30], 'representative': 904, 'size': 4}
id: 111692719
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 119, 'group_counter': 615, 'group_order': 1056, 'label': '264A1', 'order': 264, 'powers': [109, 99, 121, 50], 'representative': 4, 'size': 4}
id: 111692721
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 120, 'group_counter': 615, 'group_order': 1056, 'label': '264A-1', 'order': 264, 'powers': [110, 100, 122, 51], 'representative': 260, 'size': 4}
id: 111692722
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 121, 'group_counter': 615, 'group_order': 1056, 'label': '264A5', 'order': 264, 'powers': [111, 103, 127, 51], 'representative': 20, 'size': 4}
id: 111692723
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 122, 'group_counter': 615, 'group_order': 1056, 'label': '264A-5', 'order': 264, 'powers': [112, 104, 128, 50], 'representative': 196, 'size': 4}
id: 111692724
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 123, 'group_counter': 615, 'group_order': 1056, 'label': '264A7', 'order': 264, 'powers': [113, 105, 131, 50], 'representative': 292, 'size': 4}
id: 111692725
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 124, 'group_counter': 615, 'group_order': 1056, 'label': '264A-7', 'order': 264, 'powers': [114, 106, 132, 51], 'representative': 116, 'size': 4}
id: 111692726
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 125, 'group_counter': 615, 'group_order': 1056, 'label': '264A13', 'order': 264, 'powers': [115, 107, 120, 50], 'representative': 388, 'size': 4}
id: 111692727
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 126, 'group_counter': 615, 'group_order': 1056, 'label': '264A-13', 'order': 264, 'powers': [116, 108, 119, 51], 'representative': 212, 'size': 4}
id: 111692728
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 127, 'group_counter': 615, 'group_order': 1056, 'label': '264A19', 'order': 264, 'powers': [117, 102, 135, 50], 'representative': 100, 'size': 4}
id: 111692729
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 128, 'group_counter': 615, 'group_order': 1056, 'label': '264A-19', 'order': 264, 'powers': [118, 101, 136, 51], 'representative': 164, 'size': 4}
id: 111692730
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 129, 'group_counter': 615, 'group_order': 1056, 'label': '264A23', 'order': 264, 'powers': [110, 99, 138, 51], 'representative': 356, 'size': 4}
id: 111692732
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 130, 'group_counter': 615, 'group_order': 1056, 'label': '264A-23', 'order': 264, 'powers': [109, 100, 137, 50], 'representative': 964, 'size': 4}
id: 111692733
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 131, 'group_counter': 615, 'group_order': 1056, 'label': '264A35', 'order': 264, 'powers': [116, 107, 130, 51], 'representative': 404, 'size': 4}
id: 111692734
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 132, 'group_counter': 615, 'group_order': 1056, 'label': '264A-35', 'order': 264, 'powers': [115, 108, 129, 50], 'representative': 580, 'size': 4}
id: 111692735
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 133, 'group_counter': 615, 'group_order': 1056, 'label': '264A47', 'order': 264, 'powers': [118, 102, 123, 51], 'representative': 452, 'size': 4}
id: 111692736
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 134, 'group_counter': 615, 'group_order': 1056, 'label': '264A-47', 'order': 264, 'powers': [117, 101, 124, 50], 'representative': 868, 'size': 4}
id: 111692737
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 135, 'group_counter': 615, 'group_order': 1056, 'label': '264A59', 'order': 264, 'powers': [114, 105, 125, 51], 'representative': 500, 'size': 4}
id: 111692738
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 136, 'group_counter': 615, 'group_order': 1056, 'label': '264A-59', 'order': 264, 'powers': [113, 106, 126, 50], 'representative': 676, 'size': 4}
id: 111692739
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 137, 'group_counter': 615, 'group_order': 1056, 'label': '264A71', 'order': 264, 'powers': [111, 104, 134, 51], 'representative': 548, 'size': 4}
id: 111692740
{'aut_label': '264A1', 'centralizer': '4.f1.a1', 'counter': 138, 'group_counter': 615, 'group_order': 1056, 'label': '264A-71', 'order': 264, 'powers': [112, 103, 133, 50], 'representative': 772, '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: 4971349
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1a', '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], 'schur_index': 1}
id: 4971360
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1b', '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], 'schur_index': 1}
id: 4971371
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1c', '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], 'schur_index': 1}
id: 4971377
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1d', '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], 'schur_index': 1}
id: 4971378
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1e', '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], 'schur_index': 1}
id: 4971379
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1f', '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], 'schur_index': 1}
id: 4971380
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1g', '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], 'schur_index': 1}
id: 4971381
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1h', '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], 'schur_index': 1}
id: 4971382
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -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: 4971350
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -1, -1, 2, -2, 2, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 2, -2, 2, 2, 2, 2, 2, -1, -1, 1, 1, -1, -1, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -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: 4971351
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -1, -1, 2, 2, -2, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -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: 4971352
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -2, -2, -1, -1, 2, -2, 2, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -2, 2, 2, 2, 2, 2, 2, -1, -1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -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: 4971353
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, -1, -1, 2, 2, -2, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -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: 4971354
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, -2, 2, -1, -1, 2, -2, -2, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -2, 2, 2, 2, 2, 2, 2, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -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: 4971355
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, -2, -1, -1, 2, 2, 2, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -2, -2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -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: 4971356
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -1, -1, 2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 2, -2, 2, 2, 2, 2, 2, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -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: 4971357
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, 2, 2, -2, 2, 0, 2, 2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4971358
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 0, 2, 2, -2, -2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4971359
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2c', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, 0, -2, -2, -4, 4, 0, -2, -2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 2, 2, -2, -2, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 4971361
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2d', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 0, -2, -2, -4, -4, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 2, 2, 2, 2, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 4971370
{'cdim': 4, 'counter': 29, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 4, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, -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, 0, 0, 0, 0, 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: 4971372
{'cdim': 4, 'counter': 30, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4b', 'multiplicity': 2, 'nt': [24, 114], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, -4, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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: 4971362
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2e', 'multiplicity': 5, 'nt': [11, 2], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 0, 0, 10, 10, 10, 0, 0, 10, 10, 10, 10, 10, 10, 0, 0, 0, 0, 10, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 10, 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], 'schur_index': 1}
id: 4971363
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2f', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, -10, -10, 0, 0, 10, 10, 10, 0, 0, 10, 10, -10, -10, -10, -10, 0, 0, 0, 0, 10, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 10, 10, 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], 'schur_index': 1}
id: 4971364
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2g', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, -10, 10, 0, 0, 10, 10, 10, 0, 0, 10, 10, -10, 10, 10, -10, 0, 0, 0, 0, -10, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -10, -10, 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], 'schur_index': 1}
id: 4971365
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2h', 'multiplicity': 5, 'nt': [22, 3], 'qdim': 10, 'qvalues': [10, 10, 10, -10, 0, 0, 10, 10, 10, 0, 0, 10, 10, 10, -10, -10, 10, 0, 0, 0, 0, -10, 0, -1, -1, -1, -1, -1, 10, 10, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -10, -10, 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], 'schur_index': 1}
id: 4971366
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2i', 'multiplicity': 10, 'nt': [33, 4], 'qdim': 20, 'qvalues': [20, 20, 20, 20, 0, 0, -10, -10, 20, 0, 0, -10, -10, -10, -10, -10, -10, 0, 0, 0, 0, 20, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -10, -10, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 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: 4971367
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2j', 'multiplicity': 10, 'nt': [66, 0], 'qdim': 20, 'qvalues': [20, 20, -20, -20, 0, 0, -10, -10, 20, 0, 0, -10, -10, 10, 10, 10, 10, 0, 0, 0, 0, 20, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -10, -10, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 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: 4971368
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2k', 'multiplicity': 10, 'nt': [66, 0], 'qdim': 20, 'qvalues': [20, 20, -20, 20, 0, 0, -10, -10, 20, 0, 0, -10, -10, 10, -10, -10, 10, 0, 0, 0, 0, -20, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 10, 10, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 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: 4971369
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.2l', 'multiplicity': 10, 'nt': [66, 0], 'qdim': 20, 'qvalues': [20, 20, 20, -20, 0, 0, -10, -10, 20, 0, 0, -10, -10, -10, 10, 10, -10, 0, 0, 0, 0, -20, 0, -2, -2, -2, -2, -2, -10, -10, 0, 0, 0, 0, -2, -2, -2, -2, -2, 2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 10, 10, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 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: 4971373
{'cdim': 4, 'counter': 31, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4c', 'multiplicity': 5, 'nt': [44, 12], 'qdim': 20, 'qvalues': [20, 20, 0, 0, 0, 0, 20, 20, -20, 0, 0, 20, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -20, -20, 0, 0, 0, 0, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4971374
{'cdim': 4, 'counter': 32, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4d', 'multiplicity': 10, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 0, 0, 40, 40, 0, 0, 0, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 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: 4971375
{'cdim': 4, 'counter': 33, 'faithful': False, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4e', 'multiplicity': 10, 'nt': [132, 0], 'qdim': 40, 'qvalues': [40, 40, 0, 0, 0, 0, -20, -20, -40, 0, 0, -20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 20, 20, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
id: 4971376
{'cdim': 4, 'counter': 34, 'faithful': True, 'group': '1056.615', 'group_order': 1056, 'image': None, 'label': '1056.615.4f', 'multiplicity': 20, 'nt': [264, 0], 'qdim': 80, 'qvalues': [80, -80, 0, 0, 0, 0, -40, -40, 0, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, -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, 0, 0, 0, 0, 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: 8446566
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1056, 'label': '1056.615.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8446616
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id: 8446627
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 528, 'label': '1056.615.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8446638
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 528, 'label': '1056.615.1d', '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]]]}
id: 8446649
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 528, 'label': '1056.615.1e', '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]]]}
id: 8446660
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 528, 'label': '1056.615.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8446671
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 528, 'label': '1056.615.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8446682
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 1056, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 528, 'label': '1056.615.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8446693
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id: 8446567
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id: 8446578
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id: 8446589
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id: 8446600
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id: 8446610
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id: 8446611
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id: 8446612
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id: 8446613
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id: 8446614
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id: 8446615
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id: 8446617
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id: 8446618
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id: 8446619
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id: 8446620
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id: 8446621
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id: 8446622
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id: 8446623
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id: 8446624
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id: 8446625
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id: 8446626
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id: 8446628
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id: 8446629
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id: 8446630
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id: 8446631
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id: 8446632
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id: 8446633
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id: 8446634
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id: 8446635
{'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 37, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.615.2f2', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]]]}
id: 8446636
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id: 8446637
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id: 8446639
{'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 40, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.c1.a1', 'kernel_order': 24, 'label': '1056.615.2f5', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 4], [-1, -4]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]]]}
id: 8446640
{'center': '22.a1.a1', 'center_index': 22, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 11, 'dim': 2, 'faithful': False, 'field': [-1, 3, 3, -4, -1, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '44.3', 'image_order': 44, 'indicator': 1, 'kernel': '44.b1.a1', 'kernel_order': 24, 'label': '1056.615.2g1', 'nt': [22, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 3], [-1, -3]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[-1, 5], [-1, -5]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 3], [1, -3]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 4], [-1, -4]], [[1, 4], [1, -4]], [[1, 2], [1, -2]], [[1, 5], [1, -5]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 5], [1, -5]], [[1, 4], [1, -4]], [[1, 3], [1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[1, 3], [1, -3]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 3], [1, -3]], [[1, 4], [1, -4]], [[1, 5], [1, -5]], [[1, 5], [1, -5]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 4], [1, -4]], [[-1, 3], [-1, -3]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 5], [-1, -5]], [[-1, 5], [-1, -5]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 1], [-1, -1]], [[-1, 3], [-1, -3]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 4], [-1, -4]], [[-1, 5], [-1, -5]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 4], [-1, -4]], [[-1, 1], [-1, -1]]]}
id: 8446641
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id: 8446642
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id: 8446643
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id: 8446644
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id: 8446645
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id: 8446646
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id: 8446647
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id: 8446648
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id: 8446650
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id: 8446651
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id: 8446661
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id: 8446652
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id: 8446653
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id: 8446654
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id: 8446655
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id: 8446656
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id: 8446657
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id: 8446658
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id: 8446659
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id: 8446662
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id: 8446672
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id: 8446663
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id: 8446664
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id: 8446665
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id: 8446666
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id: 8446667
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id: 8446668
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id: 8446669
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id: 8446670
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id: 8446673
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id: 8446683
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id: 8446674
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id: 8446675
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id: 8446676
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id: 8446677
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id: 8446678
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id: 8446679
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id: 8446680
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id: 8446681
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id: 8446684
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id: 8446694
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id: 8446685
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id: 8446686
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id: 8446687
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id: 8446688
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id: 8446689
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id: 8446690
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id: 8446691
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id: 8446692
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id: 8446695
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id: 8446696
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id: 8446697
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id: 8446698
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id: 8446699
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id: 8446700
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id: 8446701
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id: 8446702
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id: 8446703
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id: 8446576
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id: 8446568
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id: 8446569
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id: 8446570
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id: 8446571
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id: 8446572
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id: 8446573
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id: 8446574
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id: 8446575
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id: 8446577
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id: 8446587
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id: 8446579
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id: 8446580
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id: 8446581
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id: 8446582
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id: 8446583
{'center': '88.a1.a1', 'center_index': 88, 'center_order': 12, 'counter': 114, 'cyclotomic_n': 33, 'dim': 4, 'faithful': False, 'field': [1, -3, 12, 1, 20, -7, 16, -2, 5, -1, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '528.130', 'image_order': 528, 'indicator': 0, 'kernel': '528.a1.a1', 'kernel_order': 2, 'label': '1056.615.4e6', 'nt': [132, 10], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 11]], [[4, -11]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 11]], [[4, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 9], [2, -9]], [[2, 3], [2, -3]], [[2, 15], [2, -15]], [[2, 6], [2, -6]], [[2, 12], [2, -12]], [[-4, 11]], [[-4, -11]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 15], [2, -15]], [[2, 3], [2, -3]], [[2, 9], [2, -9]], [[2, 12], [2, -12]], [[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]], [[0, 0]], [[0, 0]], [[-2, 4], [-2, 7], [-2, 15], [-2, -15]], [[2, 5], [2, -16]], [[2, 1], [2, 10]], [[2, 8], [2, 14]], [[-2, 6], [2, 16], [-2, -16]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 5], [2, 6], [-2, 8], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 16], [2, -15], [-2, -14]], [[-2, 3], [-2, 14], [2, -14]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 11], [2, 13], [-2, 14], [2, 16], [-2, -16], [2, -14]], [[2, 4], [2, 7]], [[2, 0], [-2, 1], [2, 3], [-2, 4], [2, 6], [-2, 7], [-2, 10], [2, 11], [2, 14], [-2, 16], [2, -16], [-2, -14]], [[-2, 6], [-2, -6]], [[-2, 9], [-2, -9]], [[-2, 12], [-2, -12]], [[-2, 15], [-2, -15]], [[-2, 3], [-2, -3]], [[2, 8], [2, 14]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 5], [2, 6], [-2, 8], [2, 9], [-2, 10], [-2, 13], [2, 15], [-2, 16], [2, -15], [-2, -14]], [[-2, 0], [2, 1], [2, 2], [-2, 3], [2, 4], [-2, 6], [2, 7], [-2, 9], [2, 10], [-2, 11], [2, 13], [-2, 14], [2, 16], [-2, -16], [2, -14]], [[-2, 4], [-2, 7], [-2, 15], [-2, -15]], [[2, 4], [2, 7]], [[-2, 6], [2, 16], [-2, -16]], [[-2, 3], [-2, 14], [2, -14]], [[2, 5], [2, -16]], [[2, 1], [2, 10]], [[2, 0], [-2, 1], [2, 3], [-2, 4], [2, 6], [-2, 7], [-2, 10], [2, 11], [2, 14], [-2, 16], [2, -16], [-2, -14]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 0], [2, 1], [2, 2], [-2, 3], [2, 5], [-2, 6], [2, 8], [-2, 9], [2, 10], [2, 13], [-2, 15], [2, 16], [-2, -15], [2, -14]], [[2, 3], [2, 14], [-2, -14]], [[2, 4], [2, 7], [2, 15], [2, -15]], [[-2, 1], [-2, 10]], [[2, 6], [-2, 16], [2, -16]], [[2, 0], [-2, 1], [-2, 2], [2, 3], [-2, 4], [2, 6], [-2, 7], [2, 9], [-2, 10], [2, 11], [-2, 13], [2, 14], [-2, 16], [2, -16], [-2, -14]], [[-2, 0], [2, 1], [-2, 3], [2, 4], [-2, 6], [2, 7], [2, 10], [-2, 11], [-2, 14], [2, 16], [-2, -16], [2, -14]], [[-2, 4], [-2, 7]], [[-2, 8], [-2, 14]], [[-2, 5], [-2, -16]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 8446584
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id: 8446585
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id: 8446586
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id: 8446588
{'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 119, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [123904, 0, -309760, 0, 557568, 0, -418176, 0, 216832, 0, -70048, 0, 16544, 0, -2640, 0, 308, 0, -22, 0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.615', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.615.4f1', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 44]], [[4, 88]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 44]], [[-4, 88]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 12], [-2, -12]], [[2, 48], [2, -48]], [[2, 24], [2, -24]], [[-2, 36], [-2, -36]], [[-2, 60], [-2, -60]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 24], [-2, -24]], [[-2, 48], [-2, -48]], [[2, 12], [2, -12]], [[2, 60], [2, 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id: 8446598
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id: 8446599
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id: 8446601
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id: 8446602
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id: 8446603
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id: 8446604
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id: 8446605
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id: 8446606
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id: 8446607
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id: 8446608
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id: 8446590
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id: 8446609
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id: 8446591
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id: 8446592
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id: 8446593
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id: 8446594
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id: 8446595
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id: 8446596
{'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 126, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [123904, 0, -309760, 0, 557568, 0, -418176, 0, 216832, 0, -70048, 0, 16544, 0, -2640, 0, 308, 0, -22, 0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.615', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.615.4f8', 'nt': [264, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 88]], [[-4, 44]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 88]], [[4, 44]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 36], [-2, -36]], [[-2, 12], [-2, -12]], [[-2, 60], [-2, -60]], [[2, 24], [2, -24]], [[2, 48], [2, -48]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 60], [2, -60]], [[2, 12], [2, -12]], [[2, 36], [2, -36]], [[-2, 48], [-2, 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id: 8446597
{'center': '176.a1.a1', 'center_index': 176, 'center_order': 6, 'counter': 127, 'cyclotomic_n': 264, 'dim': 4, 'faithful': True, 'field': [123904, 0, -309760, 0, 557568, 0, -418176, 0, 216832, 0, -70048, 0, 16544, 0, -2640, 0, 308, 0, -22, 0, 1], 'group': '1056.615', 'group_counter': 615, 'group_order': 1056, 'image': None, 'image_isoclass': '1056.615', 'image_order': 1056, 'indicator': 0, 'kernel': '1056.a1.a1', 'kernel_order': 1, 'label': '1056.615.4f9', 'nt': [264, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 44]], [[4, 88]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 44]], [[-4, 88]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 60], [-2, -60]], [[2, 24], [2, -24]], [[-2, 12], [-2, -12]], [[2, 48], [2, -48]], [[-2, 36], [-2, -36]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 12], [2, -12]], [[-2, 24], [-2, -24]], [[2, 60], [2, -60]], [[2, 36], [2, 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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: 69580125
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1056, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 66, 'label': '1056.615.1.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': '1056.615', 'subgroup_hash': 615, 'subgroup_order': 1056, 'subgroup_tex': 'C_{24}:D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580173
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 528, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.84', 'subgroup_hash': 84, 'subgroup_order': 528, 'subgroup_tex': 'D_8\\times C_{33}', 'supersolvable': True, 'sylow': 0}
id: 69580184
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 528, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.131', 'subgroup_hash': 131, 'subgroup_order': 528, 'subgroup_tex': 'C_{12}.D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580195
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 528, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '528.42', 'subgroup_hash': 42, 'subgroup_order': 528, 'subgroup_tex': 'C_{33}:D_8', 'supersolvable': True, 'sylow': 0}
id: 69580206
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 528, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, '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': '528.130', 'subgroup_hash': 130, 'subgroup_order': 528, 'subgroup_tex': 'C_{12}:D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580217
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 528, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, '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': '528.43', 'subgroup_hash': 43, 'subgroup_order': 528, 'subgroup_tex': 'C_{33}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580228
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 528, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.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': '528.32', 'subgroup_hash': 32, 'subgroup_order': 528, 'subgroup_tex': 'C_{264}:C_2', 'supersolvable': True, 'sylow': 0}
id: 69580239
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 528, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.2.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': '528.33', 'subgroup_hash': 33, 'subgroup_order': 528, 'subgroup_tex': 'C_{264}:C_2', 'supersolvable': True, 'sylow': 0}
id: 69580250
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 352, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 22, 'label': '1056.615.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '352.106', 'subgroup_hash': 106, 'subgroup_order': 352, 'subgroup_tex': 'C_8:D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580126
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 264, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.29', 'subgroup_hash': 29, 'subgroup_order': 264, 'subgroup_tex': 'D_4\\times C_{33}', 'supersolvable': True, 'sylow': 0}
id: 69580137
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 264, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.29', 'subgroup_hash': 29, 'subgroup_order': 264, 'subgroup_tex': 'D_4\\times C_{33}', 'supersolvable': True, 'sylow': 0}
id: 69580148
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 264, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.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': '4.2', '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': '264.14', 'subgroup_hash': 14, 'subgroup_order': 264, 'subgroup_tex': 'C_{12}\\times D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580159
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 264, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '264.15', 'subgroup_hash': 15, 'subgroup_order': 264, 'subgroup_tex': 'C_3\\times D_{44}', 'supersolvable': True, 'sylow': 0}
id: 69580167
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 264, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.13', 'subgroup_hash': 13, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 69580168
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 264, 'counter': 15, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.4', 'subgroup_hash': 4, 'subgroup_order': 264, 'subgroup_tex': 'C_{264}', 'supersolvable': True, 'sylow': 0}
id: 69580169
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 264, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '264.2', 'subgroup_hash': 2, 'subgroup_order': 264, 'subgroup_tex': 'C_{11}:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 69580170
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 132, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '264.17', 'subgroup_hash': 17, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
id: 69580171
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 132, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '264.16', 'subgroup_hash': 16, 'subgroup_order': 264, 'subgroup_tex': 'C_{22}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 69580172
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 132, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '264.36', 'subgroup_hash': 36, 'subgroup_order': 264, 'subgroup_tex': 'C_6\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580174
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 132, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '264.17', 'subgroup_hash': 17, 'subgroup_order': 264, 'subgroup_tex': 'C_{33}:D_4', 'supersolvable': True, 'sylow': 0}
id: 69580175
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 176, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.24', 'subgroup_hash': 24, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 69580176
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 176, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.32', 'subgroup_hash': 32, 'subgroup_order': 176, 'subgroup_tex': 'D_4:D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580177
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 176, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.14', 'subgroup_hash': 14, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:D_8', 'supersolvable': True, 'sylow': 0}
id: 69580178
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 176, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.31', 'subgroup_hash': 31, 'subgroup_order': 176, 'subgroup_tex': 'D_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580179
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 176, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.15', 'subgroup_hash': 15, 'subgroup_order': 176, 'subgroup_tex': 'C_{11}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580180
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 176, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.4', 'subgroup_hash': 4, 'subgroup_order': 176, 'subgroup_tex': 'C_{88}:C_2', 'supersolvable': True, 'sylow': 0}
id: 69580181
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 176, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '176.5', 'subgroup_hash': 5, 'subgroup_order': 176, 'subgroup_tex': 'C_{88}:C_2', 'supersolvable': True, 'sylow': 0}
id: 69580182
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 132, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580183
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 132, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': '132.4', 'subgroup_hash': 4, 'subgroup_order': 132, 'subgroup_tex': 'C_{132}', 'supersolvable': True, 'sylow': 0}
id: 69580185
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 132, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 69580186
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 66, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 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': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
id: 69580187
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 66, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.10', 'subgroup_hash': 10, 'subgroup_order': 132, 'subgroup_tex': 'C_2\\times C_{66}', 'supersolvable': True, 'sylow': 0}
id: 69580188
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 66, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580189
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 66, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.2', 'subgroup_hash': 2, 'subgroup_order': 132, 'subgroup_tex': 'C_{11}:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 69580190
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 33, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580191
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 33, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.8.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a2', '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': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580192
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 48, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '1056.615.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11.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': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.183', 'subgroup_hash': 183, 'subgroup_order': 96, 'subgroup_tex': 'D_8:C_6', 'supersolvable': True, 'sylow': 0}
id: 69580193
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 88, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.9', 'subgroup_hash': 9, 'subgroup_order': 88, 'subgroup_tex': 'D_4\\times C_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580194
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 88, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.9', 'subgroup_hash': 9, 'subgroup_order': 88, 'subgroup_tex': 'D_4\\times C_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580196
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 88, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.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': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.4', 'subgroup_hash': 4, 'subgroup_order': 88, 'subgroup_tex': 'C_4\\times D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580197
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 88, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '88.5', 'subgroup_hash': 5, 'subgroup_order': 88, 'subgroup_tex': 'D_{44}', 'supersolvable': True, 'sylow': 0}
id: 69580198
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 88, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.3', 'subgroup_hash': 3, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 69580199
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 88, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.2', 'subgroup_hash': 2, 'subgroup_order': 88, 'subgroup_tex': 'C_{88}', 'supersolvable': True, 'sylow': 0}
id: 69580200
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 88, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.1', 'subgroup_hash': 1, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:C_8', 'supersolvable': True, 'sylow': 0}
id: 69580201
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 44, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
id: 69580202
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 44, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '88.6', 'subgroup_hash': 6, 'subgroup_order': 88, 'subgroup_tex': 'C_{22}:C_4', 'supersolvable': True, 'sylow': 0}
id: 69580203
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 44, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '88.11', 'subgroup_hash': 11, 'subgroup_order': 88, 'subgroup_tex': 'C_2\\times D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580204
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 44, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.12.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': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
id: 69580205
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 66, 'counter': 49, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.16.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': '16.11', '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': ['S', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
id: 69580207
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 33, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
id: 69580208
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 33, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 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': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
id: 69580209
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 33, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580210
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 33, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580211
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 48, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '22.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 22, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 69580212
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.47', 'subgroup_hash': 47, 'subgroup_order': 48, 'subgroup_tex': 'D_4:C_6', 'supersolvable': True, 'sylow': 0}
id: 69580213
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.25', 'subgroup_hash': 25, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 69580214
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580215
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580216
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.24', 'subgroup_hash': 24, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580218
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.22.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.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': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580219
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 44, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580220
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 44, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.24.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': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.2', 'subgroup_hash': 2, 'subgroup_order': 44, 'subgroup_tex': 'C_{44}', 'supersolvable': True, 'sylow': 0}
id: 69580221
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 44, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
id: 69580222
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 22, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580223
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 22, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.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': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580224
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 22, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580225
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 22, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
id: 69580226
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 11, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580227
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 11, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.24.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a2', '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': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580229
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 33, 'counter': 70, 'cyclic': True, 'direct': False, 'hall': 33, 'label': '1056.615.32.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': '32.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
id: 69580230
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1056.615.33.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '33.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': 33, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.43', 'subgroup_hash': 43, 'subgroup_order': 32, 'subgroup_tex': 'D_8:C_2', 'supersolvable': True, 'sylow': 2}
id: 69580231
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': True, 'core_order': 24, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580232
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': True, 'core_order': 24, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580233
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 24, 'counter': 74, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '44.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '44.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 44, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 69580234
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580235
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': 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: 69580236
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': 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: 69580237
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580238
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': 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: 69580240
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 69580241
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.44.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 69580242
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.44.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': 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: 69580243
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 22, 'counter': 83, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.48.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': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580244
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 11, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580245
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': False, 'core_order': 11, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
id: 69580246
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 11, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580247
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 11, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
id: 69580248
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 66, 'characteristic': True, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.66.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '66.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '66.2', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 66, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
id: 69580249
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
id: 69580251
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.7', 'subgroup_hash': 7, 'subgroup_order': 16, 'subgroup_tex': 'D_8', 'supersolvable': True, 'sylow': 0}
id: 69580252
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': 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: 69580253
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': 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: 69580255
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.66.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '66.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': 66, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 69580256
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 12, 'counter': 95, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '88.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 88, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['U1'], '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: 69580257
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580258
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580259
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580260
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580127
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.88.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580128
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.88.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580129
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': 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: 69580130
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.88.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.h1.a2', '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': 88, 'quotient_simple': 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: 69580131
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 11, 'counter': 104, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '1056.615.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8:C_6', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
id: 69580132
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': True, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 69580133
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 132, 'characteristic': True, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.615.132.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 69580134
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': True, 'core_order': 8, 'counter': 107, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.132.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '132.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '132.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 132, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 69580135
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580136
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580138
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580139
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580140
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580141
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580142
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.132.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 69580143
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.132.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': 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: 69580144
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 6, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '176.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '176.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 176, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times D_{11}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], '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: 69580145
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 3, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.176.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69580146
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.176.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69580147
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.176.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69580149
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.176.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': 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: 69580150
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 528, 'characteristic': True, 'core_order': 4, 'counter': 121, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 69580151
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580152
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580153
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580154
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580155
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.264.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580156
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.264.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580157
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': 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: 69580158
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1056.615.264.h1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '264.h1.a2', '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': 264, 'quotient_simple': 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: 69580160
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 3, 'counter': 130, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '1056.615.352.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '352.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '352.106', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 106, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 352, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:D_{22}', '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: 69580161
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 2, 'counter': 131, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1056.615.528.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '528.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '528.130', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 130, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 528, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{22}', '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: 69580162
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.528.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, '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: 69580163
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 264, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.528.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, '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: 69580164
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.528.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, '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: 69580165
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1056.615.528.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '528.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': 528, '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: 69580166
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1056.615', 'ambient_counter': 615, 'ambient_order': 1056, 'ambient_tex': 'C_{24}:D_{22}', 'central': True, 'central_factor': False, 'centralizer_order': 1056, 'characteristic': True, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1056.615.1056.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1056.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1056.615', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 615, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1056, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C7'], '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: 69580145
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '176.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '88.b1.a1'], 'contains': ['352.a1.a1', '528.b1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6319, -1, 6742, -1, 2546, -1, 7943, -1], 'generators': [2, 704], 'label': '1056.615.176.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '176.b1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580125
{'ambient': '1056.615', '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': '176.a1.a1', 'complements': ['1056.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', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2358, 3995, 2194, 6788, 6821, 4480, 3747, 4480], 'generators': [1, 528, 132, 704, 2, 96, 792], 'label': '1056.615.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.d1.a1', '2.e1.a1', '2.b1.a1', '2.c1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580126
{'ambient': '1056.615', 'aut_centralizer_order': 44, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '160.229', 'aut_weyl_index': 44, 'centralizer': '16.a1.a1', 'complements': ['264.h1.a1', '264.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '12.a1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4167, 5289, 3192, 9542, 5132, 8369, 5139, 8369], 'generators': [2, 704, 96, 792, 528], 'label': '1056.615.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.b1.a1', '12.a1.a1', '44.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580127
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '88.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.e1.a1', '44.g1.a1', '44.h1.a1'], 'contains': ['176.a1.a1', '264.f1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6869, -1, 6456, -1, 3519, -1, 5847, -1], 'generators': [793, 704, 528], 'label': '1056.615.88.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.f1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580128
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '88.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '44.d1.a1', '44.e1.a1', '44.j1.a1'], 'contains': ['176.a1.a1', '264.g1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5799, -1, 5949, -1, 4595, -1, 5084, -1], 'generators': [3, 704, 528], 'label': '1056.615.88.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '88.g1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580129
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '44.f1.a1'], 'contains': ['176.c1.a1', '176.d1.a1', '176.e1.a1', '264.h1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8943, -1, 9786, -1, 1080, -1, 8552, -1], 'generators': [1, 134, 704], 'label': '1056.615.88.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '88.h1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580130
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '88.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a2', '44.f1.a1'], 'contains': ['176.c1.a1', '176.d1.a1', '176.e1.a1', '264.h1.a2'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8943, -1, 8794, -1, 1080, -1, 8802, -1], 'generators': [529, 134, 704], 'label': '1056.615.88.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '88.h1.a2', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.h1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580131
{'ambient': '1056.615', 'aut_centralizer_order': 704, 'aut_label': '96.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1'], 'contains': ['1056.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9417, 8434, 9228, 1135, 1449, 3177, 8930, 3177], 'generators': [96], 'label': '1056.615.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '1056.615', 'quotient_action_image': '2.1', 'quotient_action_kernel': '48.25', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580132
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '132.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 880, 'centralizer': '8.c1.a1', 'complements': ['8.h1.a1', '8.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1', '66.b1.a1', '66.c1.a1'], 'contains': ['264.a1.a1', '264.b1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2913, 2608, 2872, 6075, 7159, 8203, 3068, 8225], 'generators': [2, 792], 'label': '1056.615.132.a1.a1', 'mobius_quo': 0, 'mobius_sub': 22, 'normal_closure': '132.a1.a1', 'normal_contained_in': ['12.a1.a1', '44.a1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580133
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '132.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 880, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '44.b1.a1', '66.a1.a1', '66.d1.a1', '66.e1.a1'], 'contains': ['264.a1.a1', '264.c1.a1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3804, 320, 3860, 5434, 5819, 7724, 2936, 7724], 'generators': [134, 792], 'label': '1056.615.132.b1.a1', 'mobius_quo': 0, 'mobius_sub': 22, 'normal_closure': '132.b1.a1', 'normal_contained_in': ['12.b1.a1', '44.b1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.b1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580134
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '132.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '4.f1.a1', 'complements': ['8.h1.a1', '8.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '44.c1.a1', '66.a1.a1', '66.f1.a1', '66.g1.a1'], 'contains': ['264.a1.a1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1142, 1684, 2202, 4482, 8696, 7324, 1447, 7324], 'generators': [132], 'label': '1056.615.132.c1.a1', 'mobius_quo': 0, 'mobius_sub': 22, 'normal_closure': '132.c1.a1', 'normal_contained_in': ['12.f1.a1', '44.c1.a1', '66.a1.a1'], 'normal_contains': ['264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '132.c1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '132.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580135
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '44.d1.a1', '66.b1.a1'], 'contains': ['264.b1.a1', '264.d1.a1', '264.g1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4978, -1, 5585, -1, 4446, -1, 5231, -1], 'generators': [1, 2], 'label': '1056.615.132.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '132.d1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580136
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '44.e1.a1', '66.b1.a1'], 'contains': ['264.b1.a1', '264.f1.a1', '264.g1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5277, -1, 5333, -1, 4803, -1, 4878, -1], 'generators': [793, 2], 'label': '1056.615.132.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '132.e1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580137
{'ambient': '1056.615', 'aut_centralizer_order': 44, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '160.229', 'aut_weyl_index': 44, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '12.b1.a1', '44.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3804, 472, 3789, 4201, 3909, 7655, 4838, 7655], 'generators': [134, 704, 96, 792, 528], 'label': '1056.615.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.b1.a1', '12.b1.a1', '44.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '176.31', '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': '16.11'}
id: 69580138
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '44.f1.a1', '66.d1.a1'], 'contains': ['264.c1.a1', '264.d1.a1', '264.e1.a1', '264.h1.a1', '264.h1.a2'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7960, -1, 8266, -1, 2083, -1, 7564, -1], 'generators': [1, 134, 528], 'label': '1056.615.132.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '132.f1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580139
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '44.g1.a1', '66.d1.a1'], 'contains': ['264.c1.a1', '264.e1.a1', '264.f1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [6840, -1, 7207, -1, 3370, -1, 5994, -1], 'generators': [793, 134], 'label': '1056.615.132.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '132.g1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580140
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '132.h1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '44.h1.a1', '66.b1.a1', '66.d1.a1', '66.f1.a1'], 'contains': ['264.a1.a1', '264.d1.a1', '264.f1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4141, -1, 4570, -1, 6024, -1, 3751, -1], 'generators': [1, 792], 'label': '1056.615.132.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.h1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580141
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 880, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '44.i1.a1', '66.c1.a1', '66.d1.a1', '66.g1.a1'], 'contains': ['264.a1.a1', '264.e1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4371, -1, 4097, -1, 6228, -1, 3200, -1], 'generators': [807, 792], 'label': '1056.615.132.i1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.i1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580142
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '132.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.3', 'aut_weyl_index': 880, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '44.j1.a1', '66.b1.a1', '66.e1.a1', '66.g1.a1'], 'contains': ['264.a1.a1', '264.g1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2325, -1, 3026, -1, 7373, -1, 2643, -1], 'generators': [3, 792], 'label': '1056.615.132.j1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.j1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580143
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '132.k1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '44.k1.a1', '66.c1.a1', '66.e1.a1', '66.f1.a1'], 'contains': ['264.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1821, -1, 1420, -1, 8378, -1, 1603, -1], 'generators': [541], 'label': '1056.615.132.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '132.k1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580144
{'ambient': '1056.615', 'aut_centralizer_order': 3520, 'aut_label': '176.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1', '88.d1.a1', '88.e1.a1', '88.f1.a1', '88.g1.a1'], 'contains': ['352.a1.a1', '528.a1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7369, 7102, 7435, 2207, 2991, 3839, 6683, 3839], 'generators': [528, 704], 'label': '1056.615.176.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '176.a1.a1', 'normal_contained_in': ['16.a1.a1', '88.a1.a1'], 'normal_contains': ['352.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '1.1', 'quotient_action_kernel': '176.31', 'quotient_action_kernel_order': 176, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580146
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '176.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '88.c1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1', '528.c1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8943, -1, 9760, -1, 1665, -1, 8237, -1], 'generators': [134, 704], 'label': '1056.615.176.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '176.c1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580147
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '176.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '88.d1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1', '528.d1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8667, -1, 9305, -1, 1932, -1, 8501, -1], 'generators': [1, 704], 'label': '1056.615.176.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '176.d1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580148
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '88.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.c1.a1', '44.h1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5795, 8796, 5356, 1562, 4240, 377, 5986, 377], 'generators': [1, 704, 528, 792, 96], 'label': '1056.615.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.d1.a1', '2.b1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '176.31', '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': '88.11'}
id: 69580149
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '176.e1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '88.e1.a1', '88.h1.a1', '88.h1.a2'], 'contains': ['352.a1.a1', '528.e1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9103, -1, 9550, -1, 1799, -1, 8369, -1], 'generators': [807, 704], 'label': '1056.615.176.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '176.e1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580150
{'ambient': '1056.615', 'aut_centralizer_order': 3520, 'aut_label': '264.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1', '132.h1.a1', '132.i1.a1', '132.j1.a1', '132.k1.a1'], 'contains': ['528.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3471, 2171, 3285, 5075, 6302, 7149, 3002, 7149], 'generators': [792], 'label': '1056.615.264.a1.a1', 'mobius_quo': 0, 'mobius_sub': -88, 'normal_closure': '264.a1.a1', 'normal_contained_in': ['24.b1.a1', '88.a1.a1', '132.b1.a1', '132.a1.a1', '132.c1.a1'], 'normal_contains': ['528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '132.7', 'quotient_action_kernel_order': 132, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580151
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '88.b1.a1', '132.a1.a1', '132.d1.a1', '132.e1.a1'], 'contains': ['528.a1.a1', '528.b1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5491, -1, 5409, -1, 4253, -1, 5421, -1], 'generators': [2, 528], 'label': '1056.615.264.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '264.b1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580152
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '88.c1.a1', '132.b1.a1', '132.f1.a1', '132.g1.a1'], 'contains': ['528.a1.a1', '528.c1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7575, -1, 7770, -1, 2402, -1, 6824, -1], 'generators': [134, 528], 'label': '1056.615.264.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '132.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '264.c1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580153
{'ambient': '1056.615', 'aut_centralizer_order': 320, 'aut_label': '264.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.d1.a1', '132.d1.a1', '132.f1.a1', '132.h1.a1'], 'contains': ['528.a1.a1', '528.d1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6767, -1, 7014, -1, 2848, -1, 7202, -1], 'generators': [1, 528], 'label': '1056.615.264.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '264.d1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580154
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '264.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '88.e1.a1', '132.f1.a1', '132.g1.a1', '132.i1.a1'], 'contains': ['528.a1.a1', '528.e1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7827, -1, 8164, -1, 2696, -1, 6975, -1], 'generators': [807, 528], 'label': '1056.615.264.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '264.e1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580155
{'ambient': '1056.615', 'aut_centralizer_order': 320, 'aut_label': '264.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.f1.a1', '132.e1.a1', '132.g1.a1', '132.h1.a1'], 'contains': ['528.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6487, -1, 6149, -1, 3445, -1, 5920, -1], 'generators': [793], 'label': '1056.615.264.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '264.f1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580156
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '264.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '88.g1.a1', '132.d1.a1', '132.e1.a1', '132.j1.a1'], 'contains': ['528.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [4945, -1, 5804, -1, 4521, -1, 5157, -1], 'generators': [3], 'label': '1056.615.264.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '264.g1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580157
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '88.h1.a1', '132.f1.a1'], 'contains': ['528.c1.a1', '528.d1.a1', '528.e1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9207, -1, 9788, -1, 1358, -1, 8803, -1], 'generators': [1, 134], 'label': '1056.615.264.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '264.h1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580158
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '264.h1', 'aut_quo_index': None, 'aut_stab_index': 88, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a2', '88.h1.a2', '132.f1.a1'], 'contains': ['528.c1.a1', '528.d1.a1', '528.e1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9207, -1, 8776, -1, 1358, -1, 8954, -1], 'generators': [529, 134], 'label': '1056.615.264.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '264.h1.a2', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.h1.a2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580159
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '12.d1.a1', '44.i1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4529, 4393, 4542, 5252, 4571, 3230, 5440, 3230], 'generators': [807, 704, 528, 792, 96], 'label': '1056.615.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.d1.a1', '2.c1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580160
{'ambient': '1056.615', 'aut_centralizer_order': 3520, 'aut_label': '352.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3520, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '176.a1.a1', '176.b1.a1', '176.c1.a1', '176.d1.a1', '176.e1.a1'], 'contains': ['1056.a1.a1'], 'core': '352.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8860, 8047, 9359, 1546, 1999, 3526, 8369, 3526], 'generators': [704], 'label': '1056.615.352.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '352.a1.a1', 'normal_contained_in': ['32.a1.a1', '176.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '352.a1.a1', 'projective_image': '352.106', 'quotient_action_image': '1.1', 'quotient_action_kernel': '352.106', 'quotient_action_kernel_order': 352, 'quotient_fusion': None, 'short_label': '352.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580161
{'ambient': '1056.615', 'aut_centralizer_order': 7040, 'aut_label': '528.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1', '264.d1.a1', '264.e1.a1', '264.f1.a1', '264.g1.a1'], 'contains': ['1056.a1.a1'], 'core': '528.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6701, 7408, 6939, 2025, 2919, 3839, 6755, 3839], 'generators': [528], 'label': '1056.615.528.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '528.a1.a1', 'normal_contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1'], 'normal_contains': ['1056.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '528.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '1.1', 'quotient_action_kernel': '528.130', 'quotient_action_kernel_order': 528, 'quotient_fusion': None, 'short_label': '528.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580162
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '528.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '176.b1.a1', '264.b1.a1'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6208, -1, 6628, -1, 2313, -1, 8016, -1], 'generators': [2], 'label': '1056.615.528.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '132.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '528.b1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580163
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '528.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '176.c1.a1', '264.c1.a1', '264.h1.a1', '264.h1.a2'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9242, -1, 9629, -1, 1598, -1, 8519, -1], 'generators': [134], 'label': '1056.615.528.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '132.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '528.c1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580164
{'ambient': '1056.615', 'aut_centralizer_order': 320, 'aut_label': '528.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '176.d1.a1', '264.d1.a1', '264.h1.a1', '264.h1.a2'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [8654, -1, 9222, -1, 1865, -1, 8783, -1], 'generators': [1], 'label': '1056.615.528.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '528.d1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580165
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '528.e1', 'aut_quo_index': None, 'aut_stab_index': 44, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7040, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '176.e1.a1', '264.e1.a1', '264.h1.a1', '264.h1.a2'], 'contains': ['1056.a1.a1'], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9074, -1, 8880, -1, 1732, -1, 8651, -1], 'generators': [807], 'label': '1056.615.528.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.f1.a1', 'old_label': '528.e1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580166
{'ambient': '1056.615', 'aut_centralizer_order': None, 'aut_label': '1056.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': ['96.a1.a1', '352.a1.a1', '528.a1.a1', '528.b1.a1', '528.c1.a1', '528.d1.a1', '528.e1.a1'], 'contains': [], 'core': '1056.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8860, 8047, 9087, 1546, 1865, 3526, 8519, 3526], 'generators': [], 'label': '1056.615.1056.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1056.a1.a1', 'normal_contained_in': ['96.a1.a1', '352.a1.a1', '528.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1056.a1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1056.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 69580167
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['264.h1.a1', '264.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '8.g1.a1', '12.e1.a1', '44.j1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3187, 6267, 4161, 6397, 5687, 6452, 3738, 6452], 'generators': [3, 704, 528, 792, 96], 'label': '1056.615.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.e1.a1', '2.b1.a1', '2.g1.a1'], 'normal_contains': ['8.b1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580168
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.52', 'aut_weyl_index': 88, 'centralizer': '4.f1.a1', 'complements': ['264.h1.a1', '264.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.b1.a1', '12.f1.a1', '44.c1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [857, 1188, 2513, 2312, 7975, 7084, 1748, 7084], 'generators': [132, 96, 264, 704, 528], 'label': '1056.615.4.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.b1.a1', '12.f1.a1', '44.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580169
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '88.a1.a1', 'complements': ['264.h1.a1', '264.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.b1.a1', '12.g1.a1', '44.k1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2507, 7533, 905, 3269, 7261, 2450, 2485, 2450], 'generators': [541, 264, 528, 704, 96], 'label': '1056.615.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.e1.a1', '2.c1.a1', '2.f1.a1'], 'normal_contains': ['8.b1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '176.31', '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': '88.11'}
id: 69580170
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.g1.a1', '12.h1.a1', '44.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5368, -1, 6516, -1, 2912, -1, 6997, -1], 'generators': [1, 704, 528, 2, 96], 'label': '1056.615.4.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.h1.a1', 'projective_image': '176.31', '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': '88.11'}
id: 69580171
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.g1.a1', '12.i1.a1', '44.e1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6511, -1, 5860, -1, 3272, -1, 6641, -1], 'generators': [793, 704, 528, 2, 96], 'label': '1056.615.4.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.a1', 'projective_image': '176.31', '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': '44.3'}
id: 69580172
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.f1.a1', '8.h1.a1', '8.h1.a2', '12.j1.a1', '44.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8588, -1, 8544, -1, 1089, -1, 8757, -1], 'generators': [1, 528, 704, 134, 96], 'label': '1056.615.4.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.j1.a1', 'projective_image': '176.31', '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': '44.3'}
id: 69580173
{'ambient': '1056.615', 'aut_centralizer_order': 22, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '320.1629', 'aut_weyl_index': 22, 'centralizer': '16.a1.a1', 'complements': ['528.d1.a1', '528.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.f1.a1', '6.a1.a1', '22.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2847, 593, 2627, 9438, 6050, 8012, 3747, 8012], 'generators': [2, 528, 704, 96, 132, 792], 'label': '1056.615.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.a1.a1', '4.f1.a1', '6.a1.a1', '22.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580174
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['8.c1.a1', '8.e1.a1', '8.f1.a1', '12.k1.a1', '44.g1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7999, -1, 7533, -1, 2094, -1, 7617, -1], 'generators': [793, 704, 528, 134, 96], 'label': '1056.615.4.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '4.k1.a1', 'projective_image': '176.31', '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': '88.11'}
id: 69580175
{'ambient': '1056.615', 'aut_centralizer_order': 44, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '160.229', 'aut_weyl_index': 44, 'centralizer': '16.a1.a1', 'complements': ['176.d1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.f1.a1', '66.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2199, 494, 2378, 8006, 6330, 9083, 4066, 9083], 'generators': [2, 96, 792, 132, 528], 'label': '1056.615.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.a1.a1', '12.f1.a1', '66.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '528.130', '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': '16.11'}
id: 69580176
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['176.c1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.e1.a1', '12.h1.a1', '12.i1.a1', '66.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3353, 6267, 3387, 9370, 5396, 5769, 5700, 5769], 'generators': [1, 792, 528, 2, 96], 'label': '1056.615.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580177
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['176.c1.a1', '176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.g1.a1', '66.c1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2681, 3230, 2005, 8745, 6594, 3848, 4326, 3848], 'generators': [541, 264, 528, 2, 96], 'label': '1056.615.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.d1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580178
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1', '12.j1.a1', '12.k1.a1', '66.d1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5061, 1597, 4752, 5081, 3605, 1670, 6313, 1670], 'generators': [1, 792, 528, 134, 96], 'label': '1056.615.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.c1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580179
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1', '176.d1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1', '66.e1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1792, 4109, 1670, 6231, 6893, 5068, 3068, 5068], 'generators': [541, 264, 528, 134, 96], 'label': '1056.615.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580180
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '6.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '88.a1.a1', 'complements': ['176.b1.a1', '176.c1.a1', '176.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1', '66.f1.a1'], 'core': '6.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1173, 5611, 1337, 3946, 7774, 1052, 2197, 1052], 'generators': [1, 264, 528, 132, 96], 'label': '1056.615.6.f1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.f1.a1', 'normal_contained_in': ['2.f1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
id: 69580181
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '6.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1090', 'aut_weyl_index': 4, 'centralizer': '176.a1.a1', 'complements': ['176.b1.a1', '176.c1.a1', '176.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1', '66.g1.a1'], 'core': '6.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1437, 2581, 2830, 7069, 7553, 4366, 2773, 4366], 'generators': [3, 264, 528, 132, 96], 'label': '1056.615.6.g1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.g1.a1', 'normal_contained_in': ['2.g1.a1', '3.a1.a1'], 'normal_contains': ['12.d1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580182
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.j1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '24.a1.a1', '88.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6944, 8702, 7454, 1389, 1394, 2354, 8908, 2354], 'generators': [1, 704, 96, 528], 'label': '1056.615.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '176.31', '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': '44.3'}
id: 69580183
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '8.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '88.a1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4182, 7217, 4165, 2545, 5602, 5063, 4103, 5063], 'generators': [792, 96, 528, 704], 'label': '1056.615.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.b1.a1', '4.a1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '88.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580184
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['528.c1.a1', '528.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '4.h1.a1', '4.i1.a1', '6.b1.a1', '22.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4461, 7899, 4555, 8500, 5264, 6884, 5251, 6884], 'generators': [1, 96, 792, 704, 2, 528], 'label': '1056.615.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.c1.a1', '4.e1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580185
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.i1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '88.f1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7794, 9680, 5945, 458, 2241, 1574, 7472, 1574], 'generators': [793, 528, 96, 704], 'label': '1056.615.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
id: 69580186
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '24.d1.a1', '88.b1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6497, -1, 6316, -1, 2828, -1, 7143, -1], 'generators': [2, 704, 96, 528], 'label': '1056.615.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '176.31', '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': '4.2'}
id: 69580187
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '24.e1.a1', '88.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8294, -1, 7795, -1, 784, -1, 8306, -1], 'generators': [134, 704, 96, 528], 'label': '1056.615.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.e1.a1', 'projective_image': '176.31', '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': '4.2'}
id: 69580188
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.j1.a1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.e1.a1', '24.f1.a1', '88.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8740, -1, 8213, -1, 1089, -1, 8607, -1], 'generators': [807, 704, 96, 528], 'label': '1056.615.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '8.f1.a1', 'projective_image': '176.31', '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': '44.3'}
id: 69580189
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '24.g1.a1', '88.g1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5737, -1, 6689, -1, 3382, -1, 6346, -1], 'generators': [3, 528, 96, 704], 'label': '1056.615.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.g1.a1', 'projective_image': '176.31', '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': '44.3'}
id: 69580190
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '24.h1.a1', '88.h1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9425, -1, 9571, -1, 136, -1, 9550, -1], 'generators': [1, 704, 96, 134], 'label': '1056.615.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.h1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
id: 69580191
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1'], 'contains': ['16.c1.a1', '16.d1.a1', '16.e1.a1', '24.h1.a2', '88.h1.a2'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9425, -1, 9141, -1, 136, -1, 9851, -1], 'generators': [529, 704, 96, 134], 'label': '1056.615.8.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '8.h1.a2', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a2', 'subgroup_fusion': None, 'weyl_group': '22.1'}
id: 69580192
{'ambient': '1056.615', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '64.261', 'aut_weyl_index': 110, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.c1.a1', '22.d1.a1', '22.e1.a1', '22.f1.a1', '22.g1.a1', '33.a1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [899, -1, 859, -1, 8447, -1, 1555, -1], 'generators': [1, 528, 792, 2, 132, 704], 'label': '1056.615.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580193
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.46', 'aut_weyl_index': 88, 'centralizer': '16.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '132.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2971, 3891, 2891, 8469, 6657, 6731, 4644, 6731], 'generators': [2, 96, 528, 792], 'label': '1056.615.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580194
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '80.46', 'aut_weyl_index': 88, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '132.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3502, 772, 3756, 4778, 4634, 6017, 4343, 6017], 'generators': [134, 96, 528, 792], 'label': '1056.615.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'normal_contains': ['24.b1.a1', '132.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580195
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['528.c1.a1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.g1.a1', '6.c1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3274, 5715, 1952, 7293, 6382, 3456, 4306, 3456], 'generators': [541, 96, 704, 264, 2, 528], 'label': '1056.615.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.g1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580196
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '132.h1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4714, 6300, 4727, 3071, 4939, 3068, 5110, 3068], 'generators': [1, 528, 96, 792], 'label': '1056.615.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.d1.a1', '6.b1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '528.130', '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': '88.11'}
id: 69580197
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '132.i1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3951, 3198, 4385, 6059, 5175, 4140, 4877, 4140], 'generators': [807, 528, 96, 792], 'label': '1056.615.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.d1.a1', '6.d1.a1', '6.c1.a1', '6.g1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '528.130', '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': '176.31'}
id: 69580198
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '880.118', 'aut_weyl_index': 8, 'centralizer': '176.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.b1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '132.j1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2657, 4667, 3264, 6699, 6921, 4593, 3354, 4593], 'generators': [3, 528, 96, 792], 'label': '1056.615.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.e1.a1', '6.e1.a1', '6.b1.a1', '6.g1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580199
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '40.14', 'aut_weyl_index': 176, 'centralizer': '4.f1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '132.c1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1540, 2668, 2293, 4122, 8018, 5468, 2021, 5468], 'generators': [132, 264, 528, 96], 'label': '1056.615.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.f1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'normal_contains': ['24.b1.a1', '132.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580200
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.a1.a1', 'complements': ['88.h1.a1', '88.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.b1.a1', '132.k1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1938, 5316, 1731, 5517, 7824, 3687, 2212, 3687], 'generators': [541, 528, 96, 264], 'label': '1056.615.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.g1.a1', '6.e1.a1', '6.c1.a1', '6.f1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '88.11'}
id: 69580201
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.g1.a1', '132.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5200, -1, 5798, -1, 3090, -1, 6634, -1], 'generators': [1, 528, 96, 2], 'label': '1056.615.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '528.130', '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': '88.11'}
id: 69580202
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.b1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.g1.a1', '132.e1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5715, -1, 5466, -1, 3742, -1, 5990, -1], 'generators': [793, 528, 96, 2], 'label': '1056.615.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580203
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.f1.a1', '24.h1.a1', '24.h1.a2', '132.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7515, -1, 8398, -1, 461, -1, 9229, -1], 'generators': [1, 528, 96, 134], 'label': '1056.615.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.j1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580204
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '440.42', 'aut_weyl_index': 16, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.f1.a1', '132.g1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6927, -1, 6842, -1, 1949, -1, 7760, -1], 'generators': [793, 528, 96, 134], 'label': '1056.615.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.k1.a1', 'projective_image': '528.130', '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': '88.11'}
id: 69580205
{'ambient': '1056.615', 'aut_centralizer_order': 352, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '2.a1.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', '48.a1.a1', '176.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8126, 8233, 7452, 1389, 2241, 3103, 7408, 3103], 'generators': [528, 96, 704], 'label': '1056.615.16.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'normal_contains': ['32.a1.a1', '48.a1.a1', '176.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580206
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['528.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '4.j1.a1', '4.k1.a1', '6.d1.a1', '22.d1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5323, 1745, 5138, 3707, 4075, 2511, 5873, 2511], 'generators': [1, 96, 792, 704, 134, 528], 'label': '1056.615.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.d1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580207
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1'], 'contains': ['32.a1.a1', '48.b1.a1', '176.b1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6443, -1, 6797, -1, 1758, -1, 8347, -1], 'generators': [2, 96, 704], 'label': '1056.615.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '16.b1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580208
{'ambient': '1056.615', 'aut_centralizer_order': 88, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '48.c1.a1', '176.c1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9329, -1, 9612, -1, 262, -1, 9007, -1], 'generators': [134, 96, 704], 'label': '1056.615.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.c1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580209
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '48.d1.a1', '176.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8966, -1, 9010, -1, 801, -1, 9539, -1], 'generators': [1, 96, 704], 'label': '1056.615.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.d1.a1', 'projective_image': '352.106', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '22.1'}
id: 69580210
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.h1.a1', '8.h1.a2'], 'contains': ['32.a1.a1', '48.e1.a1', '176.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9775, -1, 9351, -1, 496, -1, 9238, -1], 'generators': [807, 96, 704], 'label': '1056.615.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '16.e1.a1', 'projective_image': '352.106', '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': '22.1'}
id: 69580211
{'ambient': '1056.615', 'aut_centralizer_order': 220, 'aut_label': '22.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '16.a1.a1', 'complements': ['48.d1.a1', '48.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '44.c1.a1', '66.a1.a1'], 'core': '22.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2274, 740, 2158, 6226, 8192, 9741, 1326, 9741], 'generators': [2, 528, 132, 704, 792], 'label': '1056.615.22.a1.a1', 'mobius_quo': 0, 'mobius_sub': 11, 'normal_closure': '22.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['44.b1.a1', '44.a1.a1', '44.c1.a1', '66.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580212
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.d1.a1', '44.e1.a1', '44.h1.a1', '44.j1.a1', '66.b1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4176, -1, 4118, -1, 6022, -1, 3408, -1], 'generators': [1, 528, 2, 792, 704], 'label': '1056.615.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580213
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.i1.a1', '44.k1.a1', '66.c1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2748, -1, 1204, -1, 8447, -1, 1962, -1], 'generators': [541, 528, 2, 704, 264], 'label': '1056.615.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580214
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '22.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.f1.a1', '44.g1.a1', '44.h1.a1', '44.i1.a1', '66.d1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4849, -1, 4748, -1, 4851, -1, 4561, -1], 'generators': [1, 528, 134, 792, 704], 'label': '1056.615.22.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.d1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580215
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '22.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '11.a1.a1'], 'contains': ['44.b1.a1', '44.j1.a1', '44.k1.a1', '66.e1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1709, -1, 751, -1, 8779, -1, 998, -1], 'generators': [541, 528, 134, 704, 264], 'label': '1056.615.22.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.e1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580216
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '22.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.14', 'aut_weyl_index': 440, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.h1.a1', '44.k1.a1', '66.f1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [713, -1, 212, -1, 9810, -1, 187, -1], 'generators': [1, 528, 132, 704, 264], 'label': '1056.615.22.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.f1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 69580217
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['528.b1.a1', '528.d1.a1', '528.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.e1.a1', '22.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2358, 4426, 1454, 5055, 6821, 5852, 3299, 5852], 'generators': [541, 96, 704, 264, 134, 528], 'label': '1056.615.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580218
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '22.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '11.a1.a1'], 'contains': ['44.c1.a1', '44.i1.a1', '44.j1.a1', '66.g1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [225, -1, 2768, -1, 9400, -1, 592, -1], 'generators': [3, 528, 132, 704, 264], 'label': '1056.615.22.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.g1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580219
{'ambient': '1056.615', 'aut_centralizer_order': 32, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.h1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '264.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7060, 6917, 7236, 2545, 1923, 3491, 8183, 3491], 'generators': [1, 96, 528], 'label': '1056.615.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580220
{'ambient': '1056.615', 'aut_centralizer_order': 352, 'aut_label': '24.b1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'contains': ['48.a1.a1', '264.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3376, 4388, 3275, 4778, 5635, 4828, 4224, 4828], 'generators': [792, 528, 96], 'label': '1056.615.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1'], 'normal_contains': ['48.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '528.130', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580221
{'ambient': '1056.615', 'aut_centralizer_order': 32, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1', '12.i1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '264.f1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6646, 7698, 6178, 1801, 3192, 2650, 6469, 2650], 'generators': [793, 96, 528], 'label': '1056.615.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580222
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '264.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5828, -1, 5456, -1, 3753, -1, 6210, -1], 'generators': [2, 96, 528], 'label': '1056.615.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '528.130', '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': '4.2'}
id: 69580223
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.b1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.c1.a1', '264.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7535, -1, 7815, -1, 1358, -1, 7789, -1], 'generators': [134, 96, 528], 'label': '1056.615.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.e1.a1', 'projective_image': '528.130', '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: 69580224
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.d1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.e1.a1', '264.e1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7900, -1, 8236, -1, 1592, -1, 8020, -1], 'generators': [807, 96, 528], 'label': '1056.615.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.f1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580225
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '220.7', 'aut_weyl_index': 32, 'centralizer': '88.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.e1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '264.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5429, -1, 5873, -1, 4015, -1, 5656, -1], 'generators': [3, 96, 528], 'label': '1056.615.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '528.130', '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': '44.3'}
id: 69580226
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.j1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '264.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9331, -1, 9434, -1, 97, -1, 9772, -1], 'generators': [1, 96, 134], 'label': '1056.615.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '24.h1.a1', 'projective_image': '1056.615', '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': '22.1'}
id: 69580227
{'ambient': '1056.615', 'aut_centralizer_order': 8, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a2', '12.j1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '264.h1.a2'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9331, -1, 8666, -1, 97, -1, 9935, -1], 'generators': [529, 96, 134], 'label': '1056.615.24.h1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '24.h1.a2', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a2', 'subgroup_fusion': None, 'weyl_group': '22.1'}
id: 69580228
{'ambient': '1056.615', 'aut_centralizer_order': 4, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1760.1272', 'aut_weyl_index': 4, 'centralizer': '88.a1.a1', 'complements': ['528.b1.a1', '528.c1.a1', '528.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '6.f1.a1', '22.f1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [901, 6840, 946, 2582, 7843, 1570, 2318, 1570], 'generators': [1, 96, 704, 264, 132, 528], 'label': '1056.615.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.f1.a1', '4.g1.a1', '6.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '176.31', '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': '88.11'}
id: 69580229
{'ambient': '1056.615', 'aut_centralizer_order': 352, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 352, 'centralizer': '2.a1.a1', 'complements': ['33.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.d1.a1', '16.e1.a1'], 'contains': ['96.a1.a1', '352.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9024, 8336, 8982, 1192, 1516, 3108, 8647, 3108], 'generators': [704, 96], 'label': '1056.615.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['96.a1.a1', '352.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '352.106', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.7', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580230
{'ambient': '1056.615', 'aut_centralizer_order': 20, 'aut_label': '33.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '32.46', 'aut_weyl_index': 220, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '11.a1.a1'], 'contains': ['66.a1.a1', '66.b1.a1', '66.c1.a1', '66.d1.a1', '66.e1.a1', '66.f1.a1', '66.g1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1227, -1, 1386, -1, 9089, -1, 1555, -1], 'generators': [1, 2, 132], 'label': '1056.615.33.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '33.a1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '33.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580231
{'ambient': '1056.615', 'aut_centralizer_order': 440, 'aut_label': '44.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '8.c1.a1', 'complements': ['24.h1.a1', '24.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.c1.a1'], 'contains': ['88.a1.a1', '88.b1.a1', '132.a1.a1'], 'core': '44.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3205, 2105, 2864, 6679, 7159, 8369, 2698, 8369], 'generators': [2, 792, 704, 528], 'label': '1056.615.44.a1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.a1.a1', 'normal_contained_in': ['4.a1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580232
{'ambient': '1056.615', 'aut_centralizer_order': 440, 'aut_label': '44.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.a1.a1', '22.d1.a1', '22.e1.a1'], 'contains': ['88.a1.a1', '88.c1.a1', '132.b1.a1'], 'core': '44.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3594, 325, 3885, 5564, 5819, 7772, 2447, 7772], 'generators': [134, 792, 704, 528], 'label': '1056.615.44.b1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.b1.a1', 'normal_contained_in': ['4.b1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580233
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '44.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '4.f1.a1', 'complements': ['24.h1.a1', '24.h1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '22.a1.a1', '22.f1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '132.c1.a1'], 'core': '44.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [554, 1373, 2262, 4555, 9162, 7280, 638, 7280], 'generators': [132, 704, 264, 528], 'label': '1056.615.44.c1.a1', 'mobius_quo': 0, 'mobius_sub': -22, 'normal_closure': '44.c1.a1', 'normal_contained_in': ['4.f1.a1', '22.a1.a1'], 'normal_contains': ['88.a1.a1', '132.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '44.c1.a1', 'projective_image': '176.31', 'quotient_action_image': '4.2', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580234
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.d1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.d1.a1', '88.g1.a1', '132.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5406, -1, 5924, -1, 4051, -1, 5686, -1], 'generators': [1, 2, 704, 528], 'label': '1056.615.44.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.d1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580235
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '44.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '22.b1.a1'], 'contains': ['88.b1.a1', '88.f1.a1', '88.g1.a1', '132.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [5823, -1, 5613, -1, 4329, -1, 5410, -1], 'generators': [793, 2, 704, 528], 'label': '1056.615.44.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.e1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580236
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.f1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '22.d1.a1'], 'contains': ['88.c1.a1', '88.d1.a1', '88.e1.a1', '88.h1.a1', '88.h1.a2', '132.f1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7911, -1, 8096, -1, 1693, -1, 8013, -1], 'generators': [1, 134, 528, 704], 'label': '1056.615.44.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '44.f1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580237
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.g1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '22.d1.a1'], 'contains': ['88.c1.a1', '88.e1.a1', '88.f1.a1', '132.g1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7586, -1, 6605, -1, 2549, -1, 6868, -1], 'generators': [793, 134, 704, 528], 'label': '1056.615.44.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '44.g1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580238
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '44.h1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '44.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1', '22.d1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '88.d1.a1', '88.f1.a1', '132.h1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4567, -1, 4721, -1, 6098, -1, 3613, -1], 'generators': [1, 792, 704, 528], 'label': '1056.615.44.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.h1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580239
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['528.b1.a1', '528.c1.a1', '528.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1', '22.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1533, 2930, 3325, 6282, 7482, 4824, 2784, 4824], 'generators': [3, 96, 704, 264, 132, 528], 'label': '1056.615.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '176.31', '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': '176.31'}
id: 69580240
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.i1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '22.c1.a1', '22.d1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.e1.a1', '132.i1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4236, -1, 4250, -1, 6377, -1, 2949, -1], 'generators': [807, 792, 704, 528], 'label': '1056.615.44.i1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.i1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.i1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580241
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '44.j1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '22.b1.a1', '22.e1.a1', '22.g1.a1'], 'contains': ['88.a1.a1', '88.g1.a1', '132.j1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2624, -1, 3520, -1, 7586, -1, 1550, -1], 'generators': [3, 792, 704, 528], 'label': '1056.615.44.j1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.j1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580242
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '44.k1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '44.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '22.c1.a1', '22.e1.a1', '22.f1.a1'], 'contains': ['88.a1.a1', '132.k1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2206, -1, 612, -1, 8631, -1, 983, -1], 'generators': [541, 704, 264, 528], 'label': '1056.615.44.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.k1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 69580243
{'ambient': '1056.615', 'aut_centralizer_order': 704, 'aut_label': '48.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '2.a1.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', '528.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6781, 7703, 7284, 1853, 2245, 3491, 7382, 3491], 'generators': [528, 96], 'label': '1056.615.48.a1.a1', 'mobius_quo': 1, '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.a1.a1', '528.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '24.10', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580244
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.d1.a1'], 'contains': ['96.a1.a1', '528.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6412, -1, 6707, -1, 2081, -1, 8090, -1], 'generators': [2, 96], 'label': '1056.615.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.i1.a1', 'old_label': '48.b1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580245
{'ambient': '1056.615', 'aut_centralizer_order': 176, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '10.2', 'aut_weyl_index': 704, 'centralizer': '8.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.e1.a1', '24.h1.a1', '24.h1.a2'], 'contains': ['96.a1.a1', '528.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9501, -1, 9237, -1, 868, -1, 9110, -1], 'generators': [134, 96], 'label': '1056.615.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.c1.a1', 'projective_image': '1056.615', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580246
{'ambient': '1056.615', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '44.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.a1.a1', '24.h1.a1', '24.h1.a2'], 'contains': ['96.a1.a1', '528.d1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8631, -1, 9427, -1, 1198, -1, 9504, -1], 'generators': [1, 96], 'label': '1056.615.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '48.d1.a1', 'projective_image': '1056.615', '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': '22.1'}
id: 69580247
{'ambient': '1056.615', 'aut_centralizer_order': 16, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '110.1', 'aut_weyl_index': 64, 'centralizer': '88.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.f1.a1', '24.h1.a1', '24.h1.a2'], 'contains': ['96.a1.a1', '528.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9304, -1, 8851, -1, 1033, -1, 9273, -1], 'generators': [807, 96], 'label': '1056.615.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.j1.a1', 'old_label': '48.e1.a1', 'projective_image': '1056.615', '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': '22.1'}
id: 69580248
{'ambient': '1056.615', 'aut_centralizer_order': 440, 'aut_label': '66.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '16.a1.a1', 'complements': ['16.d1.a1', '16.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '22.a1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.b1.a1', '132.c1.a1'], 'core': '66.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1693, 489, 2130, 5539, 8166, 8826, 1742, 8826], 'generators': [2, 132], 'label': '1056.615.66.a1.a1', 'mobius_quo': 0, 'mobius_sub': -11, 'normal_closure': '66.a1.a1', 'normal_contained_in': ['6.a1.a1', '22.a1.a1'], 'normal_contains': ['132.b1.a1', '132.a1.a1', '132.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '66.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '2.1', 'quotient_action_kernel': '33.1', 'quotient_action_kernel_order': 33, 'quotient_fusion': None, 'short_label': '66.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580249
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '66.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '88.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '22.b1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.d1.a1', '132.e1.a1', '132.h1.a1', '132.j1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2987, -1, 3243, -1, 7373, -1, 3160, -1], 'generators': [1, 2, 792], 'label': '1056.615.66.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.b1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580250
{'ambient': '1056.615', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '176.a1.a1', 'complements': ['352.a1.a1'], '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', '33.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1668, 2897, 2117, 7855, 7191, 4140, 4007, 4140], 'generators': [1, 96, 132, 792, 2, 528], 'label': '1056.615.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.d1.a1', '6.e1.a1', '6.b1.a1', '6.c1.a1', '6.f1.a1', '6.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '528.130', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '176.31'}
id: 69580251
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '66.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '22.c1.a1', '33.a1.a1'], 'contains': ['132.a1.a1', '132.i1.a1', '132.k1.a1'], 'core': '132.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2223, -1, 1276, -1, 8300, -1, 1874, -1], 'generators': [541, 2], 'label': '1056.615.66.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.c1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580252
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '66.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '88.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '22.d1.a1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.f1.a1', '132.g1.a1', '132.h1.a1', '132.i1.a1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4649, -1, 4816, -1, 5385, -1, 3888, -1], 'generators': [1, 134, 792], 'label': '1056.615.66.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.d1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 69580253
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '66.e1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '22.e1.a1', '33.a1.a1'], 'contains': ['132.b1.a1', '132.j1.a1', '132.k1.a1'], 'core': '132.b1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1505, -1, 1552, -1, 8458, -1, 1333, -1], 'generators': [541, 134], 'label': '1056.615.66.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.e1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.e1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580254
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '66.f1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '8.5', 'aut_weyl_index': 880, 'centralizer': '88.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '22.f1.a1', '33.a1.a1'], 'contains': ['132.c1.a1', '132.h1.a1', '132.k1.a1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1227, -1, 1043, -1, 8987, -1, 811, -1], 'generators': [1, 132], 'label': '1056.615.66.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.f1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 69580255
{'ambient': '1056.615', 'aut_centralizer_order': 40, 'aut_label': '66.g1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '16.11', 'aut_weyl_index': 440, 'centralizer': '176.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '22.g1.a1', '33.a1.a1'], 'contains': ['132.c1.a1', '132.i1.a1', '132.j1.a1'], 'core': '132.c1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1007, -1, 2565, -1, 8803, -1, 1154, -1], 'generators': [3, 132], 'label': '1056.615.66.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '66.g1.a1', 'projective_image': '528.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '66.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 69580256
{'ambient': '1056.615', 'aut_centralizer_order': 1760, 'aut_label': '88.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '2.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1', '44.h1.a1', '44.i1.a1', '44.j1.a1', '44.k1.a1'], 'contains': ['176.a1.a1', '264.a1.a1'], 'core': '88.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3665, 2056, 3858, 4878, 6377, 6975, 2790, 6975], 'generators': [792, 704, 528], 'label': '1056.615.88.a1.a1', 'mobius_quo': 0, 'mobius_sub': 88, 'normal_closure': '88.a1.a1', 'normal_contained_in': ['8.b1.a1', '44.b1.a1', '44.a1.a1', '44.c1.a1'], 'normal_contains': ['176.a1.a1', '264.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '176.31', 'quotient_action_image': '2.1', 'quotient_action_kernel': '44.3', 'quotient_action_kernel_order': 44, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580257
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '44.a1.a1', '44.d1.a1', '44.e1.a1'], 'contains': ['176.a1.a1', '176.b1.a1', '264.b1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6046, -1, 6182, -1, 4253, -1, 5421, -1], 'generators': [2, 528, 704], 'label': '1056.615.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '88.b1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580258
{'ambient': '1056.615', 'aut_centralizer_order': 880, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '4.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '44.b1.a1', '44.f1.a1', '44.g1.a1'], 'contains': ['176.a1.a1', '176.c1.a1', '264.c1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7586, -1, 7757, -1, 2449, -1, 6703, -1], 'generators': [134, 528, 704], 'label': '1056.615.88.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '44.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '88.c1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580259
{'ambient': '1056.615', 'aut_centralizer_order': 160, 'aut_label': '88.d1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '22.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.d1.a1', '44.f1.a1', '44.h1.a1'], 'contains': ['176.a1.a1', '176.d1.a1', '264.d1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [7285, -1, 7395, -1, 2954, -1, 7202, -1], 'generators': [1, 528, 704], 'label': '1056.615.88.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.d1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 69580260
{'ambient': '1056.615', 'aut_centralizer_order': 80, 'aut_label': '88.e1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1760, 'centralizer': '44.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '44.f1.a1', '44.g1.a1', '44.i1.a1'], 'contains': ['176.a1.a1', '176.e1.a1', '264.e1.a1'], 'core': '176.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [7887, -1, 8118, -1, 2702, -1, 6953, -1], 'generators': [807, 528, 704], 'label': '1056.615.88.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.d1.a1', 'old_label': '88.e1.a1', 'projective_image': '176.31', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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