LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-11-07T14:41:24.607183

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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 420, 'aut_gen_orders': [12, 6], 'aut_gens': [[4405687, 8386576, 7390223], [14924880, 1623736, 19248487], [4077360, 7741463, 11023207]], 'aut_group': '120960.e', 'aut_hash': 8389248707221534269, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 120960, 'aut_permdeg': 84, 'aut_perms': [672722999719274767744501941729726188400089427181724023220727738610240287956584555999137162466904149977921655048589147911960258, 61121167021398419473087545622799035140002012130573973758839065685480913758333283290029238733533933298693673240538792908121719], 'aut_phi_ratio': 26.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 21, 4, 1], [2, 105, 1, 1], [2, 105, 3, 1], [2, 105, 4, 1], [3, 70, 1, 1], [3, 280, 1, 1], [4, 210, 4, 1], [4, 630, 1, 1], [4, 630, 3, 1], [5, 504, 1, 1], [6, 70, 3, 1], [6, 210, 1, 1], [6, 210, 3, 1], [6, 280, 3, 1], [6, 420, 4, 1], [6, 840, 4, 1], [7, 720, 1, 1], [10, 504, 3, 1], [10, 504, 4, 1], [12, 420, 4, 1], [14, 720, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times S_7', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '5040.w', 'autcentquo_hash': 6283920599749723413, 'autcentquo_nilpotent': False, 'autcentquo_order': 5040, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 21, 4], [2, 105, 8], [3, 70, 1], [3, 280, 1], [4, 210, 4], [4, 630, 4], [5, 504, 1], [6, 70, 3], [6, 210, 4], [6, 280, 3], [6, 420, 4], [6, 840, 4], [7, 720, 1], [10, 504, 7], [12, 420, 4], [14, 720, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '5040.w', 'commutator_count': 1, 'commutator_label': '2520.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2520.a'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5040.w', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 21, 1, 4], [2, 105, 1, 8], [3, 70, 1, 1], [3, 280, 1, 1], [4, 210, 1, 4], [4, 630, 1, 4], [5, 504, 1, 1], [6, 70, 1, 3], [6, 210, 1, 4], [6, 280, 1, 3], [6, 420, 1, 4], [6, 840, 1, 4], [7, 720, 1, 1], [10, 504, 1, 7], [12, 420, 1, 4], [14, 720, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 21720132, 'exponent': 420, 'exponents_of_order': [6, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20160.l', 'hash': 8804660164701733268, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 420, 'inner_gen_orders': [4, 5, 7], 'inner_gens': [[4405687, 408976, 18871343], [18637927, 8386576, 12394103], [14878087, 22307776, 7390223]], 'inner_hash': 6283920599749723413, 'inner_nilpotent': False, 'inner_order': 5040, 'inner_split': True, 'inner_tex': 'S_7', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [6, 8], [14, 16], [15, 8], [20, 4], [21, 8], [35, 8]], 'label': '20160.l', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2^2*S7', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 23, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 60, 'number_divisions': 60, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 426, 'number_subgroup_classes': 1692, 'number_subgroups': 264796, 'old_label': None, 'order': 20160, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 927], [3, 350], [4, 3360], [5, 504], [6, 6930], [7, 720], [10, 3528], [12, 1680], [14, 2160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[4405687, 8386583, 7390216], [4405687, 8386567, 7390216], [4405696, 8386576, 7390223], [4405703, 8386576, 7390223]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [6, 8], [14, 16], [15, 8], [20, 4], [21, 8], [35, 8]], 'representations': {'Perm': {'d': 11, 'gens': [4405687, 8386576, 7390223]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times S_7', 'transitive_degree': 28, '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: 98152013
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 12, 'group_order': 20160, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
id: 98152024
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 12, 'group_order': 20160, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 7, 'size': 1}
id: 98152035
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 12, 'group_order': 20160, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 16, 'size': 1}
id: 98152046
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 12, 'group_order': 20160, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 23, 'size': 1}
id: 98152057
{'aut_label': '2D', 'centralizer': '21.a1', 'counter': 5, 'group_counter': 12, 'group_order': 20160, 'label': '2D', 'order': 2, 'powers': [1, 5, 5, 5], 'representative': 7620480, 'size': 21}
id: 98152068
{'aut_label': '2D', 'centralizer': '21.a1', 'counter': 6, 'group_counter': 12, 'group_order': 20160, 'label': '2E', 'order': 2, 'powers': [1, 6, 6, 6], 'representative': 136, 'size': 21}
id: 98152070
{'aut_label': '2D', 'centralizer': '21.a1', 'counter': 7, 'group_counter': 12, 'group_order': 20160, 'label': '2F', 'order': 2, 'powers': [1, 7, 7, 7], 'representative': 11289623, 'size': 21}
id: 98152071
{'aut_label': '2D', 'centralizer': '21.a1', 'counter': 8, 'group_counter': 12, 'group_order': 20160, 'label': '2G', 'order': 2, 'powers': [1, 8, 8, 8], 'representative': 7620487, 'size': 21}
id: 98152072
{'aut_label': '2H', 'centralizer': '105.b1', 'counter': 9, 'group_counter': 12, 'group_order': 20160, 'label': '2H', 'order': 2, 'powers': [1, 9, 9, 9], 'representative': 847440, 'size': 105}
id: 98152014
{'aut_label': '2I', 'centralizer': '105.a1', 'counter': 10, 'group_counter': 12, 'group_order': 20160, 'label': '2I', 'order': 2, 'powers': [1, 10, 10, 10], 'representative': 15689647, 'size': 105}
id: 98152015
{'aut_label': '2I', 'centralizer': '105.a1', 'counter': 11, 'group_counter': 12, 'group_order': 20160, 'label': '2J', 'order': 2, 'powers': [1, 11, 11, 11], 'representative': 18684743, 'size': 105}
id: 98152016
{'aut_label': '2I', 'centralizer': '105.a1', 'counter': 12, 'group_counter': 12, 'group_order': 20160, 'label': '2K', 'order': 2, 'powers': [1, 12, 12, 12], 'representative': 16062480, 'size': 105}
id: 98152017
{'aut_label': '2I', 'centralizer': '105.a1', 'counter': 13, 'group_counter': 12, 'group_order': 20160, 'label': '2L', 'order': 2, 'powers': [1, 13, 13, 13], 'representative': 3670696, 'size': 105}
id: 98152018
{'aut_label': '2M', 'centralizer': '105.b1', 'counter': 14, 'group_counter': 12, 'group_order': 20160, 'label': '2M', 'order': 2, 'powers': [1, 14, 14, 14], 'representative': 7636447, 'size': 105}
id: 98152019
{'aut_label': '2M', 'centralizer': '105.b1', 'counter': 15, 'group_counter': 12, 'group_order': 20160, 'label': '2N', 'order': 2, 'powers': [1, 15, 15, 15], 'representative': 95896, 'size': 105}
id: 98152020
{'aut_label': '2M', 'centralizer': '105.b1', 'counter': 16, 'group_counter': 12, 'group_order': 20160, 'label': '2O', 'order': 2, 'powers': [1, 16, 16, 16], 'representative': 18553703, 'size': 105}
id: 98152021
{'aut_label': '3A', 'centralizer': '70.d1', 'counter': 17, 'group_counter': 12, 'group_order': 20160, 'label': '3A', 'order': 3, 'powers': [17, 1, 17, 17], 'representative': 1440, 'size': 70}
id: 98152022
{'aut_label': '3B', 'centralizer': '280.j1', 'counter': 18, 'group_counter': 12, 'group_order': 20160, 'label': '3B', 'order': 3, 'powers': [18, 1, 18, 18], 'representative': 12434520, 'size': 280}
id: 98152023
{'aut_label': '4A', 'centralizer': '210.l1', 'counter': 19, 'group_counter': 12, 'group_order': 20160, 'label': '4A', 'order': 4, 'powers': [9, 19, 19, 19], 'representative': 892936, 'size': 210}
id: 98152025
{'aut_label': '4A', 'centralizer': '210.l1', 'counter': 20, 'group_counter': 12, 'group_order': 20160, 'label': '4B', 'order': 4, 'powers': [9, 20, 20, 20], 'representative': 161400, 'size': 210}
id: 98152026
{'aut_label': '4A', 'centralizer': '210.l1', 'counter': 21, 'group_counter': 12, 'group_order': 20160, 'label': '4C', 'order': 4, 'powers': [9, 21, 21, 21], 'representative': 408247, 'size': 210}
id: 98152027
{'aut_label': '4A', 'centralizer': '210.l1', 'counter': 22, 'group_counter': 12, 'group_order': 20160, 'label': '4D', 'order': 4, 'powers': [9, 22, 22, 22], 'representative': 772703, 'size': 210}
id: 98152028
{'aut_label': '4E', 'centralizer': '630.d1', 'counter': 23, 'group_counter': 12, 'group_order': 20160, 'label': '4E', 'order': 4, 'powers': [9, 23, 23, 23], 'representative': 1452976, 'size': 630}
id: 98152029
{'aut_label': '4E', 'centralizer': '630.d1', 'counter': 24, 'group_counter': 12, 'group_order': 20160, 'label': '4F', 'order': 4, 'powers': [9, 24, 24, 24], 'representative': 4774327, 'size': 630}
id: 98152030
{'aut_label': '4E', 'centralizer': '630.d1', 'counter': 25, 'group_counter': 12, 'group_order': 20160, 'label': '4G', 'order': 4, 'powers': [9, 25, 25, 25], 'representative': 7429823, 'size': 630}
id: 98152031
{'aut_label': '4H', 'centralizer': '630.d1', 'counter': 26, 'group_counter': 12, 'group_order': 20160, 'label': '4H', 'order': 4, 'powers': [9, 26, 26, 26], 'representative': 22273320, 'size': 630}
id: 98152032
{'aut_label': '5A', 'centralizer': '504.f1', 'counter': 27, 'group_counter': 12, 'group_order': 20160, 'label': '5A', 'order': 5, 'powers': [27, 27, 1, 27], 'representative': 23639040, 'size': 504}
id: 98152033
{'aut_label': '6A', 'centralizer': '70.d1', 'counter': 28, 'group_counter': 12, 'group_order': 20160, 'label': '6A', 'order': 6, 'powers': [17, 2, 28, 28], 'representative': 847, 'size': 70}
id: 98152034
{'aut_label': '6A', 'centralizer': '70.d1', 'counter': 29, 'group_counter': 12, 'group_order': 20160, 'label': '6B', 'order': 6, 'powers': [17, 3, 29, 29], 'representative': 856, 'size': 70}
id: 98152036
{'aut_label': '6A', 'centralizer': '70.d1', 'counter': 30, 'group_counter': 12, 'group_order': 20160, 'label': '6C', 'order': 6, 'powers': [17, 4, 30, 30], 'representative': 863, 'size': 70}
id: 98152037
{'aut_label': '6D', 'centralizer': '210.k1', 'counter': 31, 'group_counter': 12, 'group_order': 20160, 'label': '6D', 'order': 6, 'powers': [17, 9, 31, 31], 'representative': 18925320, 'size': 210}
id: 98152038
{'aut_label': '6E', 'centralizer': '210.k1', 'counter': 32, 'group_counter': 12, 'group_order': 20160, 'label': '6E', 'order': 6, 'powers': [17, 14, 32, 32], 'representative': 8362807, 'size': 210}
id: 98152039
{'aut_label': '6E', 'centralizer': '210.k1', 'counter': 33, 'group_counter': 12, 'group_order': 20160, 'label': '6F', 'order': 6, 'powers': [17, 15, 33, 33], 'representative': 5217136, 'size': 210}
id: 98152040
{'aut_label': '6E', 'centralizer': '210.k1', 'counter': 34, 'group_counter': 12, 'group_order': 20160, 'label': '6G', 'order': 6, 'powers': [17, 16, 34, 34], 'representative': 18956903, 'size': 210}
id: 98152041
{'aut_label': '6H', 'centralizer': '280.j1', 'counter': 35, 'group_counter': 12, 'group_order': 20160, 'label': '6H', 'order': 6, 'powers': [18, 2, 35, 35], 'representative': 21905407, 'size': 280}
id: 98152042
{'aut_label': '6H', 'centralizer': '280.j1', 'counter': 36, 'group_counter': 12, 'group_order': 20160, 'label': '6I', 'order': 6, 'powers': [18, 4, 36, 36], 'representative': 7259063, 'size': 280}
id: 98152043
{'aut_label': '6H', 'centralizer': '280.j1', 'counter': 37, 'group_counter': 12, 'group_order': 20160, 'label': '6J', 'order': 6, 'powers': [18, 3, 37, 37], 'representative': 20044216, 'size': 280}
id: 98152044
{'aut_label': '6K', 'centralizer': '420.ba1', 'counter': 38, 'group_counter': 12, 'group_order': 20160, 'label': '6K', 'order': 6, 'powers': [17, 5, 38, 38], 'representative': 9077160, 'size': 420}
id: 98152045
{'aut_label': '6K', 'centralizer': '420.ba1', 'counter': 39, 'group_counter': 12, 'group_order': 20160, 'label': '6L', 'order': 6, 'powers': [17, 7, 39, 39], 'representative': 11371103, 'size': 420}
id: 98152047
{'aut_label': '6K', 'centralizer': '420.ba1', 'counter': 40, 'group_counter': 12, 'group_order': 20160, 'label': '6M', 'order': 6, 'powers': [17, 6, 40, 40], 'representative': 887176, 'size': 420}
id: 98152048
{'aut_label': '6K', 'centralizer': '420.ba1', 'counter': 41, 'group_counter': 12, 'group_order': 20160, 'label': '6N', 'order': 6, 'powers': [17, 8, 41, 41], 'representative': 8346247, 'size': 420}
id: 98152049
{'aut_label': '6O', 'centralizer': '840.bb1', 'counter': 42, 'group_counter': 12, 'group_order': 20160, 'label': '6O', 'order': 6, 'powers': [18, 10, 42, 42], 'representative': 18195967, 'size': 840}
id: 98152050
{'aut_label': '6O', 'centralizer': '840.bb1', 'counter': 43, 'group_counter': 12, 'group_order': 20160, 'label': '6P', 'order': 6, 'powers': [18, 11, 43, 43], 'representative': 22217783, 'size': 840}
id: 98152051
{'aut_label': '6O', 'centralizer': '840.bb1', 'counter': 44, 'group_counter': 12, 'group_order': 20160, 'label': '6Q', 'order': 6, 'powers': [18, 12, 44, 44], 'representative': 23321520, 'size': 840}
id: 98152052
{'aut_label': '6O', 'centralizer': '840.bb1', 'counter': 45, 'group_counter': 12, 'group_order': 20160, 'label': '6R', 'order': 6, 'powers': [18, 13, 45, 45], 'representative': 8079976, 'size': 840}
id: 98152053
{'aut_label': '7A', 'centralizer': '720.b1', 'counter': 46, 'group_counter': 12, 'group_order': 20160, 'label': '7A', 'order': 7, 'powers': [46, 46, 46, 1], 'representative': 15256800, 'size': 720}
id: 98152054
{'aut_label': '10A', 'centralizer': '504.f1', 'counter': 47, 'group_counter': 12, 'group_order': 20160, 'label': '10A', 'order': 10, 'powers': [27, 47, 3, 47], 'representative': 5448976, 'size': 504}
id: 98152055
{'aut_label': '10A', 'centralizer': '504.f1', 'counter': 48, 'group_counter': 12, 'group_order': 20160, 'label': '10B', 'order': 10, 'powers': [27, 48, 2, 48], 'representative': 21777967, 'size': 504}
id: 98152056
{'aut_label': '10C', 'centralizer': '504.f1', 'counter': 49, 'group_counter': 12, 'group_order': 20160, 'label': '10C', 'order': 10, 'powers': [27, 49, 6, 49], 'representative': 12020536, 'size': 504}
id: 98152058
{'aut_label': '10C', 'centralizer': '504.f1', 'counter': 50, 'group_counter': 12, 'group_order': 20160, 'label': '10D', 'order': 10, 'powers': [27, 50, 5, 50], 'representative': 21774360, 'size': 504}
id: 98152059
{'aut_label': '10C', 'centralizer': '504.f1', 'counter': 51, 'group_counter': 12, 'group_order': 20160, 'label': '10E', 'order': 10, 'powers': [27, 51, 7, 51], 'representative': 12515903, 'size': 504}
id: 98152060
{'aut_label': '10A', 'centralizer': '504.f1', 'counter': 52, 'group_counter': 12, 'group_order': 20160, 'label': '10F', 'order': 10, 'powers': [27, 52, 4, 52], 'representative': 132623, 'size': 504}
id: 98152061
{'aut_label': '10C', 'centralizer': '504.f1', 'counter': 53, 'group_counter': 12, 'group_order': 20160, 'label': '10G', 'order': 10, 'powers': [27, 53, 8, 53], 'representative': 19722967, 'size': 504}
id: 98152062
{'aut_label': '12A', 'centralizer': '420.be1', 'counter': 54, 'group_counter': 12, 'group_order': 20160, 'label': '12A', 'order': 12, 'powers': [31, 19, 54, 54], 'representative': 16457056, 'size': 420}
id: 98152063
{'aut_label': '12A', 'centralizer': '420.be1', 'counter': 55, 'group_counter': 12, 'group_order': 20160, 'label': '12B', 'order': 12, 'powers': [31, 20, 55, 55], 'representative': 18236160, 'size': 420}
id: 98152064
{'aut_label': '12A', 'centralizer': '420.be1', 'counter': 56, 'group_counter': 12, 'group_order': 20160, 'label': '12C', 'order': 12, 'powers': [31, 21, 56, 56], 'representative': 23270407, 'size': 420}
id: 98152065
{'aut_label': '12A', 'centralizer': '420.be1', 'counter': 57, 'group_counter': 12, 'group_order': 20160, 'label': '12D', 'order': 12, 'powers': [31, 22, 57, 57], 'representative': 9239063, 'size': 420}
id: 98152066
{'aut_label': '14A', 'centralizer': '720.b1', 'counter': 58, 'group_counter': 12, 'group_order': 20160, 'label': '14A', 'order': 14, 'powers': [46, 58, 58, 4], 'representative': 19404863, 'size': 720}
id: 98152067
{'aut_label': '14A', 'centralizer': '720.b1', 'counter': 59, 'group_counter': 12, 'group_order': 20160, 'label': '14B', 'order': 14, 'powers': [46, 59, 59, 2], 'representative': 19731727, 'size': 720}
id: 98152069
{'aut_label': '14A', 'centralizer': '720.b1', 'counter': 60, 'group_counter': 12, 'group_order': 20160, 'label': '14C', 'order': 14, 'powers': [46, 60, 60, 3], 'representative': 19036096, 'size': 720}

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: 262946
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 262957
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 262968
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 262979
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 262990
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 263001
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 263003
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 263004
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.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], 'schur_index': 1}
id: 263005
{'cdim': 6, 'counter': 9, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6a', 'multiplicity': 1, 'nt': [7, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 4, 4, 4, 4, 0, 2, 0, 0, 2, 0, 2, 2, 3, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 262947
{'cdim': 6, 'counter': 10, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6b', 'multiplicity': 1, 'nt': [14, 46], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -4, -4, -4, -4, 0, 2, 0, 0, 2, 0, 2, 2, 3, 0, -2, -2, -2, -2, 0, 0, 0, 0, 1, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
id: 262948
{'cdim': 6, 'counter': 11, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6c', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, -6, -6, 6, -4, 4, -4, 4, 0, -2, 0, 0, 2, 0, -2, 2, 3, 0, -2, 2, -2, 2, 0, 0, 0, 0, 1, -3, -3, 3, -1, 1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
id: 262949
{'cdim': 6, 'counter': 12, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6d', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 4, -4, 4, -4, 0, -2, 0, 0, 2, 0, -2, 2, 3, 0, 2, -2, 2, -2, 0, 0, 0, 0, 1, -3, -3, 3, -1, 1, 1, -1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
id: 262950
{'cdim': 6, 'counter': 13, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6e', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, -6, 6, -6, -4, -4, 4, 4, 0, -2, 0, 0, 2, 0, 2, -2, 3, 0, -2, -2, 2, 2, 0, 0, 0, 0, 1, -3, 3, -3, -1, 1, -1, 1, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1], 'schur_index': 1}
id: 262951
{'cdim': 6, 'counter': 14, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6f', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 4, 4, -4, -4, 0, -2, 0, 0, 2, 0, 2, -2, 3, 0, 2, 2, -2, -2, 0, 0, 0, 0, 1, -3, 3, -3, -1, 1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1], 'schur_index': 1}
id: 262952
{'cdim': 6, 'counter': 15, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6g', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, 6, -6, -6, -4, 4, 4, -4, 0, 2, 0, 0, 2, 0, -2, -2, 3, 0, -2, 2, 2, -2, 0, 0, 0, 0, 1, 3, -3, -3, -1, -1, 1, 1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
id: 262953
{'cdim': 6, 'counter': 16, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.6h', 'multiplicity': 1, 'nt': [14, 49], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 4, -4, -4, 4, 0, 2, 0, 0, 2, 0, -2, -2, 3, 0, 2, -2, -2, 2, 0, 0, 0, 0, 1, 3, -3, -3, -1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
id: 262954
{'cdim': 14, 'counter': 17, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14a', 'multiplicity': 1, 'nt': [21, 38], 'qdim': 14, 'qvalues': [14, 14, 14, 14, 6, 6, 6, 6, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1, 0, -1, 1, -1, -1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262955
{'cdim': 14, 'counter': 18, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14b', 'multiplicity': 1, 'nt': [30, 565], 'qdim': 14, 'qvalues': [14, 14, 14, 14, -4, -4, -4, -4, 0, 2, 0, 0, 2, 0, 2, 2, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262956
{'cdim': 14, 'counter': 19, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14c', 'multiplicity': 1, 'nt': [30, 565], 'qdim': 14, 'qvalues': [14, 14, 14, 14, 4, 4, 4, 4, 0, 2, 0, 0, 2, 0, 2, 2, -1, 2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 262958
{'cdim': 14, 'counter': 20, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14d', 'multiplicity': 1, 'nt': [42, 413], 'qdim': 14, 'qvalues': [14, 14, 14, 14, -6, -6, -6, -6, -2, 2, -2, -2, 2, -2, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262959
{'cdim': 14, 'counter': 21, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14e', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, -14, -14, 14, -6, 6, -6, 6, 2, -2, -2, -2, 2, 2, -2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 2, 2, -2, -2, 2, 1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 1, 0, 1, 1, -1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262960
{'cdim': 14, 'counter': 22, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14f', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, -14, -14, 14, 6, -6, 6, -6, -2, -2, 2, 2, 2, -2, -2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, -2, 2, 2, -2, -2, 2, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 1, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262961
{'cdim': 14, 'counter': 23, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14g', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, -14, 14, -14, -6, -6, 6, 6, 2, -2, -2, 2, 2, -2, 2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 2, -2, 2, -2, 2, -2, -1, 1, 1, 0, 0, 0, 0, -1, -1, 1, 1, 0, -1, -1, 1, 1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262962
{'cdim': 14, 'counter': 24, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14h', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, -14, 14, -14, 6, 6, -6, -6, -2, -2, 2, -2, 2, 2, 2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 2, -2, 2, -2, 2, -2, -1, 1, 1, 0, 0, 0, 0, 1, 1, -1, -1, 0, -1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262963
{'cdim': 14, 'counter': 25, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14i', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, 14, -14, -14, -6, 6, 6, -6, -2, 2, -2, 2, 2, 2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -2, -2, 2, 2, -2, -2, 1, -1, 1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 1, 1, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262964
{'cdim': 14, 'counter': 26, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14j', 'multiplicity': 1, 'nt': [42, 549], 'qdim': 14, 'qvalues': [14, 14, -14, -14, 6, -6, -6, 6, 2, 2, 2, -2, 2, -2, -2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -2, -2, 2, 2, -2, -2, 1, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 0, 1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 262965
{'cdim': 14, 'counter': 27, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14k', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, -14, -14, 14, -4, 4, -4, 4, 0, -2, 0, 0, 2, 0, -2, 2, -1, 2, 2, -2, 2, -2, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, 1, -1, -2, -2, 2, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 262966
{'cdim': 14, 'counter': 28, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14l', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, -14, -14, 14, 4, -4, 4, -4, 0, -2, 0, 0, 2, 0, -2, 2, -1, 2, -2, 2, -2, 2, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, 1, -1, -2, -2, 2, 1, -1, 1, -1, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0], 'schur_index': 1}
id: 262967
{'cdim': 14, 'counter': 29, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14m', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, -14, 14, -14, -4, -4, 4, 4, 0, -2, 0, 0, 2, 0, 2, -2, -1, 2, 2, 2, -2, -2, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, 2, -2, -2, -1, 1, 1, -1, 0, 0, 0, 0, 0, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 262969
{'cdim': 14, 'counter': 30, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14n', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, -14, 14, -14, 4, 4, -4, -4, 0, -2, 0, 0, 2, 0, 2, -2, -1, 2, -2, -2, 2, 2, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, -1, 1, 2, -2, -2, 1, -1, -1, 1, 0, 0, 0, 0, 0, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262970
{'cdim': 14, 'counter': 31, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14o', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, 14, -14, -14, -4, 4, 4, -4, 0, 2, 0, 0, 2, 0, -2, -2, -1, 2, 2, -2, -2, 2, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1, -2, 2, -2, -1, -1, 1, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 0], 'schur_index': 1}
id: 262971
{'cdim': 14, 'counter': 32, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.14p', 'multiplicity': 1, 'nt': [60, 0], 'qdim': 14, 'qvalues': [14, 14, -14, -14, 4, -4, -4, 4, 0, 2, 0, 0, 2, 0, -2, -2, -1, 2, -2, 2, 2, -2, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1, 1, -2, 2, -2, 1, 1, -1, -1, 0, 0, 0, 0, 0, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 262972
{'cdim': 15, 'counter': 33, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15a', 'multiplicity': 1, 'nt': [42, 411], 'qdim': 15, 'qvalues': [15, 15, 15, 15, -5, -5, -5, -5, 3, -1, 3, 3, -1, 3, -1, -1, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, 0, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
id: 262973
{'cdim': 15, 'counter': 34, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15b', 'multiplicity': 1, 'nt': [42, 412], 'qdim': 15, 'qvalues': [15, 15, 15, 15, 5, 5, 5, 5, -3, -1, -3, -3, -1, -3, -1, -1, 3, 0, 1, 1, 1, 1, -1, -1, -1, -1, 0, 3, 3, 3, -1, -1, -1, -1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 262974
{'cdim': 15, 'counter': 35, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15c', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, -15, -15, 15, -5, 5, -5, 5, -3, 1, 3, 3, -1, -3, 1, -1, 3, 0, -1, 1, -1, 1, 1, 1, -1, -1, 0, -3, -3, 3, -1, 1, 1, -1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1, -1], 'schur_index': 1}
id: 262975
{'cdim': 15, 'counter': 36, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15d', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, -15, -15, 15, 5, -5, 5, -5, 3, 1, -3, -3, -1, 3, 1, -1, 3, 0, 1, -1, 1, -1, 1, 1, -1, -1, 0, -3, -3, 3, -1, 1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
id: 262976
{'cdim': 15, 'counter': 37, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15e', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, -15, 15, -15, -5, -5, 5, 5, -3, 1, 3, -3, -1, 3, -1, 1, 3, 0, -1, -1, 1, 1, 1, -1, -1, 1, 0, -3, 3, -3, -1, 1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, -1, -1, 1], 'schur_index': 1}
id: 262977
{'cdim': 15, 'counter': 38, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15f', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, -15, 15, -15, 5, 5, -5, -5, 3, 1, -3, 3, -1, -3, -1, 1, 3, 0, 1, 1, -1, -1, 1, -1, -1, 1, 0, -3, 3, -3, -1, 1, -1, 1, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, -1, 1], 'schur_index': 1}
id: 262978
{'cdim': 15, 'counter': 39, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15g', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, 15, -15, -15, -5, 5, 5, -5, 3, -1, 3, -3, -1, -3, 1, 1, 3, 0, -1, 1, 1, -1, -1, 1, -1, 1, 0, 3, -3, -3, -1, -1, 1, 1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
id: 262980
{'cdim': 15, 'counter': 40, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.15h', 'multiplicity': 1, 'nt': [42, 550], 'qdim': 15, 'qvalues': [15, 15, -15, -15, 5, -5, -5, 5, -3, -1, -3, 3, -1, 3, 1, 1, 3, 0, 1, -1, -1, 1, -1, 1, -1, 1, 0, 3, -3, -3, -1, -1, 1, 1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
id: 262981
{'cdim': 20, 'counter': 41, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.20a', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 20, 'qvalues': [20, -20, -20, 20, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, 4, -4, 2, 2, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 1}
id: 262982
{'cdim': 20, 'counter': 42, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.20b', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 20, 'qvalues': [20, -20, 20, -20, 0, 0, 0, 0, 0, 4, 0, 0, -4, 0, -4, 4, 2, 2, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1], 'schur_index': 1}
id: 262983
{'cdim': 20, 'counter': 43, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.20c', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 20, 'qvalues': [20, 20, -20, -20, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, 4, 4, 2, 2, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1], 'schur_index': 1}
id: 262984
{'cdim': 20, 'counter': 44, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.20d', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 20, 'qvalues': [20, 20, 20, 20, 0, 0, 0, 0, 0, -4, 0, 0, -4, 0, -4, -4, 2, 2, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
id: 262985
{'cdim': 21, 'counter': 45, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21a', 'multiplicity': 1, 'nt': [42, 418], 'qdim': 21, 'qvalues': [21, 21, 21, 21, -1, -1, -1, -1, 3, 1, 3, 3, 1, 3, 1, 1, -3, 0, 1, 1, 1, 1, -1, -1, -1, -1, 1, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0, 0, 0, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 262986
{'cdim': 21, 'counter': 46, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21b', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, -21, -21, 21, -1, 1, -1, 1, -3, -1, 3, 3, 1, -3, -1, 1, -3, 0, 1, -1, 1, -1, 1, 1, -1, -1, 1, 3, 3, -3, 1, -1, -1, 1, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0], 'schur_index': 1}
id: 262987
{'cdim': 21, 'counter': 47, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21c', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, -21, -21, 21, 1, -1, 1, -1, 3, -1, -3, -3, 1, 3, -1, 1, -3, 0, -1, 1, -1, 1, 1, 1, -1, -1, 1, 3, 3, -3, 1, -1, -1, 1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 262988
{'cdim': 21, 'counter': 48, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21d', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, -21, 21, -21, -1, -1, 1, 1, -3, -1, 3, -3, 1, 3, 1, -1, -3, 0, 1, 1, -1, -1, 1, -1, -1, 1, 1, 3, -3, 3, 1, -1, 1, -1, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 0, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262989
{'cdim': 21, 'counter': 49, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21e', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, -21, 21, -21, 1, 1, -1, -1, 3, -1, -3, 3, 1, -3, 1, -1, -3, 0, -1, -1, 1, 1, 1, -1, -1, 1, 1, 3, -3, 3, 1, -1, 1, -1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 262991
{'cdim': 21, 'counter': 50, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21f', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, 21, -21, -21, -1, 1, 1, -1, 3, 1, 3, -3, 1, -3, -1, -1, -3, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, -3, 3, 3, 1, 1, -1, -1, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 262992
{'cdim': 21, 'counter': 51, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21g', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, 21, -21, -21, 1, -1, -1, 1, -3, 1, -3, 3, 1, 3, -1, -1, -3, 0, -1, 1, 1, -1, -1, 1, -1, 1, 1, -3, 3, 3, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 0, 0, 0], 'schur_index': 1}
id: 262993
{'cdim': 21, 'counter': 52, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.21h', 'multiplicity': 1, 'nt': [84, 0], 'qdim': 21, 'qvalues': [21, 21, 21, 21, 1, 1, 1, 1, -3, 1, -3, -3, 1, -3, 1, 1, -3, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, -3, -3, -3, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262994
{'cdim': 35, 'counter': 53, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35a', 'multiplicity': 1, 'nt': [70, 0], 'qdim': 35, 'qvalues': [35, 35, 35, 35, 5, 5, 5, 5, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262995
{'cdim': 35, 'counter': 54, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35b', 'multiplicity': 1, 'nt': [126, 0], 'qdim': 35, 'qvalues': [35, 35, 35, 35, -5, -5, -5, -5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 262996
{'cdim': 35, 'counter': 55, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35c', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, -35, -35, 35, -5, 5, -5, 5, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0], 'schur_index': 1}
id: 262997
{'cdim': 35, 'counter': 56, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35d', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, -35, -35, 35, 5, -5, 5, -5, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 262998
{'cdim': 35, 'counter': 57, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35e', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, -35, 35, -35, -5, -5, 5, 5, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 262999
{'cdim': 35, 'counter': 58, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35f', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, -35, 35, -35, 5, 5, -5, -5, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 263000
{'cdim': 35, 'counter': 59, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35g', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, 35, -35, -35, -5, 5, 5, -5, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 0, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0], 'schur_index': 1}
id: 263002
{'cdim': 35, 'counter': 60, 'faithful': False, 'group': '20160.l', 'group_order': 20160, 'image': None, 'label': '20160.l.35h', 'multiplicity': 1, 'nt': [140, 0], 'qdim': 35, 'qvalues': [35, 35, -35, -35, 5, -5, -5, 5, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 0, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 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: 369619
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 20160, 'label': '20160.l.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]]]}
id: 369630
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 369641
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369652
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369663
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369674
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369676
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369677
{'center': '1.a1', 'center_index': 1, 'center_order': 20160, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 10080, 'label': '20160.l.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]]]}
id: 369678
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 9, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.6a', 'nt': [7, 7], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[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: 369620
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 10, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.6b', 'nt': [14, 46], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 369621
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 11, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6c', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 369622
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 12, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6d', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[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: 369623
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 13, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6e', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-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: 369624
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 14, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6f', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-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: 369625
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 15, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6g', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 369626
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 16, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.6h', 'nt': [14, 49], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-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: 369627
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 17, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.14a', 'nt': [21, 38], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[14, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369628
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 18, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.14b', 'nt': [30, 565], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[14, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369629
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 19, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.14c', 'nt': [30, 565], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[14, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369631
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 20, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.14d', 'nt': [42, 413], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[14, 0]], [[14, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369632
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14e', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[-14, 0]], [[14, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369633
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14f', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[-14, 0]], [[14, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369634
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14g', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369635
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14h', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369636
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14i', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[-14, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369637
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14j', 'nt': [42, 549], 'q_character': None, 'values': [[[14, 0]], [[14, 0]], [[-14, 0]], [[-14, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369638
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14k', 'nt': [60, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[-14, 0]], [[14, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369639
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 28, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14l', 'nt': [60, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[-14, 0]], [[14, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369640
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 29, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14m', 'nt': [60, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369642
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 30, 'cyclotomic_n': 1, 'dim': 14, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.14n', 'nt': [60, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[14, 0]], [[-14, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369643
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id: 369644
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id: 369645
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id: 369646
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id: 369647
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id: 369648
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id: 369649
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.15e', 'nt': [42, 550], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[15, 0]], [[-15, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
id: 369650
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 38, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.15f', 'nt': [42, 550], 'q_character': None, 'values': [[[15, 0]], [[-15, 0]], [[15, 0]], [[-15, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
id: 369651
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 39, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.15g', 'nt': [42, 550], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-15, 0]], [[-15, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 369653
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 40, 'cyclotomic_n': 1, 'dim': 15, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.15h', 'nt': [42, 550], 'q_character': None, 'values': [[[15, 0]], [[15, 0]], [[-15, 0]], [[-15, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[-3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 369654
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 41, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.20a', 'nt': [70, 0], 'q_character': None, 'values': [[[20, 0]], [[-20, 0]], [[-20, 0]], [[20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 369655
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id: 369656
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 43, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.20c', 'nt': [70, 0], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[-20, 0]], [[-20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 369657
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 1, 'dim': 20, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.20d', 'nt': [70, 0], 'q_character': None, 'values': [[[20, 0]], [[20, 0]], [[20, 0]], [[20, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 369658
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.21a', 'nt': [42, 418], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[21, 0]], [[21, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369659
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21b', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[-21, 0]], [[-21, 0]], [[21, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369660
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21c', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[-21, 0]], [[-21, 0]], [[21, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369661
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21d', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[-21, 0]], [[21, 0]], [[-21, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369662
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21e', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[-21, 0]], [[21, 0]], [[-21, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369664
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21f', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-21, 0]], [[-21, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369665
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.21g', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-21, 0]], [[-21, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369666
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 52, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.21h', 'nt': [84, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[21, 0]], [[21, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369667
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 53, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.35a', 'nt': [70, 0], 'q_character': None, 'values': [[[35, 0]], [[35, 0]], [[35, 0]], [[35, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369668
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '5040.w', 'image_order': 5040, 'indicator': 1, 'kernel': '5040.a1', 'kernel_order': 4, 'label': '20160.l.35b', 'nt': [126, 0], 'q_character': None, 'values': [[[35, 0]], [[35, 0]], [[35, 0]], [[35, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369669
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 55, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35c', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[-35, 0]], [[-35, 0]], [[35, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369670
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 56, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35d', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[-35, 0]], [[-35, 0]], [[35, 0]], [[5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369671
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 57, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35e', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[-35, 0]], [[35, 0]], [[-35, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369672
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 58, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35f', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[-35, 0]], [[35, 0]], [[-35, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369673
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 59, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35g', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[35, 0]], [[-35, 0]], [[-35, 0]], [[-5, 0]], [[5, 0]], [[5, 0]], [[-5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 369675
{'center': '5040.a1', 'center_index': 5040, 'center_order': 4, 'counter': 60, 'cyclotomic_n': 1, 'dim': 35, 'faithful': False, 'field': [0, 1], 'group': '20160.l', 'group_counter': 12, 'group_order': 20160, 'image': None, 'image_isoclass': '10080.l', 'image_order': 10080, 'indicator': 1, 'kernel': '10080.a1', 'kernel_order': 2, 'label': '20160.l.35h', 'nt': [140, 0], 'q_character': None, 'values': [[[35, 0]], [[35, 0]], [[-35, 0]], [[-35, 0]], [[5, 0]], [[-5, 0]], [[-5, 0]], [[5, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 20952422
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 20160, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 210, 'label': '20160.l.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '20160.l', 'subgroup_hash': 8804660164701733268, 'subgroup_order': 20160, 'subgroup_tex': 'C_2^2\\times S_7', 'supersolvable': False, 'sylow': 0}
id: 20952533
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 10080, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '20160.l.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10080.l', 'subgroup_hash': 3593093372306498606, 'subgroup_order': 10080, 'subgroup_tex': 'C_2\\times S_7', 'supersolvable': False, 'sylow': 0}
id: 20952644
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 10080, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '20160.l.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': ['S', 'C1', 'S', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10080.n', 'subgroup_hash': 3434028034273258019, 'subgroup_order': 10080, 'subgroup_tex': 'C_2^2\\times A_7', 'supersolvable': False, 'sylow': 0}
id: 20952755
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5040, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '20160.l.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5040.v', 'subgroup_hash': 4764235641843610755, 'subgroup_order': 5040, 'subgroup_tex': 'C_2\\times A_7', 'supersolvable': False, 'sylow': 0}
id: 20952793
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 5040, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '20160.l.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5040.w', 'subgroup_hash': 6283920599749723413, 'subgroup_order': 5040, 'subgroup_tex': 'S_7', 'supersolvable': False, 'sylow': 0}
id: 20952804
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '20160.l.7.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '7.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 7, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2880.du', 'subgroup_hash': 7330512212170881535, 'subgroup_order': 2880, 'subgroup_tex': 'C_2^2\\times S_6', 'supersolvable': False, 'sylow': 0}
id: 20952815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2520, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '20160.l.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': True, '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': True, 'solvable': False, 'special_labels': ['D', 'PC', 'L1', 'D1', 'D', 'PC', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2520.a', 'subgroup_hash': 1290983011404564636, 'subgroup_order': 2520, 'subgroup_tex': 'A_7', 'supersolvable': False, 'sylow': 0}
id: 20952826
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5842', 'subgroup_hash': 5842, 'subgroup_order': 1440, 'subgroup_tex': 'C_2\\times S_6', 'supersolvable': False, 'sylow': 0}
id: 20952837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '14.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1440.5845', 'subgroup_hash': 5845, 'subgroup_order': 1440, 'subgroup_tex': 'C_2^2\\times A_6', 'supersolvable': False, 'sylow': 0}
id: 20952423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.21.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '960.11355', 'subgroup_hash': 11355, 'subgroup_order': 960, 'subgroup_tex': 'C_2^3\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.766', 'subgroup_hash': 766, 'subgroup_order': 720, 'subgroup_tex': 'C_2\\times A_6', 'supersolvable': False, 'sylow': 0}
id: 20952445
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '720.763', 'subgroup_hash': 763, 'subgroup_order': 720, 'subgroup_tex': 'S_6', 'supersolvable': False, 'sylow': 0}
id: 20952456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.30.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1255', 'subgroup_hash': 1255, 'subgroup_order': 672, 'subgroup_tex': 'C_2^2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
id: 20952467
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '20160.l.35.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '35.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 35, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8659', 'subgroup_hash': 8659, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2:D_6^2', 'supersolvable': False, 'sylow': 0}
id: 20952478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1187', 'subgroup_hash': 1187, 'subgroup_order': 480, 'subgroup_tex': 'C_2^3\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952511
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952522
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.42.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '42.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '480.1186', 'subgroup_hash': 1186, 'subgroup_order': 480, 'subgroup_tex': 'C_2^2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.118', 'subgroup_hash': 118, 'subgroup_order': 360, 'subgroup_tex': 'A_6', 'supersolvable': False, 'sylow': 0}
id: 20952556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.60.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.209', 'subgroup_hash': 209, 'subgroup_order': 336, 'subgroup_tex': 'C_2\\times \\GL(3,2)', 'supersolvable': False, 'sylow': 0}
id: 20952567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1028', 'subgroup_hash': 1028, 'subgroup_order': 288, 'subgroup_tex': 'D_6\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952589
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1037', 'subgroup_hash': 1037, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
id: 20952600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1033', 'subgroup_hash': 1033, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1031', 'subgroup_hash': 1031, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:D_4', 'supersolvable': False, 'sylow': 0}
id: 20952622
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.70.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '70.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 70, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1034', 'subgroup_hash': 1034, 'subgroup_order': 288, 'subgroup_tex': 'C_2\\times C_6:S_4', 'supersolvable': False, 'sylow': 0}
id: 20952633
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952645
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952656
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952689
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952700
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.190', 'subgroup_hash': 190, 'subgroup_order': 240, 'subgroup_tex': 'C_2^2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952711
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952722
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.84.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.189', 'subgroup_hash': 189, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times S_5', 'supersolvable': False, 'sylow': 0}
id: 20952733
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.105.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '105.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 105, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952744
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.105.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '105.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 105, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1514', 'subgroup_hash': 1514, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952756
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.105.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '105.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 105, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1537', 'subgroup_hash': 1537, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952767
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.120.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.47', 'subgroup_hash': 47, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times F_7', 'supersolvable': True, 'sylow': 0}
id: 20952778
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.120.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.b1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.42', 'subgroup_hash': 42, 'subgroup_order': 168, 'subgroup_tex': '\\PSL(2,7)', 'supersolvable': False, 'sylow': 0}
id: 20952786
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.126.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.236', 'subgroup_hash': 236, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952787
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.190', 'subgroup_hash': 190, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times D_6', 'supersolvable': False, 'sylow': 0}
id: 20952788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952789
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
id: 20952790
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.186', 'subgroup_hash': 186, 'subgroup_order': 144, 'subgroup_tex': 'S_3^2:C_2^2', 'supersolvable': False, 'sylow': 0}
id: 20952791
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
id: 20952792
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.189', 'subgroup_hash': 189, 'subgroup_order': 144, 'subgroup_tex': 'C_6:S_4', 'supersolvable': False, 'sylow': 0}
id: 20952794
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
id: 20952795
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.193', 'subgroup_hash': 193, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:C_6^2', 'supersolvable': False, 'sylow': 0}
id: 20952796
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.192', 'subgroup_hash': 192, 'subgroup_order': 144, 'subgroup_tex': 'D_6^2', 'supersolvable': True, 'sylow': 0}
id: 20952797
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.191', 'subgroup_hash': 191, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 20952798
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.140.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '140.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 140, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.183', 'subgroup_hash': 183, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952800
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952801
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952802
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.35', 'subgroup_hash': 35, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times A_5', 'supersolvable': False, 'sylow': 0}
id: 20952803
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
id: 20952805
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
id: 20952806
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
id: 20952807
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.168.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.34', 'subgroup_hash': 34, 'subgroup_order': 120, 'subgroup_tex': 'S_5', 'supersolvable': False, 'sylow': 0}
id: 20952808
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952809
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952810
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952811
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952812
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952813
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952816
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952817
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952818
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
id: 20952819
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '210.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.221', 'subgroup_hash': 221, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
id: 20952820
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
id: 20952821
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952822
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952823
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.230', 'subgroup_hash': 230, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.207', 'subgroup_hash': 207, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.219', 'subgroup_hash': 219, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:D_6', 'supersolvable': True, 'sylow': 0}
id: 20952829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952831
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.210.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '210.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.226', 'subgroup_hash': 226, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952832
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.240.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
id: 20952833
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.240.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '240.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
id: 20952834
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.252.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952835
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.252.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952836
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.252.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.51', 'subgroup_hash': 51, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952838
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.252.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952839
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.252.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952840
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952841
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952842
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952843
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952844
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 20952845
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 20952846
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952847
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952424
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
id: 20952425
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952426
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.44', 'subgroup_hash': 44, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952428
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
id: 20952429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
id: 20952430
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
id: 20952431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.280.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '280.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 280, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
id: 20952432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '20160.l.315.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '315.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 315, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 2}
id: 20952433
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.336.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
id: 20952435
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.336.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.b1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
id: 20952436
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.360.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '360.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20952437
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952438
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': 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: 20952441
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': 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: 20952442
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952443
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952444
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952446
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952447
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952448
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.t2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.t2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952463
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952464
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952465
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.y2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.y2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952466
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952468
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 20952469
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952472
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952473
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
id: 20952474
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952475
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '420.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.52', 'subgroup_hash': 52, 'subgroup_order': 48, 'subgroup_tex': 'C_2^3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 20952476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952477
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952479
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bj2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bj2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952481
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952485
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952486
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952487
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952490
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.420.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '420.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
id: 20952491
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.480.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
id: 20952492
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.480.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '480.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 480, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
id: 20952493
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952494
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952495
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952496
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952497
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952498
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952502
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952503
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.504.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
id: 20952504
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 20952506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952507
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 20952508
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '560.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
id: 20952509
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 20952510
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 20952512
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952513
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 20952514
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 20952515
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 20952516
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.560.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '560.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 560, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 20952517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952519
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952521
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20952523
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 20952524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952526
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 20952527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.630.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '630.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 630, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 20952529
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.720.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '720.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
id: 20952530
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.720.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '720.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 720, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20952531
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952532
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952535
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952536
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952537
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952538
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952539
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952540
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952541
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952542
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952543
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 20952544
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 20952546
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952547
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952548
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952549
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952550
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952551
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952552
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.r2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.r2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952553
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952554
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952555
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952557
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952558
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952559
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952560
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952561
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952562
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952563
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952564
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952565
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952566
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '840.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': 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: 20952572
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952573
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952574
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bl1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952575
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bm1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20952576
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bn1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bn1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bo1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bo1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952579
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bp1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bp1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952580
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bq1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bq1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952581
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.br1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.br1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952582
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bs1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bs1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 20952583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bt1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bt1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bu1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bu1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bv1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bv1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bw1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bw1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bx1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bx1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.by1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.by1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.bz1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.bz1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952591
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.ca1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.ca1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.ca2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.ca2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.cb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.cb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
id: 20952594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.cc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.cc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.cd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.cd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20952596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.ce1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.ce1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.cf1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.cf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.840.cf2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '840.cf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 840, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20952599
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.960.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '960.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 960, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
id: 20952601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952602
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952603
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952604
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952605
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952606
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952607
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952608
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
id: 20952609
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
id: 20952610
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1008.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
id: 20952612
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1120.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1120.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 20952613
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1120.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952614
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1120.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 20952615
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1120.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 20952616
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1120.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1120.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 20952617
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20952618
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20952619
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952620
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952623
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952624
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952626
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952627
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952630
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952631
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952634
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952636
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20952639
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20952640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952641
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.u2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.u2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 20952642
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952643
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952646
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.x2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.x2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1260.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1260.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1260, 'quotient_simple': 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: 20952649
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 2, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.1440.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1440.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
id: 20952650
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1440.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1440.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
id: 20952651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952652
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952654
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952655
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952658
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952659
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952660
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952661
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952662
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 4, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952664
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952665
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952666
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952670
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952671
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952672
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952673
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952674
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952675
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952676
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952677
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 329, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.1680.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952679
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 20952680
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 20952681
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952682
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952684
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
id: 20952685
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
id: 20952686
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bf2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bf2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
id: 20952687
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bg1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952688
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bh1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952690
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bi1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bj1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1680.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': 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: 20952692
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.1680.bk1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1680.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20952693
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 343, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.2016.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952694
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.2016.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 20952695
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2016.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
id: 20952696
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2016.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
id: 20952697
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2016.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2016, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
id: 20952698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '20160.l.2240.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2240.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2240, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
id: 20952699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952702
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952703
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952706
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952710
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952712
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952713
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952714
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 4, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952715
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952716
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 4, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952717
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952718
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952719
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952720
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952721
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952723
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952724
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952725
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952726
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952727
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952728
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952729
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952730
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952731
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952732
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952734
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952735
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952737
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.2520.bf1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2520.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2520, 'quotient_simple': 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: 20952738
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '20160.l.2880.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2880.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 2880, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
id: 20952739
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 385, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952740
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 386, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952741
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952742
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952743
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952745
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952746
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952747
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952748
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952749
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952750
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.3360.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3360.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': 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: 20952751
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952752
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.3360.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3360.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20952753
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '20160.l.4032.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4032.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4032, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 20952754
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': True, 'central_factor': False, 'centralizer_order': 20160, 'characteristic': True, 'core_order': 4, 'counter': 399, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '20160.l.5040.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5040.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '5040.w', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6283920599749723413, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5040, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_7', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'C2', 'Z', 'F', 'R', 'U0', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20952757
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 2, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952758
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952759
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952760
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952761
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952762
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952766
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952769
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.5040.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952770
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.5040.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952771
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.5040.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952772
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952773
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.o2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.o2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952774
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952775
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952776
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '20160.l.5040.q2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5040.q2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5040, 'quotient_simple': 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: 20952777
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.6720.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6720, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 20952779
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.6720.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6720.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6720, '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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 20952780
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': True, 'central_factor': False, 'centralizer_order': 20160, 'characteristic': False, 'core_order': 2, 'counter': 421, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '20160.l.10080.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '10080.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10080.l', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3593093372306498606, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10080, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_7', 'simple': True, 'solvable': True, 'special_labels': ['C3', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 20952781
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 960, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.10080.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, '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: 20952782
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.10080.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, '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: 20952783
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.10080.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, '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: 20952784
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '20160.l.10080.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '10080.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10080, '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: 20952785
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '20160.l', 'ambient_counter': 12, 'ambient_order': 20160, 'ambient_tex': 'C_2^2\\times S_7', 'central': True, 'central_factor': False, 'centralizer_order': 20160, 'characteristic': True, 'core_order': 1, 'counter': 426, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '20160.l.20160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20160.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '20160.l', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8804660164701733268, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20160, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times S_7', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1', 'C4', 'Phi', 'U1', 'C4'], '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: 20952778
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '60.a1'], 'contains': ['840.cf1', '840.cf2', '960.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [394, -1, 156, -1], 'generators': [12782280, 7752360], 'label': '20160.l.120.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '120.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
id: 20952609
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.f1', '504.d1', '504.e1', '504.i1'], 'contains': ['2016.c1', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [4533, -1, 5262, -1], 'generators': [10931887, 15689520, 15321600], 'label': '20160.l.1008.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.i1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952610
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.g1', '504.d1', '504.j1'], 'contains': ['2016.c1', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [1923, -1, 2909, -1], 'generators': [10931880, 15689520, 15321600], 'label': '20160.l.1008.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.j1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952692
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.n1', '840.s1', '840.bs1'], 'contains': ['3360.k1', '3360.l1', '5040.q2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8499, -1, 6889, -1], 'generators': [40447, 3628943, 45360], 'label': '20160.l.1680.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.bk1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bk1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952693
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2016.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1008.a1', '1008.b1', '1008.c1', '1008.d1', '1008.e1'], 'contains': ['4032.a1', '10080.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [9780, -1, 8883, -1], 'generators': [7, 5574367], 'label': '20160.l.2016.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '2016.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952694
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2016.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1008.a1', '1008.f1', '1008.g1'], 'contains': ['4032.a1', '10080.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [9909, -1, 7949, -1], 'generators': [40320, 23678040], 'label': '20160.l.2016.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '2016.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952423
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['42.a1', '42.b1', '42.c1', '42.d1', '42.f1', '105.c1', '126.a1', '210.o1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8202, -1, 7212, -1], 'generators': [23, 40463, 5530440, 7, 40336], 'label': '20160.l.21.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '21.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952422
{'ambient': '20160.l', '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': '5040.a1', 'complements': ['20160.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '7.a1', '21.a1', '35.a1', '120.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2899, 4718, 3613, 4476], 'generators': [8156280, 23, 3628800, 7], 'label': '20160.l.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952424
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.f1', '140.g1', '140.i1', '140.j1'], 'contains': ['560.b1', '560.d1', '560.e1', '840.z1', '840.ba1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2872, -1, 2786, -1], 'generators': [23, 5126416, 18679696, 7, 166440], 'label': '20160.l.280.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.i1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.i1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952425
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.i1'], 'contains': ['560.c1', '560.e1', '840.bb1', '840.bd1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [2497, -1, 2644, -1], 'generators': [23, 8356343, 11743216, 7, 15362663], 'label': '20160.l.280.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '280.j1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952426
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['140.a1', '140.k1', '140.l1'], 'contains': ['560.h1', '840.be1', '840.bn1', '1120.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [3615, -1, 2964, -1], 'generators': [1135560, 51120, 11370960, 18593280, 1134000], 'label': '20160.l.280.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '280.k1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952427
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['140.b1', '140.k1', '140.l1'], 'contains': ['560.h1', '840.bi1', '840.bt1', '1120.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [3433, -1, 2458, -1], 'generators': [1135560, 51120, 11370960, 40327, 18593280], 'label': '20160.l.280.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '280.l1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.l1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952428
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['140.c1', '140.d1'], 'contains': ['560.f1', '560.i1', '560.j1', '2520.t1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1509, -1, 699, -1], 'generators': [11370960, 15362640, 11743200, 1497616, 8356327], 'label': '20160.l.280.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.m1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.m1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952429
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '140.c1'], 'contains': ['560.f1', '560.i1', '560.k1', '2520.u1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1024, -1, 352, -1], 'generators': [15362640, 8356320, 11370960, 1497600, 11743200], 'label': '20160.l.280.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.n1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.n1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952430
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.e1', '140.f1', '140.k1'], 'contains': ['560.h1', '840.by1', '840.bz1', '840.ca1', '1120.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [3326, -1, 2390, -1], 'generators': [23679480, 20050560, 1583287, 45360, 18553080], 'label': '20160.l.280.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '280.o1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.o1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952431
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '140.f1', '140.l1'], 'contains': ['560.h1', '840.cd1', '840.ce1', '840.cf2', '1120.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [802, -1, 626, -1], 'generators': [23679480, 1583280, 20050560, 45360, 18553080], 'label': '20160.l.280.p1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '280.p1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.p1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952432
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '315.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.a1', '105.b1', '105.c1'], 'contains': ['630.a1', '630.b1', '630.b2', '630.c1', '630.d1', '630.e1', '630.f1', '630.g1', '630.h1', '630.i1', '630.j1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5938, -1, 6400, -1], 'generators': [3714496, 23, 90736, 15291360, 3719527, 7], 'label': '20160.l.315.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '315.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '315.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952433
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '168.a1', '168.c1', '168.d1', '168.f1', '168.g1'], 'contains': ['1680.be1', '2016.c1', '3360.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [3177, -1, 2392, -1], 'generators': [87240, 9077880], 'label': '20160.l.336.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '336.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952434
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '14.a1', '14.b1'], 'contains': ['56.a1', '168.a1', '168.b1', '280.e1', '420.x1', '420.y1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1275, -1, 1668, -1], 'generators': [23, 23765063, 22308623], 'label': '20160.l.28.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952435
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '168.b1', '168.e1'], 'contains': ['1680.bf1', '2016.c1', '3360.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [328, -1, 199, -1], 'generators': [18915840, 7259040], 'label': '20160.l.336.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '336.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952436
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1'], 'contains': ['720.a1', '720.b1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [68, -1, 9111, -1], 'generators': [23, 16497367, 18643680, 7], 'label': '20160.l.360.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '360.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952437
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.a1', '140.a1', '210.g1', '210.h1', '210.i1'], 'contains': ['840.q1', '840.be1', '1260.d1', '1680.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8167, -1, 6421, -1], 'generators': [23, 3760576, 3669856, 3719527, 121703], 'label': '20160.l.420.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '420.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952438
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.f1', '210.j1'], 'contains': ['840.c1', '840.i1', '840.k1', '840.bf1', '840.bg1', '1260.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6594, -1, 5099, -1], 'generators': [23, 18593280, 12096023, 40343, 1135583], 'label': '20160.l.420.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952439
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.d1', '210.e1', '210.j1'], 'contains': ['840.c1', '840.i1', '840.l1', '840.bf1', '1260.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6481, -1, 5698, -1], 'generators': [12096016, 23, 18593280, 40343, 1135583], 'label': '20160.l.420.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952440
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.e1', '210.k1'], 'contains': ['840.c1', '840.j1', '840.m1', '840.bh1', '1260.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6787, -1, 6206, -1], 'generators': [23, 18593280, 11370976, 40343, 1135583], 'label': '20160.l.420.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20952441
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.y1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.b1', '210.d1', '210.f1', '210.k1'], 'contains': ['840.c1', '840.j1', '840.p1', '840.bh1', '840.bi1', '1260.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6854, -1, 5008, -1], 'generators': [23, 18593280, 11370983, 40343, 1135583], 'label': '20160.l.420.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20952442
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.f1', '210.l1'], 'contains': ['840.e1', '840.j1', '840.k1', '840.bj1', '840.bk1', '1260.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5452, -1, 5308, -1], 'generators': [23, 18593280, 11260103, 1135583, 1134000], 'label': '20160.l.420.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.f1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952443
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.d1', '210.e1', '210.l1'], 'contains': ['840.e1', '840.j1', '840.l1', '840.bj1', '1260.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6072, -1, 6002, -1], 'generators': [23, 18593280, 11260096, 1135583, 1134000], 'label': '20160.l.420.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952444
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.e1', '210.n1'], 'contains': ['840.e1', '840.f1', '840.i1', '840.m1', '840.v1', '840.bl1', '840.bo1', '1260.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7166, -1, 7030, -1], 'generators': [18593280, 1134007, 11370983, 1135576, 16], 'label': '20160.l.420.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952445
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '14.a1'], 'contains': ['56.a1', '168.d1', '168.e1', '280.n1', '420.bm1', '420.bt1'], 'core': '20160.a1', 'coset_action_label': '28T431', 'count': 28, 'diagramx': [934, -1, 1075, -1], 'generators': [3719520, 4037040], 'label': '20160.l.28.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952446
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.a1', '210.b1', '210.m1'], 'contains': ['840.r1', '840.bm1', '1260.j1', '1680.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [2270, -1, 1860, -1], 'generators': [90727, 3714487, 3719536, 8472967, 7], 'label': '20160.l.420.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.i1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952447
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.a1', '210.d1', '210.f1', '210.n1'], 'contains': ['840.e1', '840.i1', '840.p1', '840.bl1', '840.bn1', '1260.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7242, -1, 5519, -1], 'generators': [1135560, 11370960, 18593280, 1134007, 7], 'label': '20160.l.420.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '420.j1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952448
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.d1', '210.o1'], 'contains': ['840.b1', '840.c1', '840.e1', '840.h1', '840.n1', '840.bp1', '840.bs1', '1260.i1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7408, -1, 7124, -1], 'generators': [41063, 16, 3669120, 856, 40336], 'label': '20160.l.420.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.k1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952449
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.a1', '210.o1'], 'contains': ['840.a1', '840.b1', '840.d1', '840.f1', '840.g1', '840.h1', '840.s1', '840.bq1', '840.bs1', '1260.i1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9315, -1, 8668, -1], 'generators': [41056, 23, 3669127, 863, 40336], 'label': '20160.l.420.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '420.l1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952450
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.b1', '210.e1', '210.f1', '210.o1'], 'contains': ['840.a1', '840.c1', '840.e1', '840.g1', '840.t1', '840.bp1', '840.bq1', '840.br1', '1260.j1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4598, -1, 4429, -1], 'generators': [41063, 23, 40343, 3669120, 863], 'label': '20160.l.420.m1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.m1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.m1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952451
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.b1', '140.b1', '210.g1', '210.h1', '210.p1'], 'contains': ['840.q1', '840.bt1', '1260.h1', '1680.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7574, -1, 6311, -1], 'generators': [12419280, 10823, 11300407, 7, 3639600], 'label': '20160.l.420.n1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '420.n1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.n1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952452
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '210.d1', '210.r1'], 'contains': ['840.i1', '840.j1', '840.n1', '840.bu1', '1260.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6687, -1, 6115, -1], 'generators': [12096016, 23, 18593280, 11260103, 1135583], 'label': '20160.l.420.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.o1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.o1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952453
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['210.c1', '210.s1'], 'contains': ['840.k1', '840.m1', '840.n1', '840.bv1', '840.bw1', '1260.l1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5562, -1, 5422, -1], 'generators': [23, 23679480, 20050576, 45360, 1583296], 'label': '20160.l.420.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.p1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.p1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952454
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.c1', '210.a1', '210.b1', '210.q1'], 'contains': ['840.r1', '840.bx1', '1260.m1', '1680.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [1890, -1, 1772, -1], 'generators': [3669863, 3755536, 18990720, 16, 131776], 'label': '20160.l.420.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.q1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.q1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952455
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.e1', '210.d1', '210.s1'], 'contains': ['840.l1', '840.n1', '840.p1', '840.bv1', '840.by1', '1260.n1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5359, -1, 4192, -1], 'generators': [23679480, 20050567, 45367, 1583303, 7], 'label': '20160.l.420.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.r1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952456
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['60.a1', '210.u1', '210.u2', '240.b1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [2058, -1, 1945, -1], 'generators': [23, 12782280, 7, 7752376], 'label': '20160.l.30.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '30.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
id: 20952457
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.d1', '140.e1', '210.g1', '210.t1'], 'contains': ['840.q1', '840.bz1', '1260.n1', '1680.j1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6939, -1, 5607, -1], 'generators': [22308616, 23, 363600, 1219680, 126000], 'label': '20160.l.420.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '420.s1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.s1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952458
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.e1', '210.u2'], 'contains': ['840.r2', '840.ca1', '1260.n1', '1680.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3204, -1, 2883, -1], 'generators': [18679696, 16, 19242720, 5167, 7620600], 'label': '20160.l.420.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.u2', 'old_label': '420.t1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.t1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952459
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.t2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['210.a1', '210.u1'], 'contains': ['840.r1', '840.ca2', '1260.n2', '1680.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [2056, -1, 2065, -1], 'generators': [23, 18276480, 7620607, 1219680, 22308623], 'label': '20160.l.420.t2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.t2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.t2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952460
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.e1', '210.f1', '210.r1'], 'contains': ['840.i1', '840.j1', '840.t1', '840.bu1', '840.cb1', '1260.m1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6163, -1, 4917, -1], 'generators': [12096016, 23, 18593280, 11260096, 1135583], 'label': '20160.l.420.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.u1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.u1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952461
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['210.e1', '210.s1'], 'contains': ['840.l1', '840.m1', '840.t1', '840.bv1', '840.cc1', '1260.n2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5110, -1, 4689, -1], 'generators': [23679480, 1583280, 45367, 20050576, 7], 'label': '20160.l.420.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.v1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.v1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952462
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.f1', '210.f1', '210.s1'], 'contains': ['840.k1', '840.p1', '840.t1', '840.bw1', '840.by1', '840.cc1', '840.cd1', '1260.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [2870, -1, 3182, -1], 'generators': [23679480, 20050567, 1583280, 45367, 7], 'label': '20160.l.420.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.w1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.w1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952463
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['28.a1', '84.e1', '140.f1', '210.h1', '210.t1'], 'contains': ['840.q1', '840.bz1', '840.ce1', '1260.o1', '1680.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [1662, -1, 3091, -1], 'generators': [23, 363600, 22308623, 1219680, 126000], 'label': '20160.l.420.x1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '420.x1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.x1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952464
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['28.a1', '60.a1', '210.b1', '210.u1'], 'contains': ['840.r1', '840.ca2', '840.cf1', '1260.o1', '1680.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [1056, -1, 948, -1], 'generators': [23, 18276480, 1219680, 22308623, 7620600], 'label': '20160.l.420.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.y1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.y1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952465
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['60.a1', '140.f1', '210.u2'], 'contains': ['840.r2', '840.ca1', '840.cf2', '1260.o1', '1680.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [1325, -1, 1251, -1], 'generators': [18679687, 19242720, 5167, 7620600, 7], 'label': '20160.l.420.y2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.u2', 'old_label': '420.y2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.y2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952466
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.c1', '210.o1'], 'contains': ['840.a1', '840.b1', '840.w1', '840.z1', '840.bc1', '1260.p1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [9135, -1, 9067, -1], 'generators': [23, 16057447, 7, 14925000, 40336], 'label': '20160.l.420.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '420.z1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952467
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '35.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['70.a1', '70.b1', '70.c1', '70.d1', '70.f1', '105.b1', '105.c1', '140.g1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [6856, -1, 4319, -1], 'generators': [23, 18593280, 1134007, 11370983, 1135583, 51127, 7, 40336], 'label': '20160.l.35.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '35.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '35.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952468
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.j1', '210.k1', '210.o1'], 'contains': ['840.c1', '840.d1', '840.w1', '840.y1', '1260.q1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8054, -1, 8074, -1], 'generators': [23, 3669127, 863, 7, 40336], 'label': '20160.l.420.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.ba1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952469
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.l1', '210.n1', '210.o1'], 'contains': ['840.e1', '840.f1', '840.x1', '840.y1', '840.bc1', '1260.p1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7959, -1, 8785, -1], 'generators': [23, 736, 3669127, 863, 7], 'label': '20160.l.420.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bb1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952470
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.d1', '105.c1', '140.g1', '210.o1'], 'contains': ['840.g1', '840.h1', '840.w1', '840.x1', '840.z1', '1260.q1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8753, -1, 8973, -1], 'generators': [23, 10823, 3991680, 7620487, 7], 'label': '20160.l.420.bc1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '420.bc1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952471
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.j1', '210.n1', '210.r1'], 'contains': ['840.i1', '840.v1', '840.y1', '840.bc1', '1260.r1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7503, -1, 7980, -1], 'generators': [12096016, 23, 18593280, 1135583, 7], 'label': '20160.l.420.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bd1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952472
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.be1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.k1', '210.l1', '210.r1'], 'contains': ['840.j1', '840.y1', '1260.s1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7325, -1, 7393, -1], 'generators': [23, 18593280, 11260103, 1135583, 7], 'label': '20160.l.420.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.be1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952473
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.j1', '210.l1', '210.s1'], 'contains': ['840.k1', '840.l1', '840.y1', '1260.t1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5685, -1, 6714, -1], 'generators': [23, 18275896, 23679480, 45367, 7], 'label': '20160.l.420.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bf1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bf1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952474
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.e1', '105.a1', '140.i1'], 'contains': ['840.o1', '840.u1', '840.ba1', '840.bb1', '840.bd1', '1260.r1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2577, -1, 2270, -1], 'generators': [23, 19727287, 3669863, 16007760, 7], 'label': '20160.l.420.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '420.bg1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bg1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952475
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.h1', '210.k1', '210.n1', '210.s1'], 'contains': ['840.m1', '840.p1', '840.y1', '1260.u1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7770, -1, 7695, -1], 'generators': [23, 23679480, 45367, 20050576, 7], 'label': '20160.l.420.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '420.bh1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bh1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952476
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.f1', '140.h1', '210.i1', '210.p1', '210.t1'], 'contains': ['840.q1', '1260.u1', '1680.l1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [8335, -1, 8214, -1], 'generators': [3714496, 23, 448560, 8351280, 7], 'label': '20160.l.420.bi1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '420.bi1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bi1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952477
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.g1', '210.m1', '210.q1', '210.u1'], 'contains': ['840.r1', '1260.u2', '1680.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [3022, -1, 3502, -1], 'generators': [23, 19968480, 85800, 3628920, 7], 'label': '20160.l.420.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.bj1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bj1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952478
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['21.a1'], 'contains': ['84.a1', '84.b1', '84.d1', '84.h1', '210.g1', '252.b1', '420.l1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [8278, -1, 7212, -1], 'generators': [23, 5530447, 40456, 40343], 'label': '20160.l.42.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952479
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bj2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.h1', '210.u2'], 'contains': ['840.r2', '1260.u1', '1680.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [4504, -1, 4546, -1], 'generators': [23, 18679696, 19242720, 7620600, 7], 'label': '20160.l.420.bj2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.f1', 'old_label': '420.bj2', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bj2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952480
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.f1', '210.o1', '210.r1', '210.s1'], 'contains': ['840.n1', '840.s1', '840.t1', '840.y1', '840.z1', '1260.u2'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7029, -1, 6913, -1], 'generators': [23, 3628920, 40463, 45367, 7], 'label': '20160.l.420.bk1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bk1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952481
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['210.a1', '210.b1'], 'contains': ['840.bm1', '840.bx1', '840.ca2', '1260.x1', '1680.bh1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [1820, -1, 1029, -1], 'generators': [8472960, 15291367, 3714480, 3719536, 90720], 'label': '20160.l.420.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.bl1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bl1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952482
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '210.b1'], 'contains': ['840.bm1', '840.bx1', '840.cf1', '1260.y1', '1680.bb1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [933, -1, 557, -1], 'generators': [8472960, 3719520, 15291360, 3714480, 90720], 'label': '20160.l.420.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '420.bm1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952483
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['210.c1', '210.d1', '210.e1'], 'contains': ['840.bf1', '840.bh1', '840.bj1', '840.bl1', '840.bp1', '840.bu1', '840.bv1', '1260.v1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [6311, -1, 4780, -1], 'generators': [1135560, 18593280, 11370976, 40343, 1134000], 'label': '20160.l.420.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bn1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bn1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952484
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['210.c1', '210.f1'], 'contains': ['840.bg1', '840.bh1', '840.bk1', '840.bl1', '840.bp1', '840.bu1', '840.bw1', '1260.w1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4816, -1, 4100, -1], 'generators': [1135560, 18593280, 11370976, 1134000, 40336], 'label': '20160.l.420.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bo1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bo1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952485
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['140.k1', '210.d1', '210.f1'], 'contains': ['840.bf1', '840.bi1', '840.bj1', '840.bn1', '840.bp1', '840.bu1', '840.by1', '1260.x2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3568, -1, 3296, -1], 'generators': [1135560, 11370960, 18593280, 1134007, 40336], 'label': '20160.l.420.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bp1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bp1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952486
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['210.e1', '210.f1'], 'contains': ['840.bf1', '840.bh1', '840.bj1', '840.bl1', '840.br1', '840.cb1', '840.cc1', '1260.x1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4368, -1, 4018, -1], 'generators': [1135560, 1134023, 18593280, 11370976, 40343], 'label': '20160.l.420.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.bq1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bq1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952487
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['140.l1', '210.f1'], 'contains': ['840.bg1', '840.bi1', '840.bk1', '840.bn1', '840.br1', '840.cb1', '840.cd1', '1260.y1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2685, -1, 2540, -1], 'generators': [1135560, 11370960, 40327, 18593280, 1134007], 'label': '20160.l.420.br1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '420.br1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.br1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952488
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['84.h1', '140.k1', '210.g1', '210.h1'], 'contains': ['840.be1', '840.bt1', '840.bz1', '1260.x2', '1680.u1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3671, -1, 3636, -1], 'generators': [3760567, 3755536, 3669847, 121680, 3719527], 'label': '20160.l.420.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '420.bs1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bs1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952489
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '21.a1'], 'contains': ['84.a1', '84.b1', '84.e1', '84.h1', '84.i1', '210.h1', '252.a1', '420.m1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5123, -1, 4429, -1], 'generators': [40456, 16, 5530440, 40336], 'label': '20160.l.42.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952490
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '420.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '84.i1', '140.l1', '210.h1'], 'contains': ['840.be1', '840.bt1', '840.ce1', '1260.y1', '1680.t1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [830, -1, 1332, -1], 'generators': [3760576, 3755520, 3669856, 121680, 3719536], 'label': '20160.l.420.bt1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '420.bt1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '420.bt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952491
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['60.a1', '240.a1', '240.b1'], 'contains': ['960.a1', '1440.a1', '3360.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [233, -1, 1881, -1], 'generators': [14596696, 16, 18316096], 'label': '20160.l.480.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '480.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952492
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '480.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '240.a1'], 'contains': ['960.a1', '1440.b1', '3360.h1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 480, 'diagramx': [117, -1, 1309, -1], 'generators': [16497360, 22147320, 18643680], 'label': '20160.l.480.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '480.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952493
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.a1', '252.a1', '252.b1', '252.c1'], 'contains': ['1008.a1', '1008.b1', '1008.c1', '1008.f1', '1008.g1', '2520.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [9743, -1, 9657, -1], 'generators': [16, 40343, 23678040, 3629520], 'label': '20160.l.504.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952494
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['252.c1'], 'contains': ['1008.a1', '1008.c1', '1008.d1', '1008.g1', '2520.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [9949, -1, 9752, -1], 'generators': [3629527, 23, 40343, 23678040], 'label': '20160.l.504.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952495
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.b1', '84.c1', '252.a1', '252.b1', '252.d1'], 'contains': ['1008.b1', '1008.h1', '2520.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [5028, -1, 7714, -1], 'generators': [5121360, 12338640, 16, 19319056], 'label': '20160.l.504.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952496
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.e1', '252.a1', '252.e1'], 'contains': ['1008.b1', '1008.i1', '1008.j1', '2520.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [4236, -1, 5829, -1], 'generators': [10931880, 15689520, 15321607, 7], 'label': '20160.l.504.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952497
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.d1', '252.b1', '252.e1'], 'contains': ['1008.b1', '1008.i1', '2520.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [9218, -1, 8529, -1], 'generators': [23, 10931887, 15689520, 15321600], 'label': '20160.l.504.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952498
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.c1'], 'contains': ['1008.a1', '1008.e1', '2520.l1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9859, -1, 9950, -1], 'generators': [23, 23678040, 7, 40336], 'label': '20160.l.504.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.f1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.f1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952499
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.f1', '84.g1', '252.c1', '252.d1', '252.e1'], 'contains': ['1008.b1', '1008.d1', '1008.e1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9014, -1, 9373, -1], 'generators': [1260120, 23, 5574376, 7], 'label': '20160.l.504.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.g1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952500
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1'], 'contains': ['84.a1', '84.f1', '210.i1', '252.c1', '420.z1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8701, -1, 7757, -1], 'generators': [23, 18552247, 1498320, 7, 40336], 'label': '20160.l.42.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.c1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952501
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.c1'], 'contains': ['1008.c1', '1008.e1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9667, -1, 9847, -1], 'generators': [23, 3669863, 23678040, 7], 'label': '20160.l.504.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.h1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952502
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['84.h1', '252.a1', '252.b1'], 'contains': ['1008.f1', '1008.h1', '1008.i1', '2520.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1512, 'diagramx': [4685, -1, 5910, -1], 'generators': [18230543, 23679480, 40327, 23316480], 'label': '20160.l.504.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.i1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952503
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '504.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.i1', '252.a1'], 'contains': ['1008.f1', '1008.h1', '1008.j1', '2520.p1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [2493, -1, 2548, -1], 'generators': [18230520, 23679480, 40327, 23316480], 'label': '20160.l.504.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '504.j1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952504
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.a1', '140.b1', '280.a1', '280.b1', '280.h1'], 'contains': ['1120.a1', '1120.b1', '1680.a1', '1680.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [8082, -1, 4334, -1], 'generators': [23, 11743223, 1497616, 15362663], 'label': '20160.l.560.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.g1', 'old_label': '560.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952505
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.f1', '280.a1', '280.d1', '280.e1', '280.f1', '280.i1'], 'contains': ['1120.a1', '1120.c1', '1120.e1', '1680.d1', '1680.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1609, -1, 1073, -1], 'generators': [5126416, 18679696, 16, 166440], 'label': '20160.l.560.b1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952506
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['280.d1', '280.g1', '280.j1'], 'contains': ['1120.a1', '1120.d1', '1680.f1', '1680.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2130, -1, 1521, -1], 'generators': [11743207, 15362640, 8356343, 7], 'label': '20160.l.560.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '560.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952507
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.e1', '280.b1', '280.g1', '280.i1'], 'contains': ['1120.a1', '1120.e1', '1680.j1', '1680.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3000, -1, 2271, -1], 'generators': [23, 18679696, 5126423, 166440], 'label': '20160.l.560.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952508
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '560.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.h1', '280.h1', '280.i1', '280.j1'], 'contains': ['1120.a1', '1680.l1', '1680.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [4446, -1, 3753, -1], 'generators': [23, 5126416, 7, 166440], 'label': '20160.l.560.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.e1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 20952509
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['140.l1', '280.a1', '280.m1', '280.n1'], 'contains': ['1120.b1', '1120.c1', '1680.t1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1169, -1, 386, -1], 'generators': [11370960, 15362640, 11743200, 1497616], 'label': '20160.l.560.f1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.f1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952510
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.k1', '280.a1', '280.b1'], 'contains': ['1120.b1', '1120.e1', '1680.u1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [3615, -1, 2345, -1], 'generators': [15362640, 11743200, 1497607, 11370976], 'label': '20160.l.560.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.g1', 'old_label': '560.g1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952511
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1', '21.a1'], 'contains': ['84.b1', '84.f1', '210.p1', '252.d1', '420.bc1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8202, -1, 7604, -1], 'generators': [7994160, 23, 3628800, 7], 'label': '20160.l.42.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.d1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952512
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.c1', '280.k1', '280.l1', '280.o1', '280.p1'], 'contains': ['1680.bd1', '1680.be1', '1680.bf2', '2240.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3092, -1, 1985, -1], 'generators': [23679480, 20050560, 45360, 18553080], 'label': '20160.l.560.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '560.h1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.h1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952513
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['280.d1', '280.m1', '280.n1'], 'contains': ['1120.c1', '1120.d1', '1680.bb1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 280, 'diagramx': [1208, -1, 314, -1], 'generators': [11370960, 15362640, 8356320, 11743200], 'label': '20160.l.560.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.i1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952514
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.e1', '280.f1', '280.m1'], 'contains': ['1120.c1', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1406, -1, 514, -1], 'generators': [5126400, 18679680, 23234416, 166440], 'label': '20160.l.560.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.j1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.j1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952515
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '280.e1', '280.n1'], 'contains': ['1120.c1', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [747, -1, 31, -1], 'generators': [5126400, 18679680, 23234400, 166440], 'label': '20160.l.560.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '560.k1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.k1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952516
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '560.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['280.d1', '280.g1'], 'contains': ['1120.d1', '1120.e1', '1680.bh1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1966, -1, 836, -1], 'generators': [11370967, 15362640, 11743200, 8356327], 'label': '20160.l.560.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '560.l1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '560.l1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952517
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.c1', '315.a1'], 'contains': ['1260.a1', '1260.c1', '1260.e1', '1260.g1', '1260.i1', '1260.k1', '1260.l1', '1260.v1', '1260.w1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6215, -1, 5891, -1], 'generators': [90736, 3714487, 3719527, 7, 15291383], 'label': '20160.l.630.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952518
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.a1', '210.e1', '315.a1'], 'contains': ['1260.b1', '1260.c1', '1260.f1', '1260.g1', '1260.j1', '1260.m1', '1260.n2', '1260.v1', '1260.x1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5629, -1, 5197, -1], 'generators': [23, 3719520, 15291367, 90743, 3714503], 'label': '20160.l.630.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952519
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.d1', '210.g1', '315.a1'], 'contains': ['1260.b1', '1260.d1', '1260.f1', '1260.h1', '1260.i1', '1260.k1', '1260.n1', '1260.v1', '1260.x2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6395, -1, 5796, -1], 'generators': [3714496, 3719520, 15291360, 16, 90743], 'label': '20160.l.630.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.b2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952520
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.b1', '210.f1', '210.h1', '315.a1'], 'contains': ['1260.a1', '1260.d1', '1260.e1', '1260.h1', '1260.j1', '1260.m1', '1260.o1', '1260.w1', '1260.x1', '1260.x2', '1260.y1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [1672, -1, 3384, -1], 'generators': [23, 3719520, 15291360, 90743, 3714503], 'label': '20160.l.630.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952521
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1', '210.l1', '315.a1'], 'contains': ['1260.a1', '1260.b1', '1260.p1', '1260.s1', '1260.t1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6101, -1, 7290, -1], 'generators': [3714496, 23, 8391616, 3719527, 7], 'label': '20160.l.630.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.d1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952522
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['84.c1', '84.g1', '210.q1', '252.d1', '420.bg1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [3098, -1, 3000, -1], 'generators': [23, 4112656, 3719527, 7], 'label': '20160.l.42.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '42.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.e1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952523
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.i1', '210.n1', '315.a1'], 'contains': ['1260.c1', '1260.d1', '1260.p1', '1260.r1', '1260.u1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8310, -1, 7862, -1], 'generators': [3714496, 23, 15291360, 3719527, 7], 'label': '20160.l.630.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '630.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952524
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.e1', '210.j1', '315.a1'], 'contains': ['1260.e1', '1260.f1', '1260.q1', '1260.r1', '1260.t1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5987, -1, 6819, -1], 'generators': [23, 1502663, 8356343, 1497616, 7], 'label': '20160.l.630.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.f1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952525
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.k1', '210.p1', '315.a1'], 'contains': ['1260.g1', '1260.h1', '1260.q1', '1260.s1', '1260.u1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8369, -1, 7790, -1], 'generators': [23, 12419280, 10823, 3639623, 7], 'label': '20160.l.630.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '630.g1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952526
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.m1', '210.o1', '315.a1'], 'contains': ['1260.i1', '1260.j1', '1260.p1', '1260.q1', '1260.u2'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6553, -1, 7195, -1], 'generators': [3714496, 23, 90736, 3719527, 7], 'label': '20160.l.630.h1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '630.h1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952527
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.q1', '210.r1', '315.a1'], 'contains': ['1260.k1', '1260.m1', '1260.r1', '1260.s1', '1260.u2'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5892, -1, 6610, -1], 'generators': [23, 3669863, 3755536, 131783, 7], 'label': '20160.l.630.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.i1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.i1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952528
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '630.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.s1', '210.t1', '210.u1', '210.u2', '315.a1'], 'contains': ['1260.l1', '1260.n1', '1260.n2', '1260.o1', '1260.t1', '1260.u1', '1260.u2'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [4266, -1, 4335, -1], 'generators': [23, 22308623, 1219680, 363607, 7], 'label': '20160.l.630.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '630.j1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '630.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952529
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['240.a1', '360.a1'], 'contains': ['1440.a1', '1440.b1', '5040.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [17, -1, 6938, -1], 'generators': [16497360, 23, 18643680], 'label': '20160.l.720.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '720.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952530
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1', '360.a1'], 'contains': ['1440.a1', '5040.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [196, -1, 7854, -1], 'generators': [23, 14596696, 7], 'label': '20160.l.720.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '720.b1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '720.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 20952531
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.a1', '420.l1', '420.m1', '420.z1'], 'contains': ['1680.a1', '1680.d1', '1680.g1', '1680.n1', '1680.o1', '2520.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9544, -1, 8617, -1], 'generators': [16057447, 7, 14925000, 40336], 'label': '20160.l.840.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952532
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.k1', '420.l1', '420.z1'], 'contains': ['1680.a1', '1680.g1', '1680.j1', '1680.o1', '2520.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9620, -1, 9017, -1], 'generators': [16057456, 7, 14925000, 40336], 'label': '20160.l.840.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952533
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': ['10080.b1', '10080.d1', '10080.a1', '10080.e1'], 'conjugacy_class_count': 6, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '14.a1', '42.b1', '70.b1', '240.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1943, 5764, 2058, 5499], 'generators': [3628807, 8156287, 16], 'label': '20160.l.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '10080.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952534
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '42.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '21.a1'], 'contains': ['84.d1', '84.e1', '84.f1', '210.t1', '252.e1', '420.bk1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [6697, -1, 6670, -1], 'generators': [23, 4803263, 5167, 7], 'label': '20160.l.42.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '42.f1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.f1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952535
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.b1', '420.c1', '420.d1', '420.e1', '420.k1', '420.m1', '420.ba1'], 'contains': ['1680.a1', '1680.c1', '1680.p1', '1680.q1', '2520.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7435, -1, 6630, -1], 'generators': [23, 40343, 3669120, 863], 'label': '20160.l.840.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952536
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.l1', '420.ba1'], 'contains': ['1680.a1', '1680.i1', '1680.q1', '2520.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9468, -1, 8805, -1], 'generators': [23, 3669127, 863, 40336], 'label': '20160.l.840.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952537
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.f1', '420.g1', '420.h1', '420.j1', '420.k1', '420.m1', '420.bb1'], 'contains': ['1680.b1', '1680.c1', '1680.g1', '1680.r1', '1680.s1', '2520.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7626, -1, 7478, -1], 'generators': [736, 3669127, 840, 7], 'label': '20160.l.840.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952538
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.h1', '420.l1', '420.bb1'], 'contains': ['1680.b1', '1680.g1', '1680.i1', '1680.s1', '2520.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8583, -1, 8923, -1], 'generators': [23, 743, 3669127, 863], 'label': '20160.l.840.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952539
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.b1', '210.h1', '280.a1', '420.l1', '420.m1', '420.bc1'], 'contains': ['1680.a1', '1680.b1', '1680.d1', '1680.t1', '1680.u1', '2520.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4323, -1, 7290, -1], 'generators': [10816, 16, 3991680, 7620480], 'label': '20160.l.840.g1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952540
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.g1', '280.b1', '420.k1', '420.l1', '420.bc1'], 'contains': ['1680.a1', '1680.b1', '1680.j1', '1680.u1', '2520.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [8959, -1, 8274, -1], 'generators': [23, 10823, 3991680, 7620487], 'label': '20160.l.840.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952541
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.b1', '420.c1', '420.h1', '420.j1', '420.o1', '420.u1', '420.bd1'], 'contains': ['1680.c1', '1680.g1', '1680.v1', '1680.bi1', '2520.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7245, -1, 6535, -1], 'generators': [18593280, 12096023, 1135576, 16], 'label': '20160.l.840.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.i1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952542
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.be1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.d1', '420.e1', '420.f1', '420.g1', '420.o1', '420.u1', '420.be1'], 'contains': ['1680.c1', '1680.y1', '2520.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7082, -1, 6308, -1], 'generators': [18593280, 11260103, 1135576, 16], 'label': '20160.l.840.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.j1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952543
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.b1', '420.f1', '420.p1', '420.w1', '420.bf1'], 'contains': ['1680.c1', '1680.z1', '1680.ba1', '2520.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5266, -1, 5283, -1], 'generators': [23, 23679480, 45360, 18275903], 'label': '20160.l.840.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.k1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952544
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.c1', '420.g1', '420.r1', '420.v1', '420.bf1'], 'contains': ['1680.c1', '1680.z1', '2520.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5420, -1, 5643, -1], 'generators': [23679480, 16, 45360, 18275903], 'label': '20160.l.840.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.l1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952545
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '28.a1', '28.b1'], 'contains': ['336.a1', '336.b1', '560.k1', '840.ce1', '840.cf1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [774, -1, 222, -1], 'generators': [22308600, 23765040], 'label': '20160.l.56.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952546
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.d1', '420.h1', '420.p1', '420.v1', '420.bh1'], 'contains': ['1680.c1', '1680.i1', '1680.w1', '1680.bj1', '2520.i1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7359, -1, 7196, -1], 'generators': [23, 23679480, 20050576, 45360], 'label': '20160.l.840.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.m1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952547
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.k1', '420.o1', '420.p1', '420.r1', '420.bk1'], 'contains': ['1680.c1', '1680.j1', '1680.x1', '1680.bk1', '2520.i2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6875, -1, 6889, -1], 'generators': [3628920, 16, 40463, 45360], 'label': '20160.l.840.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.n1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952548
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['84.c1', '210.b1', '280.d1', '420.bg1'], 'contains': ['1680.e1', '1680.f1', '1680.h1', '1680.bb1', '1680.bh1', '2520.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [1090, -1, 907, -1], 'generators': [23, 19727287, 3669856, 16007760], 'label': '20160.l.840.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '840.o1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952549
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.c1', '420.e1', '420.j1', '420.r1', '420.w1', '420.bh1'], 'contains': ['1680.c1', '1680.w1', '1680.bd1', '2520.j1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7512, -1, 4997, -1], 'generators': [23, 23679480, 20050583, 45360], 'label': '20160.l.840.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '840.p1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.p1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952550
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.a1', '280.c1', '420.a1', '420.n1', '420.s1', '420.x1', '420.bi1'], 'contains': ['1680.be1', '2520.j1', '3360.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8158, -1, 6398, -1], 'generators': [3714496, 16, 448560, 8351280], 'label': '20160.l.840.q1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '840.q1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.q1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952551
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.b1', '420.i1', '420.q1', '420.t2', '420.y1', '420.bj1'], 'contains': ['1680.bf1', '2520.j2', '3360.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [1844, -1, 1394, -1], 'generators': [23, 19968480, 85800, 3628920], 'label': '20160.l.840.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '840.r1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.r1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952552
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.r2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.c1', '420.t1', '420.y2', '420.bj2'], 'contains': ['1680.bf2', '2520.j1', '3360.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3686, -1, 3062, -1], 'generators': [23, 19242720, 7620600, 18679703], 'label': '20160.l.840.r2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.f1', 'old_label': '840.r2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.r2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952553
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.d1', '420.l1', '420.bk1'], 'contains': ['1680.d1', '1680.i1', '1680.j1', '1680.bc1', '1680.bk1', '2520.i2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9391, -1, 8086, -1], 'generators': [3628927, 40456, 16, 45360], 'label': '20160.l.840.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.s1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952554
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.e1', '420.m1', '420.u1', '420.v1', '420.w1', '420.bk1'], 'contains': ['1680.c1', '1680.d1', '1680.x1', '1680.bc1', '1680.bg1', '2520.j2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [4957, -1, 4197, -1], 'generators': [23, 3628920, 40463, 45360], 'label': '20160.l.840.t1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.t1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.t1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952555
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['210.a1', '280.g1', '420.bg1'], 'contains': ['1680.f1', '1680.h1', '1680.k1', '1680.bh1', '2520.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [2274, -1, 1609, -1], 'generators': [19727280, 3669863, 16, 16007760], 'label': '20160.l.840.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '840.u1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952556
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '30.a1'], 'contains': ['120.b1', '420.y1', '420.y2', '480.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 90, 'diagramx': [1081, -1, 961, -1], 'generators': [16, 12782280, 7752376], 'label': '20160.l.60.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1', 'old_label': '60.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1', 'subgroup_fusion': None, 'weyl_group': '168.42'}
id: 20952557
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.h1', '420.bd1'], 'contains': ['1680.g1', '1680.i1', '1680.bi1', '2520.k1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7958, -1, 8180, -1], 'generators': [12096023, 1135576, 16, 18593287], 'label': '20160.l.840.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.n1', 'old_label': '840.v1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.v1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952558
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.i1', '280.h1', '420.z1', '420.ba1', '420.bc1'], 'contains': ['1680.a1', '1680.l1', '2520.l1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [9072, -1, 9562, -1], 'generators': [23, 10823, 3991680, 7], 'label': '20160.l.840.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.w1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.w1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952559
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.p1', '280.h1', '420.bb1', '420.bc1'], 'contains': ['1680.b1', '1680.l1', '2520.l1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [9148, -1, 9467, -1], 'generators': [23, 10823, 11300407, 7], 'label': '20160.l.840.x1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '840.x1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.x1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952560
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.ba1', '420.bb1', '420.bd1', '420.be1', '420.bf1', '420.bh1', '420.bk1'], 'contains': ['1680.c1', '1680.i1', '1680.l1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8068, -1, 8369, -1], 'generators': [23, 3628920, 45367, 7], 'label': '20160.l.840.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.y1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.y1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952561
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.f1', '210.t1', '280.i1', '420.z1', '420.bc1', '420.bk1'], 'contains': ['1680.d1', '1680.j1', '1680.l1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8882, -1, 8711, -1], 'generators': [14883136, 23, 1946280, 7], 'label': '20160.l.840.z1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.z1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.z1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952562
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.g1', '210.u1', '210.u2', '280.i1', '420.bg1'], 'contains': ['1680.e1', '1680.k1', '1680.m1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2197, -1, 1726, -1], 'generators': [23, 20008920, 15049583, 7], 'label': '20160.l.840.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '840.ba1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.ba1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952563
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bb1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1', '210.m1', '280.j1', '420.bg1'], 'contains': ['1680.f1', '1680.m1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2512, -1, 3275, -1], 'generators': [23, 3669863, 16007760, 7], 'label': '20160.l.840.bb1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '840.bb1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952564
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.z1', '420.bb1', '420.bd1'], 'contains': ['1680.g1', '1680.l1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8507, -1, 9255, -1], 'generators': [23, 16097783, 7, 14925000], 'label': '20160.l.840.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bc1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952565
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bd1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['210.q1', '280.j1', '420.bg1'], 'contains': ['1680.h1', '1680.m1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [2588, -1, 2974, -1], 'generators': [23, 3669863, 18990727, 7], 'label': '20160.l.840.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '840.bd1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bd1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952566
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.c1', '280.k1', '420.a1', '420.bs1', '420.bt1'], 'contains': ['1680.be1', '2520.r1', '3360.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3545, -1, 3187, -1], 'generators': [3669840, 3719520, 121680, 3760560], 'label': '20160.l.840.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '840.be1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.be1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952567
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['35.a1'], 'contains': ['140.a1', '140.b1', '140.e1', '140.k1', '210.d1', '210.g1', '280.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7046, -1, 4319, -1], 'generators': [1135583, 1134007, 23, 51120, 11370983, 40343, 18593280], 'label': '20160.l.70.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '70.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952568
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.b1', '420.c1', '420.bn1', '420.bp1', '420.bq1'], 'contains': ['1680.p1', '1680.v1', '1680.z1', '2520.t1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6460, -1, 4403, -1], 'generators': [1135560, 18593280, 12096007, 40336], 'label': '20160.l.840.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bf1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bf1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952569
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.b1', '420.bo1', '420.br1'], 'contains': ['1680.p1', '1680.v1', '1680.ba1', '2520.u1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4747, -1, 3563, -1], 'generators': [1135560, 40327, 18593280, 12096007], 'label': '20160.l.840.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bg1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bg1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952570
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.y1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.d1', '420.e1', '420.bn1', '420.bo1', '420.bq1'], 'contains': ['1680.p1', '1680.w1', '1680.y1', '2520.v1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6553, -1, 4759, -1], 'generators': [1135560, 40320, 18593280, 11370976], 'label': '20160.l.840.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bh1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bh1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20952571
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.y1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['280.l1', '420.e1', '420.bp1', '420.br1'], 'contains': ['1680.p1', '1680.y1', '1680.bd1', '2520.w1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3360, -1, 2630, -1], 'generators': [1135560, 11370960, 18593280, 40343], 'label': '20160.l.840.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bi1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bi1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20952572
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.f1', '420.g1', '420.bn1', '420.bp1', '420.bq1'], 'contains': ['1680.r1', '1680.y1', '1680.z1', '2520.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [5091, -1, 4608, -1], 'generators': [1135560, 1134016, 18593280, 11260103], 'label': '20160.l.840.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bj1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bj1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952573
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.f1', '420.bo1', '420.br1'], 'contains': ['1680.r1', '1680.y1', '1680.ba1', '2520.p1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4641, -1, 3687, -1], 'generators': [1135560, 11260087, 18593280, 1134007], 'label': '20160.l.840.bk1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bk1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bk1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952574
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.h1', '420.j1', '420.bn1', '420.bo1', '420.bq1'], 'contains': ['1680.r1', '1680.s1', '1680.v1', '1680.w1', '1680.bi1', '2520.q1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6687, -1, 5463, -1], 'generators': [1135560, 18593280, 1134007, 11370983], 'label': '20160.l.840.bl1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bl1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bl1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952575
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.i1', '420.bl1', '420.bm1'], 'contains': ['1680.bf1', '2520.y1', '3360.h1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1214, -1, 635, -1], 'generators': [8472960, 3714480, 90720, 3719527], 'label': '20160.l.840.bm1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '840.bm1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bm1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952576
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['280.k1', '420.j1', '420.bp1', '420.br1'], 'contains': ['1680.r1', '1680.v1', '1680.bd1', '2520.r1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [3457, -1, 2774, -1], 'generators': [1135560, 11370960, 1134023, 18593280], 'label': '20160.l.840.bn1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '840.bn1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bn1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952577
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.h1'], 'contains': ['1680.s1', '1680.bi1', '1680.bj1', '2520.s1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [7758, -1, 7384, -1], 'generators': [1135560, 1134007, 11370983, 18593287], 'label': '20160.l.840.bo1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.n1', 'old_label': '840.bo1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bo1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952578
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '35.a1'], 'contains': ['140.a1', '140.b1', '140.f1', '140.k1', '140.l1', '210.f1', '210.h1', '280.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2325, -1, 3388, -1], 'generators': [51120, 23, 18593280, 11370983, 40343, 1135583, 1134000], 'label': '20160.l.70.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '70.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952579
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.k1', '420.m1', '420.bn1', '420.bo1', '420.bp1'], 'contains': ['1680.o1', '1680.p1', '1680.r1', '1680.u1', '1680.x1', '2520.x1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4878, -1, 4903, -1], 'generators': [41063, 3669120, 840, 40336], 'label': '20160.l.840.bp1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bp1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bp1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952580
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['84.h1', '420.l1', '420.m1'], 'contains': ['1680.n1', '1680.o1', '1680.q1', '1680.s1', '1680.t1', '1680.u1', '1680.bc1', '2520.x1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [4089, -1, 6212, -1], 'generators': [40320, 3669127, 41040, 840], 'label': '20160.l.840.bq1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.bq1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bq1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952581
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.i1', '420.m1', '420.bq1', '420.br1'], 'contains': ['1680.n1', '1680.p1', '1680.r1', '1680.t1', '1680.bg1', '2520.y1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3171, -1, 2460, -1], 'generators': [40327, 3669120, 41040, 840], 'label': '20160.l.840.br1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.br1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.br1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952582
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.k1', '420.l1'], 'contains': ['1680.o1', '1680.q1', '1680.s1', '1680.u1', '1680.bk1', '2520.z1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [8788, -1, 7802, -1], 'generators': [41056, 840, 3669143, 40336], 'label': '20160.l.840.bs1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '840.bs1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bs1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952583
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '280.l1', '420.n1', '420.bs1', '420.bt1'], 'contains': ['1680.be1', '2520.w1', '3360.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [3060, -1, 2093, -1], 'generators': [12419280, 10823, 11300400, 3639600], 'label': '20160.l.840.bt1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '840.bt1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bt1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952584
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.o1', '420.u1', '420.bn1', '420.bo1', '420.bp1'], 'contains': ['1680.v1', '1680.x1', '1680.y1', '2520.ba1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [6106, -1, 4458, -1], 'generators': [1135560, 11260087, 12096016, 18593280], 'label': '20160.l.840.bu1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bu1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bu1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952585
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.p1', '420.r1', '420.v1', '420.bn1'], 'contains': ['1680.w1', '1680.x1', '1680.z1', '2520.bb1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [5202, -1, 4828, -1], 'generators': [23679480, 20050576, 45360, 1583303], 'label': '20160.l.840.bv1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bv1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bv1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952586
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.p1', '420.w1', '420.bo1'], 'contains': ['1680.w1', '1680.x1', '1680.ba1', '2520.bc1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [4697, -1, 3911, -1], 'generators': [23679480, 20050576, 45360, 1583296], 'label': '20160.l.840.bw1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.bw1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bw1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952587
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.e1', '420.q1', '420.bl1', '420.bm1'], 'contains': ['1680.bf1', '2520.bd1', '3360.j1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1164, -1, 456, -1], 'generators': [3669840, 3755520, 18990720, 131760], 'label': '20160.l.840.bx1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '840.bx1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bx1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952588
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.o1', '420.r1', '420.w1', '420.bp1'], 'contains': ['1680.x1', '1680.z1', '1680.bd1', '2520.be1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [3268, -1, 2699, -1], 'generators': [23679480, 20050560, 45360, 1583296], 'label': '20160.l.840.by1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.by1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.by1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952589
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1'], 'contains': ['140.a1', '140.h1', '210.i1', '210.n1', '280.h1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7247, -1, 7361, -1], 'generators': [23, 18593280, 1134007, 11370983, 1135583, 51127, 7], 'label': '20160.l.70.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '70.c1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.c1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952590
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.f1', '280.o1', '420.s1', '420.x1', '420.bs1'], 'contains': ['1680.be1', '2520.be1', '3360.l1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [3308, -1, 3124, -1], 'generators': [22308607, 363600, 1219680, 126000], 'label': '20160.l.840.bz1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '840.bz1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.bz1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952591
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.o1', '420.t1', '420.y2'], 'contains': ['1680.bf2', '2520.be1', '3360.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [2736, -1, 1795, -1], 'generators': [18679680, 5183, 19242720, 7620600], 'label': '20160.l.840.ca1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.u2', 'old_label': '840.ca1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.ca1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952592
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.ca2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.t2', '420.y1', '420.bl1'], 'contains': ['1680.bf1', '2520.be2', '3360.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [1270, -1, 766, -1], 'generators': [22308600, 18276480, 1219680, 7620616], 'label': '20160.l.840.ca2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '840.ca2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.ca2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952593
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.u1', '420.bq1', '420.br1'], 'contains': ['1680.v1', '1680.y1', '1680.bg1', '2520.bd1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3934, -1, 3395, -1], 'generators': [1135560, 18593280, 11260080, 12096000], 'label': '20160.l.840.cb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.cb1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.cb1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952594
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.v1', '420.w1', '420.bq1'], 'contains': ['1680.w1', '1680.z1', '1680.bg1', '2520.be2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [3890, -1, 3619, -1], 'generators': [23679480, 20050567, 1583280, 45360], 'label': '20160.l.840.cc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.cc1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.cc1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952595
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.p1', '420.w1', '420.br1'], 'contains': ['1680.ba1', '1680.bd1', '1680.bg1', '2520.bf1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [1547, -1, 1196, -1], 'generators': [23679480, 1583280, 20050560, 45360], 'label': '20160.l.840.cd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '840.cd1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.cd1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952596
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '168.g1', '280.p1', '420.x1', '420.bt1'], 'contains': ['1680.be1', '2520.bf1', '3360.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [514, -1, 572, -1], 'generators': [22308600, 363600, 1219680, 126000], 'label': '20160.l.840.ce1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '840.ce1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.ce1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952597
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '120.b1', '420.y1', '420.bm1'], 'contains': ['1680.bf1', '2520.bf1', '3360.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [402, -1, 90, -1], 'generators': [22308600, 18276480, 1219680, 7620600], 'label': '20160.l.840.cf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '840.cf1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.cf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952598
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '840.cf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1', '280.p1', '420.y2'], 'contains': ['1680.bf2', '2520.bf1', '3360.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [459, -1, 156, -1], 'generators': [18679680, 5160, 19242720, 7620600], 'label': '20160.l.840.cf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.u2', 'old_label': '840.cf2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '840.cf2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952599
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '960.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1', '480.a1', '480.b1'], 'contains': ['2880.a1', '6720.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [147, -1, 1329, -1], 'generators': [14596680, 18316080], 'label': '20160.l.960.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '960.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '960.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952600
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1'], 'contains': ['140.b1', '140.h1', '210.k1', '210.p1', '280.h1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7355, -1, 7065, -1], 'generators': [23, 18593280, 11370983, 1135583, 51127, 7, 40336], 'label': '20160.l.70.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '70.d1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.d1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952601
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['504.a1', '504.b1', '504.f1'], 'contains': ['2016.a1', '2016.b1', '5040.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [9983, -1, 9200, -1], 'generators': [16, 23678040, 40336], 'label': '20160.l.1008.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952602
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.a1', '168.b1', '504.a1', '504.c1', '504.d1', '504.e1', '504.g1'], 'contains': ['2016.a1', '2016.c1', '2016.e1', '5040.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [8617, -1, 7929, -1], 'generators': [1260120, 7, 5574367], 'label': '20160.l.1008.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952603
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['504.a1', '504.b1', '504.h1'], 'contains': ['2016.a1', '2016.d1', '5040.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [9878, -1, 8974, -1], 'generators': [3669863, 23678040, 7], 'label': '20160.l.1008.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952604
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['504.b1', '504.g1'], 'contains': ['2016.a1', '2016.e1', '5040.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [9736, -1, 8883, -1], 'generators': [1260143, 7, 5574367], 'label': '20160.l.1008.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952605
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.f1', '504.g1', '504.h1'], 'contains': ['2016.a1', '5040.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9797, -1, 9373, -1], 'generators': [23, 5574376, 7], 'label': '20160.l.1008.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.e1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952606
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.c1', '504.a1', '504.i1', '504.j1'], 'contains': ['2016.b1', '2016.c1', '2016.d1', '5040.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [3883, -1, 5871, -1], 'generators': [23678040, 3629520, 40336], 'label': '20160.l.1008.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.f1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952607
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['504.a1', '504.b1'], 'contains': ['2016.b1', '2016.d1', '2016.e1', '5040.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1512, 'diagramx': [9921, -1, 8530, -1], 'generators': [40327, 23678040, 3629543], 'label': '20160.l.1008.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.g1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952608
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1008.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '168.e1', '504.c1', '504.i1', '504.j1'], 'contains': ['2016.c1', '5040.l1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [2477, -1, 3525, -1], 'generators': [12338640, 5121376, 19319040], 'label': '20160.l.1008.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '1008.h1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952611
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['140.c1', '140.d1', '140.g1', '140.i1', '140.j1', '630.f1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2869, -1, 2260, -1], 'generators': [23, 11370983, 8356343, 1497616, 11743216, 7, 15362663], 'label': '20160.l.70.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '70.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.e1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952612
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '560.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.c1', '560.a1', '560.b1', '560.c1', '560.d1', '560.e1'], 'contains': ['2240.a1', '3360.a1', '3360.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2797, -1, 3038, -1], 'generators': [23, 5126423, 166440], 'label': '20160.l.1120.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '1120.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 20952613
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['280.k1', '280.l1', '560.a1', '560.f1', '560.g1'], 'contains': ['2240.a1', '3360.c1', '3360.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [3483, -1, 2191, -1], 'generators': [1497600, 15362640, 11743200], 'label': '20160.l.1120.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.g1', 'old_label': '1120.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952614
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['280.p1', '560.b1', '560.f1', '560.i1', '560.j1', '560.k1'], 'contains': ['2240.a1', '3360.f1', '3360.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [814, -1, 514, -1], 'generators': [5126400, 18679680, 166440], 'label': '20160.l.1120.c1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '1120.c1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952615
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.m1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['560.c1', '560.i1', '560.l1'], 'contains': ['2240.a1', '3360.h1', '3360.j1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [1418, -1, 1247, -1], 'generators': [15362640, 8356320, 11743200], 'label': '20160.l.1120.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '1120.d1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952616
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.o1', '560.b1', '560.d1', '560.g1', '560.l1'], 'contains': ['2240.a1', '3360.l1', '3360.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2575, -1, 1537, -1], 'generators': [5126400, 18679696, 166440], 'label': '20160.l.1120.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '1120.e1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1120.e1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952617
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['252.a1', '420.f1', '630.a1', '630.c1', '630.d1'], 'contains': ['2520.a1', '2520.f1', '2520.g1', '2520.o1', '2520.p1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5012, -1, 5741, -1], 'generators': [3714496, 8391623, 16, 3719527], 'label': '20160.l.1260.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952618
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['252.b1', '420.g1', '630.b1', '630.b2', '630.d1'], 'contains': ['2520.a1', '2520.f1', '2520.h1', '2520.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6416, -1, 7101, -1], 'generators': [3714496, 8391623, 3719520, 16], 'label': '20160.l.1260.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952619
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.h1', '630.a1', '630.b1', '630.e1'], 'contains': ['2520.a1', '2520.b1', '2520.e1', '2520.i1', '2520.k1', '2520.q1', '2520.s1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [7157, -1, 7550, -1], 'generators': [3714496, 15291360, 16, 3719527], 'label': '20160.l.1260.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952620
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.a1', '420.j1', '630.b2', '630.c1', '630.e1'], 'contains': ['2520.a1', '2520.e1', '2520.j1', '2520.q1', '2520.r1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7700, -1, 6141, -1], 'generators': [15291360, 3714487, 3719527, 7], 'label': '20160.l.1260.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '1260.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952621
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.c1', '420.b1', '630.a1', '630.c1', '630.f1'], 'contains': ['2520.c1', '2520.e1', '2520.g1', '2520.t1', '2520.u1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5714, -1, 5109, -1], 'generators': [8356343, 1497616, 1502640, 7], 'label': '20160.l.1260.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952622
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '70.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '35.a1'], 'contains': ['140.e1', '140.f1', '140.h1', '210.s1', '210.t1', '210.u2', '280.i1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [5328, -1, 3691, -1], 'generators': [23, 23679480, 45367, 7, 20050576, 18553087, 1583303], 'label': '20160.l.70.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '70.f1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '70.f1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952623
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.d1', '420.c1', '630.b1', '630.b2', '630.f1'], 'contains': ['2520.c1', '2520.e1', '2520.h1', '2520.t1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5989, -1, 5992, -1], 'generators': [1502656, 8356343, 16, 1497616], 'label': '20160.l.1260.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952624
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bb1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.d1', '630.a1', '630.b1', '630.g1'], 'contains': ['2520.c1', '2520.f1', '2520.i1', '2520.v1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6854, -1, 6801, -1], 'generators': [3639616, 10823, 16, 12419287], 'label': '20160.l.1260.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1260.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952625
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bb1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.e1', '420.n1', '630.b2', '630.c1', '630.g1'], 'contains': ['2520.c1', '2520.f1', '2520.j1', '2520.v1', '2520.w1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7631, -1, 6074, -1], 'generators': [12419280, 10823, 7, 3639600], 'label': '20160.l.1260.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1260.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952626
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.k1', '420.l1', '630.a1', '630.b2', '630.h1'], 'contains': ['2520.a1', '2520.b1', '2520.c1', '2520.d1', '2520.i2', '2520.x1', '2520.z1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [7067, -1, 7599, -1], 'generators': [3714496, 3719520, 16, 90743], 'label': '20160.l.1260.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.i1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952627
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.i1', '420.m1', '630.b1', '630.c1', '630.h1'], 'contains': ['2520.a1', '2520.c1', '2520.j2', '2520.x1', '2520.y1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [3826, -1, 4269, -1], 'generators': [23, 3719520, 90743, 3714503], 'label': '20160.l.1260.j1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '1260.j1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952628
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.o1', '630.a1', '630.b2', '630.i1'], 'contains': ['2520.e1', '2520.f1', '2520.i2', '2520.ba1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6667, -1, 6718, -1], 'generators': [3669840, 3755536, 131760, 7], 'label': '20160.l.1260.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.k1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952629
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.p1', '630.a1', '630.j1'], 'contains': ['2520.g1', '2520.i1', '2520.i2', '2520.bb1', '2520.bc1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [5647, -1, 5552, -1], 'generators': [22308623, 1219680, 363616, 7], 'label': '20160.l.1260.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.l1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952630
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.q1', '420.u1', '630.b1', '630.c1', '630.i1'], 'contains': ['2520.e1', '2520.f1', '2520.j2', '2520.ba1', '2520.bd1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5318, -1, 4526, -1], 'generators': [3669840, 3755527, 131760, 7], 'label': '20160.l.1260.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.m1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952631
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.r1', '420.s1', '420.t1', '630.b2', '630.j1'], 'contains': ['2520.h1', '2520.i2', '2520.j1', '2520.bb1', '2520.be1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [5121, -1, 5192, -1], 'generators': [22308623, 1219680, 363607, 7], 'label': '20160.l.1260.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.n1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.n1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952632
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.n2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.t2', '420.v1', '630.b1', '630.j1'], 'contains': ['2520.h1', '2520.i1', '2520.j2', '2520.bb1', '2520.be2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [4884, -1, 4063, -1], 'generators': [22308600, 1219680, 363616, 7], 'label': '20160.l.1260.n2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.n2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.n2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952633
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.a1', '42.b1', '42.c1'], 'contains': ['168.a1', '168.c1', '420.a1', '504.a1', '840.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [8546, -1, 7300, -1], 'generators': [18552247, 40327, 1498320, 7], 'label': '20160.l.84.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952634
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.w1', '420.x1', '420.y1', '420.y2', '630.c1', '630.j1'], 'contains': ['2520.g1', '2520.j1', '2520.j2', '2520.bc1', '2520.be1', '2520.be2', '2520.bf1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [1499, -1, 2156, -1], 'generators': [23, 363600, 22308623, 1219680], 'label': '20160.l.1260.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.o1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952635
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '315.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.c1', '420.z1', '420.bb1', '630.d1', '630.e1', '630.h1'], 'contains': ['2520.a1', '2520.b1', '2520.l1', '2520.m1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8435, -1, 9184, -1], 'generators': [23, 15291360, 10823, 7], 'label': '20160.l.1260.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.p1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952636
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.o1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.ba1', '420.bc1', '630.f1', '630.g1', '630.h1'], 'contains': ['2520.c1', '2520.d1', '2520.l1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8749, -1, 8441, -1], 'generators': [23, 10823, 3639623, 7], 'label': '20160.l.1260.q1', 'mobius_quo': None, 'mobius_sub': 24, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1260.q1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952637
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.bd1', '420.bg1', '630.e1', '630.f1', '630.i1'], 'contains': ['2520.e1', '2520.k1', '2520.m1', '2520.n1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6245, -1, 7649, -1], 'generators': [23, 3669863, 131783, 7], 'label': '20160.l.1260.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.r1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952638
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.d1', '420.be1', '630.d1', '630.g1', '630.i1'], 'contains': ['2520.f1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7936, -1, 7919, -1], 'generators': [12424343, 23, 3639623, 7], 'label': '20160.l.1260.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1260.s1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952639
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['140.j1', '252.e1', '420.bf1', '630.d1', '630.f1', '630.j1'], 'contains': ['2520.g1', '2520.h1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5880, -1, 7007, -1], 'generators': [23, 18679696, 23234400, 7], 'label': '20160.l.1260.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.t1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952640
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.bh1', '420.bi1', '420.bj2', '630.e1', '630.g1', '630.j1'], 'contains': ['2520.i1', '2520.j1', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [8081, -1, 8014, -1], 'generators': [3714496, 23, 8351280, 7], 'label': '20160.l.1260.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '1260.u1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952641
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.bj1', '420.bk1', '630.h1', '630.i1', '630.j1'], 'contains': ['2520.i2', '2520.j2', '2520.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5576, -1, 6464, -1], 'generators': [23, 85800, 3628920, 7], 'label': '20160.l.1260.u2', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '1260.u2', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.u2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952642
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['420.bn1', '630.a1', '630.b1', '630.b2'], 'contains': ['2520.o1', '2520.q1', '2520.t1', '2520.v1', '2520.x1', '2520.ba1', '2520.bb1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 7560, 'diagramx': [6506, -1, 5375, -1], 'generators': [15291360, 90727, 3714480, 3719536], 'label': '20160.l.1260.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.v1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952643
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.bo1', '630.a1', '630.c1'], 'contains': ['2520.p1', '2520.q1', '2520.u1', '2520.v1', '2520.x1', '2520.ba1', '2520.bc1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [4093, -1, 3980, -1], 'generators': [90736, 15291360, 3714480, 3719536], 'label': '20160.l.1260.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.w1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952644
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': ['10080.b1', '10080.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '14.b1', '30.a1', '42.f1', '70.f1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2876, 1850, 2812, 1765], 'generators': [7988543, 23, 21819023, 7], 'label': '20160.l.2.b1', 'mobius_quo': -2, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '5040.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '5040.w', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952645
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['14.a1', '42.a1', '42.b1', '42.d1'], 'contains': ['168.a1', '168.d1', '420.n1', '504.c1', '840.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5482, -1, 6876, -1], 'generators': [7994160, 23, 3628800], 'label': '20160.l.84.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952646
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.bl1', '420.bq1', '630.b1', '630.c1'], 'contains': ['2520.o1', '2520.q1', '2520.t1', '2520.v1', '2520.y1', '2520.bd1', '2520.be2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [2815, -1, 2863, -1], 'generators': [15291367, 3714480, 3719536, 90720], 'label': '20160.l.1260.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.x1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.x1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952647
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.x2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.bp1', '420.bs1', '630.b2', '630.c1'], 'contains': ['2520.o1', '2520.r1', '2520.t1', '2520.w1', '2520.x1', '2520.ba1', '2520.be1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [3475, -1, 3819, -1], 'generators': [90727, 15291367, 3714480, 3719527], 'label': '20160.l.1260.x2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.x2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.x2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952648
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1260.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['420.bm1', '420.br1', '420.bt1', '630.c1'], 'contains': ['2520.p1', '2520.r1', '2520.u1', '2520.w1', '2520.y1', '2520.bd1', '2520.bf1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [814, -1, 1265, -1], 'generators': [3719543, 3714480, 90720, 15291383], 'label': '20160.l.1260.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '1260.y1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1260.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952649
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['480.a1', '720.a1', '720.b1'], 'contains': ['2880.a1', '10080.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 360, 'diagramx': [208, -1, 6582, -1], 'generators': [7, 14596687], 'label': '20160.l.1440.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '1440.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 20952650
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.b1', '720.a1'], 'contains': ['2880.a1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 480, 'diagramx': [84, -1, 4357, -1], 'generators': [16497360, 18643687], 'label': '20160.l.1440.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '1440.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1440.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952651
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.a1', '560.a1', '840.a1', '840.b1', '840.c1', '840.d1', '840.g1', '840.h1', '840.w1'], 'contains': ['3360.a1', '3360.c1', '5040.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [9308, -1, 7997, -1], 'generators': [10816, 23, 3991680], 'label': '20160.l.1680.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952652
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.n1', '560.a1', '840.e1', '840.f1', '840.g1', '840.h1', '840.x1'], 'contains': ['3360.a1', '3360.d1', '5040.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8264, -1, 7540, -1], 'generators': [10823, 11300407, 7], 'label': '20160.l.1680.b1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '1680.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952653
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.c1', '840.e1', '840.i1', '840.j1', '840.k1', '840.l1', '840.m1', '840.n1', '840.p1', '840.t1', '840.y1'], 'contains': ['3360.a1', '3360.e1', '3360.k1', '5040.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7360, -1, 6210, -1], 'generators': [23, 3628920, 45360], 'label': '20160.l.1680.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952654
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.a1', '420.x1', '560.b1', '840.a1', '840.g1', '840.s1', '840.t1', '840.z1'], 'contains': ['3360.a1', '3360.f1', '3360.l1', '5040.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7833, -1, 6503, -1], 'generators': [1946280, 7, 14883127], 'label': '20160.l.1680.d1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952655
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.b1', '420.y1', '420.y2', '560.b1', '840.o1', '840.ba1'], 'contains': ['3360.b1', '3360.g1', '3360.m1', '5040.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [1013, -1, 1465, -1], 'generators': [23, 20008920, 15049583], 'label': '20160.l.1680.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '1680.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952656
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['14.a1', '42.e1'], 'contains': ['168.b1', '168.e1', '420.q1', '504.c1', '840.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [1317, -1, 1866, -1], 'generators': [23, 4112656, 3719527], 'label': '20160.l.84.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '84.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952657
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bb1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['240.a1', '420.i1', '560.c1', '840.o1', '840.u1', '840.bb1'], 'contains': ['3360.b1', '3360.h1', '5040.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [1731, -1, 1672, -1], 'generators': [23, 3669856, 16007760], 'label': '20160.l.1680.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '1680.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952658
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.a1', '840.b1', '840.e1', '840.f1', '840.i1', '840.v1', '840.bc1'], 'contains': ['3360.a1', '3360.i1', '5040.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8638, -1, 8060, -1], 'generators': [23, 16097783, 14925000], 'label': '20160.l.1680.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952659
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bd1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['420.q1', '560.c1', '840.o1', '840.u1', '840.bd1'], 'contains': ['3360.b1', '3360.j1', '5040.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [1681, -1, 1609, -1], 'generators': [23, 3669863, 18990720], 'label': '20160.l.1680.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '1680.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952660
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.d1', '840.f1', '840.m1', '840.s1', '840.v1', '840.y1'], 'contains': ['3360.a1', '3360.k1', '5040.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8565, -1, 7714, -1], 'generators': [3628927, 23, 45360], 'label': '20160.l.1680.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.i1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952661
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.s1', '560.d1', '840.b1', '840.h1', '840.n1', '840.s1', '840.z1'], 'contains': ['3360.a1', '3360.l1', '5040.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8990, -1, 7269, -1], 'generators': [1946303, 7, 14883127], 'label': '20160.l.1680.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.j1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952662
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['420.t1', '420.t2', '560.d1', '840.u1', '840.ba1'], 'contains': ['3360.b1', '3360.m1', '5040.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [2015, -1, 1734, -1], 'generators': [16, 20008920, 15049583], 'label': '20160.l.1680.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '1680.k1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952663
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '70.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['420.bi1', '560.e1', '840.w1', '840.x1', '840.y1', '840.z1', '840.bc1'], 'contains': ['3360.a1', '5040.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [8939, -1, 8412, -1], 'generators': [23, 448560, 7], 'label': '20160.l.1680.l1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '1680.l1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952664
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '280.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.b1', '420.bj1', '420.bj2', '560.e1', '840.ba1', '840.bb1', '840.bd1'], 'contains': ['3360.b1', '5040.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [2307, -1, 3852, -1], 'generators': [23, 19968480, 7], 'label': '20160.l.1680.m1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '1680.m1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952665
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.c1', '840.a1', '840.bq1', '840.br1'], 'contains': ['3360.c1', '3360.f1', '3360.i1', '5040.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [3700, -1, 5305, -1], 'generators': [40343, 16057440, 14925000], 'label': '20160.l.1680.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.n1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952666
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.a1', '840.b1', '840.bp1', '840.bq1', '840.bs1'], 'contains': ['3360.c1', '3360.i1', '3360.l1', '5040.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [8421, -1, 6633, -1], 'generators': [40327, 16057463, 14925000], 'label': '20160.l.1680.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.o1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952667
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['42.a1', '42.f1'], 'contains': ['168.a1', '168.f1', '420.s1', '504.e1', '840.s1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8192, -1, 7212, -1], 'generators': [4803263, 5176, 7], 'label': '20160.l.84.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952668
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.c1', '840.bf1', '840.bg1', '840.bh1', '840.bi1', '840.bp1', '840.br1'], 'contains': ['3360.c1', '3360.e1', '5040.h1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4501, -1, 4389, -1], 'generators': [3669120, 840, 40336], 'label': '20160.l.1680.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.p1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.p1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952669
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.c1', '840.d1', '840.bq1', '840.bs1'], 'contains': ['3360.c1', '3360.k1', '5040.i1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [8371, -1, 6695, -1], 'generators': [40320, 3669127, 840], 'label': '20160.l.1680.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.q1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952670
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.e1', '840.bj1', '840.bk1', '840.bl1', '840.bn1', '840.bp1', '840.br1'], 'contains': ['3360.d1', '3360.e1', '3360.i1', '5040.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4618, -1, 4733, -1], 'generators': [720, 3669120, 840], 'label': '20160.l.1680.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.r1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952671
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.e1', '840.f1', '840.bl1', '840.bo1', '840.bq1', '840.bs1'], 'contains': ['3360.d1', '3360.i1', '3360.k1', '5040.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [7762, -1, 6590, -1], 'generators': [3669136, 736, 840], 'label': '20160.l.1680.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.s1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.s1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952672
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.d1', '420.bt1', '560.f1', '840.g1', '840.bq1', '840.br1'], 'contains': ['3360.c1', '3360.d1', '3360.f1', '5040.h1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [2834, -1, 2952, -1], 'generators': [10816, 7620496, 3991680], 'label': '20160.l.1680.t1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.t1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.t1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952673
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.bs1', '560.g1', '840.g1', '840.h1', '840.bp1', '840.bq1', '840.bs1'], 'contains': ['3360.c1', '3360.d1', '3360.l1', '5040.i1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [3952, -1, 5745, -1], 'generators': [7620503, 10816, 3991680], 'label': '20160.l.1680.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.u1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.u1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952674
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.i1', '840.bf1', '840.bg1', '840.bl1', '840.bn1', '840.bu1', '840.cb1'], 'contains': ['3360.e1', '3360.i1', '5040.j1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6387, -1, 4494, -1], 'generators': [1135560, 12096016, 18593280], 'label': '20160.l.1680.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.v1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.v1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952675
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.m1', '840.p1', '840.bh1', '840.bl1', '840.bv1', '840.bw1', '840.cc1'], 'contains': ['3360.e1', '3360.k1', '5040.k1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [6712, -1, 4839, -1], 'generators': [23679480, 20050576, 45360], 'label': '20160.l.1680.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.w1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952676
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.n1', '840.t1', '840.bp1', '840.bu1', '840.bv1', '840.bw1', '840.by1'], 'contains': ['3360.e1', '3360.l1', '5040.k2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [4738, -1, 4689, -1], 'generators': [40447, 3628920, 45360], 'label': '20160.l.1680.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.x1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.x1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952677
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.be1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.j1', '840.bh1', '840.bi1', '840.bj1', '840.bk1', '840.bu1', '840.cb1'], 'contains': ['3360.e1', '5040.l1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4952, -1, 4543, -1], 'generators': [1135560, 11260087, 18593280], 'label': '20160.l.1680.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.y1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.y1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952678
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '42.b1', '42.f1'], 'contains': ['168.a1', '168.f1', '168.g1', '420.x1', '504.d1', '840.t1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [2387, -1, 3782, -1], 'generators': [23, 4803263, 5160], 'label': '20160.l.84.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952679
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.k1', '840.l1', '840.bf1', '840.bj1', '840.bv1', '840.by1', '840.cc1'], 'contains': ['3360.e1', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5304, -1, 4597, -1], 'generators': [23679480, 18275887, 45360], 'label': '20160.l.1680.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.z1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.z1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952680
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.k1', '840.bg1', '840.bk1', '840.bw1', '840.cd1'], 'contains': ['3360.e1', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [4334, -1, 3920, -1], 'generators': [18275880, 23679480, 45360], 'label': '20160.l.1680.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.ba1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.ba1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952681
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['168.e1', '420.bm1', '560.i1', '840.o1'], 'contains': ['3360.g1', '3360.h1', '3360.j1', '5040.j1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [677, -1, 907, -1], 'generators': [19727287, 16007760, 3669847], 'label': '20160.l.1680.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '1680.bb1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bb1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952682
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['168.f1', '840.s1', '840.t1', '840.bq1'], 'contains': ['3360.f1', '3360.k1', '3360.l1', '5040.k2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4146, -1, 5520, -1], 'generators': [40440, 3628943, 45360], 'label': '20160.l.1680.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '1680.bc1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bc1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952683
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.h1', '840.p1', '840.bi1', '840.bn1', '840.by1', '840.cd1'], 'contains': ['3360.e1', '5040.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3052, -1, 3165, -1], 'generators': [23679480, 20050560, 45360], 'label': '20160.l.1680.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '1680.bd1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bd1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952684
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1', '560.h1', '840.q1', '840.be1', '840.bt1', '840.bz1', '840.ce1'], 'contains': ['5040.o1', '6720.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3102, -1, 2816, -1], 'generators': [448560, 8351280, 3714480], 'label': '20160.l.1680.be1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '1680.be1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.be1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952685
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.b1', '840.r1', '840.bm1', '840.bx1', '840.ca2', '840.cf1'], 'contains': ['5040.o2', '6720.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [1055, -1, 951, -1], 'generators': [19968480, 85800, 3628920], 'label': '20160.l.1680.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '1680.bf1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bf1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952686
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.h1', '840.r2', '840.ca1', '840.cf2'], 'contains': ['5040.o1', '6720.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2460, -1, 1786, -1], 'generators': [18679680, 19242720, 7620600], 'label': '20160.l.1680.bf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.f1', 'old_label': '1680.bf2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bf2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952687
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.g1', '840.t1', '840.br1', '840.cb1', '840.cc1', '840.cd1'], 'contains': ['3360.e1', '3360.f1', '5040.o2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [3321, -1, 3352, -1], 'generators': [40440, 3628920, 45360], 'label': '20160.l.1680.bg1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '1680.bg1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bg1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952688
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['420.bl1', '560.l1', '840.o1', '840.u1'], 'contains': ['3360.h1', '3360.j1', '3360.m1', '5040.p1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 5040, 'diagramx': [1313, -1, 1421, -1], 'generators': [19727287, 3669863, 16007760], 'label': '20160.l.1680.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '1680.bh1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bh1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952689
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1', '42.c1', '42.d1', '42.f1'], 'contains': ['168.a1', '420.bi1', '504.g1', '840.z1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [8325, -1, 7604, -1], 'generators': [23, 9077880, 87256, 7], 'label': '20160.l.84.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.f1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952690
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.i1', '840.v1', '840.bl1', '840.bo1'], 'contains': ['3360.i1', '3360.k1', '5040.p1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [7486, -1, 6546, -1], 'generators': [1135560, 12096016, 18593296], 'label': '20160.l.1680.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.n1', 'old_label': '1680.bi1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bi1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952691
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '1680.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bh1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.m1', '840.bo1'], 'contains': ['3360.k1', '5040.q1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [8009, -1, 6777, -1], 'generators': [20050576, 45360, 23679487], 'label': '20160.l.1680.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.n1', 'old_label': '1680.bj1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1680.bj1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952695
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2016.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1', '336.b1', '1008.b1', '1008.f1', '1008.h1', '1008.i1', '1008.j1'], 'contains': ['4032.a1', '10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [2516, -1, 4450, -1], 'generators': [1260120, 5574360], 'label': '20160.l.2016.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '2016.c1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952696
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2016.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1008.c1', '1008.f1', '1008.g1'], 'contains': ['4032.a1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [9853, -1, 7900, -1], 'generators': [3669847, 23678040], 'label': '20160.l.2016.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '2016.d1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952697
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2016.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1008.b1', '1008.d1', '1008.g1'], 'contains': ['4032.a1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [9740, -1, 7997, -1], 'generators': [1260127, 5574360], 'label': '20160.l.2016.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '2016.e1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952698
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '560.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.h1', '1120.a1', '1120.b1', '1120.c1', '1120.d1', '1120.e1'], 'contains': ['6720.a1', '6720.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2588, -1, 1612, -1], 'generators': [5126400, 166440], 'label': '20160.l.2240.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '2240.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2240.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 20952699
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '315.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['504.a1', '840.a1', '840.e1', '1260.a1', '1260.b1', '1260.c1', '1260.d1', '1260.i1', '1260.j1', '1260.p1'], 'contains': ['5040.b1', '5040.c1', '5040.d1', '5040.f1', '5040.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [7403, -1, 7101, -1], 'generators': [10816, 23, 15291367], 'label': '20160.l.2520.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952700
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1', '42.e1'], 'contains': ['168.b1', '420.bj1', '504.g1', '840.ba1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [2934, -1, 2906, -1], 'generators': [23, 18915863, 7259040, 7], 'label': '20160.l.84.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '84.g1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.g1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952701
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '315.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['504.b1', '840.b1', '840.f1', '1260.c1', '1260.i1', '1260.p1'], 'contains': ['5040.b1', '5040.d1', '5040.e1', '5040.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [8765, -1, 8107, -1], 'generators': [10816, 23, 15291360], 'label': '20160.l.2520.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952702
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.c1', '840.g1', '1260.e1', '1260.f1', '1260.g1', '1260.h1', '1260.i1', '1260.j1', '1260.q1'], 'contains': ['5040.b1', '5040.c1', '5040.h1', '5040.i1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7051, -1, 6276, -1], 'generators': [10816, 23, 3639623], 'label': '20160.l.2520.c1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952703
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.o1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.d1', '840.h1', '1260.i1', '1260.q1'], 'contains': ['5040.b1', '5040.e1', '5040.i1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [9213, -1, 7780, -1], 'generators': [10823, 3639623, 7], 'label': '20160.l.2520.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '2520.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952704
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.i1', '840.o1', '1260.c1', '1260.d1', '1260.e1', '1260.f1', '1260.k1', '1260.m1', '1260.r1'], 'contains': ['5040.c1', '5040.d1', '5040.j1', '5040.p1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6508, -1, 6145, -1], 'generators': [23, 3669856, 131783], 'label': '20160.l.2520.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952705
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['504.c1', '840.j1', '1260.a1', '1260.b1', '1260.g1', '1260.h1', '1260.k1', '1260.m1', '1260.s1'], 'contains': ['5040.c1', '5040.l1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6740, -1, 6342, -1], 'generators': [23, 12424336, 3639623], 'label': '20160.l.2520.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952706
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.e1', '504.d1', '840.k1', '1260.a1', '1260.e1', '1260.l1', '1260.o1', '1260.t1'], 'contains': ['5040.c1', '5040.m1', '5040.n1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [5100, -1, 5018, -1], 'generators': [23234400, 18679687, 7], 'label': '20160.l.2520.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952707
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['280.f1', '504.e1', '840.l1', '1260.b1', '1260.f1', '1260.n1', '1260.n2', '1260.t1'], 'contains': ['5040.c1', '5040.m1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [5304, -1, 5663, -1], 'generators': [23, 23234407, 18679703], 'label': '20160.l.2520.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952708
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.m1', '1260.c1', '1260.g1', '1260.l1', '1260.n2', '1260.u1'], 'contains': ['5040.c1', '5040.e1', '5040.k1', '5040.q1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7168, -1, 6457, -1], 'generators': [3714496, 8351287, 16], 'label': '20160.l.2520.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.i1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952709
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.n1', '840.s1', '1260.i1', '1260.k1', '1260.l1', '1260.n1', '1260.u2'], 'contains': ['5040.c1', '5040.e1', '5040.k2', '5040.q2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [5989, -1, 6407, -1], 'generators': [85807, 23, 3628920], 'label': '20160.l.2520.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.i2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.i2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952710
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.p1', '840.q1', '840.r2', '1260.d1', '1260.h1', '1260.n1', '1260.o1', '1260.u1'], 'contains': ['5040.c1', '5040.k1', '5040.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7681, -1, 5215, -1], 'generators': [3714496, 16, 8351280], 'label': '20160.l.2520.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '2520.j1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952711
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['42.a1', '42.b1'], 'contains': ['168.c1', '168.d1', '168.f1', '420.bs1', '504.i1', '840.bq1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [4117, -1, 4195, -1], 'generators': [40447, 5530447, 40343], 'label': '20160.l.84.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.h1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.h1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952712
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.r1', '840.t1', '1260.j1', '1260.m1', '1260.n2', '1260.o1', '1260.u2'], 'contains': ['5040.c1', '5040.k2', '5040.o2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [4510, -1, 4233, -1], 'generators': [85800, 3628920, 7], 'label': '20160.l.2520.j2', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '2520.j2', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.j2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952713
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.u1', '840.v1', '1260.c1', '1260.r1'], 'contains': ['5040.d1', '5040.e1', '5040.p1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [6977, -1, 7223, -1], 'generators': [3669863, 16, 131783], 'label': '20160.l.2520.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.e1', 'old_label': '2520.k1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952714
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.f1', '840.w1', '840.x1', '1260.p1', '1260.q1'], 'contains': ['5040.a1', '5040.b1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [9361, -1, 8478, -1], 'generators': [23, 10823, 7], 'label': '20160.l.2520.l1', 'mobius_quo': None, 'mobius_sub': -120, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '2520.l1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952736
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.be2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.ca2', '840.cc1', '1260.n2', '1260.o1', '1260.x1'], 'contains': ['5040.k1', '5040.m1', '5040.o2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [2909, -1, 3569, -1], 'generators': [22308600, 1219680, 363616], 'label': '20160.l.2520.be2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.be2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.be2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952715
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.g1', '840.y1', '840.z1', '840.ba1', '1260.p1', '1260.q1', '1260.r1', '1260.s1', '1260.t1', '1260.u1', '1260.u2'], 'contains': ['5040.a1', '5040.c1', '5040.e1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8109, -1, 7649, -1], 'generators': [23, 8351280, 7], 'label': '20160.l.2520.m1', 'mobius_quo': None, 'mobius_sub': -24, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.m1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952716
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1', '504.h1', '840.bb1', '840.bc1', '840.bd1', '1260.p1', '1260.r1'], 'contains': ['5040.a1', '5040.d1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6687, -1, 8156, -1], 'generators': [23, 3669863, 7], 'label': '20160.l.2520.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '2520.n1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952717
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['504.i1', '840.bj1', '1260.a1', '1260.b1', '1260.v1', '1260.x1', '1260.x2'], 'contains': ['5040.f1', '5040.l1', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [4853, -1, 5100, -1], 'generators': [3719543, 3714480, 8391607], 'label': '20160.l.2520.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.o1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.o1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952718
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['504.j1', '840.bk1', '1260.a1', '1260.w1', '1260.y1'], 'contains': ['5040.f1', '5040.l1', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [3906, -1, 3724, -1], 'generators': [8391616, 3714480, 3719536], 'label': '20160.l.2520.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.p1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952719
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.bl1', '1260.c1', '1260.d1', '1260.v1', '1260.w1', '1260.x1'], 'contains': ['5040.f1', '5040.g1', '5040.j1', '5040.k1', '5040.p1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [6823, -1, 5375, -1], 'generators': [3714496, 15291367, 3719527], 'label': '20160.l.2520.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.q1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.q1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952720
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.be1', '840.bn1', '1260.d1', '1260.x2', '1260.y1'], 'contains': ['5040.f1', '5040.j1', '5040.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3506, -1, 3658, -1], 'generators': [15291367, 3714480, 3719527], 'label': '20160.l.2520.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '2520.r1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952721
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bo1', '1260.c1'], 'contains': ['5040.g1', '5040.p1', '5040.q1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [7551, -1, 6843, -1], 'generators': [15291360, 3714503, 3719527], 'label': '20160.l.2520.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.e1', 'old_label': '2520.s1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.s1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952722
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '84.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '42.b1'], 'contains': ['168.c1', '168.d1', '168.g1', '420.bt1', '504.j1', '840.br1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [1435, -1, 1385, -1], 'generators': [40440, 5530440, 40336], 'label': '20160.l.84.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '84.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.i1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952723
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['280.m1', '840.bf1', '1260.e1', '1260.f1', '1260.v1', '1260.x1', '1260.x2'], 'contains': ['5040.h1', '5040.j1', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [5190, -1, 4451, -1], 'generators': [1497607, 8356336, 1502640], 'label': '20160.l.2520.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.t1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.t1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952724
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['280.n1', '840.bg1', '1260.e1', '1260.w1', '1260.y1'], 'contains': ['5040.h1', '5040.j1', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4057, -1, 3439, -1], 'generators': [1497607, 8356327, 1502640], 'label': '20160.l.2520.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.u1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.u1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952725
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bb1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.bh1', '1260.g1', '1260.h1', '1260.v1', '1260.w1', '1260.x1'], 'contains': ['5040.h1', '5040.k1', '5040.l1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [5426, -1, 4776, -1], 'generators': [10823, 3639600, 12419303], 'label': '20160.l.2520.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.v1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.v1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952726
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bi1', '840.bt1', '1260.h1', '1260.x2', '1260.y1'], 'contains': ['5040.h1', '5040.l1', '5040.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3377, -1, 3482, -1], 'generators': [10816, 12419280, 3639600], 'label': '20160.l.2520.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '2520.w1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.w1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952727
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.bp1', '840.bq1', '1260.i1', '1260.j1', '1260.v1', '1260.w1', '1260.x2'], 'contains': ['5040.f1', '5040.g1', '5040.h1', '5040.i1', '5040.k2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [4392, -1, 5166, -1], 'generators': [3719536, 90743, 3714503], 'label': '20160.l.2520.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.x1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.x1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952728
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bm1', '840.br1', '1260.j1', '1260.x1', '1260.y1'], 'contains': ['5040.f1', '5040.h1', '5040.o2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2709, -1, 2863, -1], 'generators': [3719543, 3714480, 90720], 'label': '20160.l.2520.y1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '2520.y1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.y1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952729
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bs1', '1260.i1'], 'contains': ['5040.g1', '5040.i1', '5040.q2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 2520, 'diagramx': [8069, -1, 7151, -1], 'generators': [3714496, 3719520, 90743], 'label': '20160.l.2520.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.h1', 'old_label': '2520.z1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.z1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952730
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['840.bu1', '1260.k1', '1260.m1', '1260.v1', '1260.w1', '1260.x2'], 'contains': ['5040.j1', '5040.k2', '5040.l1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [5355, -1, 4646, -1], 'generators': [3669856, 3755543, 131760], 'label': '20160.l.2520.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.ba1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.ba1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952731
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['840.bv1', '1260.l1', '1260.n1', '1260.n2', '1260.v1'], 'contains': ['5040.k1', '5040.k2', '5040.m1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1890, 'diagramx': [5026, -1, 4901, -1], 'generators': [22308623, 1219680, 363616], 'label': '20160.l.2520.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.bb1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bb1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952732
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.bw1', '1260.l1', '1260.o1', '1260.w1'], 'contains': ['5040.k1', '5040.k2', '5040.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [4218, -1, 3980, -1], 'generators': [22308616, 1219680, 363616], 'label': '20160.l.2520.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.bc1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bc1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952733
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '105.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['210.a1', '210.b1', '210.m1', '210.q1', '210.u1', '315.a1', '420.bg1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [2731, -1, 2906, -1], 'generators': [90736, 8472967, 15291360, 23, 3714496, 7, 3719527], 'label': '20160.l.105.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '105.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '105.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952734
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bx1', '840.cb1', '1260.m1', '1260.x1', '1260.y1'], 'contains': ['5040.j1', '5040.l1', '5040.o2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [2875, -1, 3395, -1], 'generators': [3755520, 3669856, 131760], 'label': '20160.l.2520.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.bd1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bd1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952735
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.by1', '840.bz1', '840.ca1', '1260.n1', '1260.o1', '1260.x2'], 'contains': ['5040.k2', '5040.m1', '5040.o1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [3256, -1, 3612, -1], 'generators': [363600, 22308623, 1219680], 'label': '20160.l.2520.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.be1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.be1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952737
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2520.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.p1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['840.cd1', '840.ce1', '840.cf1', '840.cf2', '1260.o1', '1260.y1'], 'contains': ['5040.n1', '5040.o1', '5040.o2'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [838, -1, 841, -1], 'generators': [22308600, 363600, 1219680], 'label': '20160.l.2520.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '2520.bf1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2520.bf1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20952738
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '2880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '720.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1', '1440.a1', '1440.b1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [162, -1, 4429, -1], 'generators': [14596680], 'label': '20160.l.2880.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '2880.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2880.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
id: 20952739
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '70.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.q1', '1120.a1', '1680.a1', '1680.b1', '1680.c1', '1680.d1', '1680.g1', '1680.i1', '1680.j1', '1680.l1'], 'contains': ['6720.a1', '10080.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8567, -1, 7196, -1], 'generators': [23, 448560], 'label': '20160.l.3360.a1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '3360.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952740
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '280.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['480.a1', '840.r1', '840.r2', '1120.a1', '1680.e1', '1680.f1', '1680.h1', '1680.k1', '1680.m1'], 'contains': ['6720.b1', '10080.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1913, -1, 1734, -1], 'generators': [23, 19968480], 'label': '20160.l.3360.b1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '3360.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952741
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '420.ba1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.be1', '1120.b1', '1680.a1', '1680.n1', '1680.o1', '1680.p1', '1680.q1', '1680.t1', '1680.u1'], 'contains': ['6720.a1', '10080.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 840, 'diagramx': [3710, -1, 5305, -1], 'generators': [10823, 3991680], 'label': '20160.l.3360.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '3360.c1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952742
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.p1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bt1', '1120.b1', '1680.b1', '1680.r1', '1680.s1', '1680.t1', '1680.u1'], 'contains': ['6720.a1', '10080.b1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [3554, -1, 4770, -1], 'generators': [10823, 11300400], 'label': '20160.l.3360.d1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '3360.d1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952743
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.c1', '1680.p1', '1680.r1', '1680.v1', '1680.w1', '1680.x1', '1680.y1', '1680.z1', '1680.ba1', '1680.bd1', '1680.bg1'], 'contains': ['6720.a1', '10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [4612, -1, 4543, -1], 'generators': [3628920, 45360], 'label': '20160.l.3360.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '3360.e1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952744
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '105.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1'], 'contains': ['210.c1', '210.d1', '210.e1', '210.f1', '210.j1', '210.k1', '210.l1', '210.n1', '210.o1', '210.r1', '210.s1', '315.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6701, -1, 6400, -1], 'generators': [23, 18593280, 1134007, 11370983, 1135583, 7, 40336], 'label': '20160.l.105.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '105.b1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '105.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952745
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1', '840.ce1', '1120.c1', '1680.d1', '1680.n1', '1680.t1', '1680.bc1', '1680.bg1'], 'contains': ['6720.a1', '10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [3094, -1, 4041, -1], 'generators': [14883120, 1946280], 'label': '20160.l.3360.f1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '3360.f1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952746
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.b1', '840.cf1', '840.cf2', '1120.c1', '1680.e1', '1680.bb1'], 'contains': ['6720.b1', '10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [440, -1, 711, -1], 'generators': [15049560, 20008920], 'label': '20160.l.3360.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '3360.g1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952747
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bb1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['480.b1', '840.bm1', '1120.d1', '1680.f1', '1680.bb1', '1680.bh1'], 'contains': ['6720.b1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1680, 'diagramx': [1068, -1, 1422, -1], 'generators': [3669863, 16007760], 'label': '20160.l.3360.h1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '3360.h1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952748
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1680.g1', '1680.n1', '1680.o1', '1680.r1', '1680.s1', '1680.v1', '1680.bi1'], 'contains': ['6720.a1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [7451, -1, 6262, -1], 'generators': [16097783, 14925000], 'label': '20160.l.3360.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '3360.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952749
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.bd1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['840.bx1', '1120.d1', '1680.h1', '1680.bb1', '1680.bh1'], 'contains': ['6720.b1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 560, 'diagramx': [1227, -1, 1379, -1], 'generators': [18990720, 3669847], 'label': '20160.l.3360.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '3360.j1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952750
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.k1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1680.c1', '1680.i1', '1680.q1', '1680.s1', '1680.w1', '1680.bc1', '1680.bi1', '1680.bj1', '1680.bk1'], 'contains': ['6720.a1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7792, -1, 6355, -1], 'generators': [3628927, 45360], 'label': '20160.l.3360.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '3360.k1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952751
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.bz1', '1120.e1', '1680.d1', '1680.j1', '1680.o1', '1680.u1', '1680.x1', '1680.bc1', '1680.bk1'], 'contains': ['6720.a1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4813, -1, 5745, -1], 'generators': [1946296, 14883120], 'label': '20160.l.3360.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '3360.l1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952752
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '3360.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['840.ca1', '840.ca2', '1120.e1', '1680.e1', '1680.k1', '1680.bh1'], 'contains': ['6720.b1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [1398, -1, 1466, -1], 'generators': [20008920, 15049583], 'label': '20160.l.3360.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '420.bg1', 'old_label': '3360.m1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3360.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952753
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '4032.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2016.a1', '2016.b1', '2016.c1', '2016.d1', '2016.e1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9779, -1, 7924, -1], 'generators': [5574360], 'label': '20160.l.4032.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '4032.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 20952754
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['4.b1'], 'conjugacy_class_count': 1, 'contained_in': ['720.b1', '1008.e1', '1680.l1', '1680.m1', '2520.l1', '2520.m1', '2520.n1'], 'contains': ['10080.a1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8526, 8150, 7854, 9181], 'generators': [23, 7], 'label': '20160.l.5040.a1', 'mobius_quo': 2, 'mobius_sub': 2520, 'normal_closure': '5040.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['10080.a1'], 'normalizer': '1.a1', 'old_label': '5040.a1', 'projective_image': '5040.w', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5040.w', 'quotient_action_kernel_order': 5040, 'quotient_fusion': None, 'short_label': '5040.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952755
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': ['5040.g1', '5040.i1', '5040.p1', '5040.b1', '5040.d1'], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '28.a1', '60.a1', '84.e1', '140.f1'], 'core': '4.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1901, 2976, 1833, 2839], 'generators': [7988543, 23, 21819023], 'label': '20160.l.4.a1', 'mobius_quo': 1, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '10080.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '10080.l', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952756
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '105.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1', '21.a1', '35.a1'], 'contains': ['210.g1', '210.h1', '210.i1', '210.p1', '210.t1', '315.a1', '420.bc1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7181, -1, 6764, -1], 'generators': [3760583, 23, 121696, 3755536, 3669863, 3719527, 7], 'label': '20160.l.105.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '105.c1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '105.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952757
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1008.a1', '1680.a1', '1680.b1', '2520.a1', '2520.b1', '2520.c1', '2520.d1', '2520.l1'], 'contains': ['10080.a1', '10080.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9032, -1, 7691, -1], 'generators': [10816, 16], 'label': '20160.l.5040.b1', 'mobius_quo': None, 'mobius_sub': 120, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '5040.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952758
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1008.b1', '1680.c1', '1680.d1', '1680.e1', '2520.a1', '2520.c1', '2520.e1', '2520.f1', '2520.g1', '2520.h1', '2520.i1', '2520.i2', '2520.j1', '2520.j2', '2520.m1'], 'contains': ['10080.a1', '10080.c1', '10080.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7118, -1, 6216, -1], 'generators': [16, 8351280], 'label': '20160.l.5040.c1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '5040.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952759
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['720.a1', '1008.c1', '1680.f1', '1680.g1', '1680.h1', '2520.a1', '2520.b1', '2520.e1', '2520.k1', '2520.n1'], 'contains': ['10080.a1', '10080.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6833, -1, 7130, -1], 'generators': [23, 3669856], 'label': '20160.l.5040.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '5040.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952760
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1008.d1', '1680.i1', '1680.j1', '1680.k1', '2520.b1', '2520.d1', '2520.i1', '2520.i2', '2520.k1', '2520.m1'], 'contains': ['10080.a1', '10080.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [8727, -1, 7260, -1], 'generators': [8351287, 16], 'label': '20160.l.5040.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '5040.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952761
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '315.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1008.f1', '1680.n1', '1680.r1', '2520.a1', '2520.o1', '2520.p1', '2520.q1', '2520.r1', '2520.x1', '2520.y1'], 'contains': ['10080.b1', '10080.c1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4379, -1, 5166, -1], 'generators': [10823, 15291383], 'label': '20160.l.5040.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.f1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952762
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '315.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['1008.g1', '1680.o1', '1680.s1', '2520.a1', '2520.b1', '2520.q1', '2520.s1', '2520.x1', '2520.z1'], 'contains': ['10080.b1', '10080.d1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [7828, -1, 6633, -1], 'generators': [10816, 15291383], 'label': '20160.l.5040.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.g1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952763
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.o1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1680.p1', '1680.t1', '2520.c1', '2520.t1', '2520.u1', '2520.v1', '2520.w1', '2520.x1', '2520.y1'], 'contains': ['10080.b1', '10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4229, -1, 4404, -1], 'generators': [10823, 3639600], 'label': '20160.l.5040.h1', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '5040.h1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952764
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.o1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1680.q1', '1680.u1', '2520.c1', '2520.d1', '2520.x1', '2520.z1'], 'contains': ['10080.b1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [7492, -1, 6401, -1], 'generators': [3639616, 10823], 'label': '20160.l.5040.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.o1', 'old_label': '5040.i1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952765
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1680.v1', '1680.bb1', '2520.e1', '2520.q1', '2520.r1', '2520.t1', '2520.u1', '2520.ba1', '2520.bd1'], 'contains': ['10080.c1', '10080.d1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 1260, 'diagramx': [4921, -1, 4497, -1], 'generators': [3669840, 131760], 'label': '20160.l.5040.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.j1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952766
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1680.w1', '2520.i1', '2520.j1', '2520.q1', '2520.v1', '2520.bb1', '2520.bc1', '2520.be2'], 'contains': ['10080.c1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [5518, -1, 4870, -1], 'generators': [3714487, 8351280], 'label': '20160.l.5040.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '5040.k1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952767
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['240.a1', '240.b1', '360.a1', '840.bb1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [198, -1, 7600, -1], 'generators': [23, 16497367, 18643680, 22147336, 7], 'label': '20160.l.120.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '120.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952768
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1680.x1', '1680.bc1', '2520.i2', '2520.j2', '2520.x1', '2520.ba1', '2520.bb1', '2520.bc1', '2520.be1'], 'contains': ['10080.c1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [4481, -1, 4816, -1], 'generators': [85816, 3628920], 'label': '20160.l.5040.k2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.k2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.k2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952769
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1008.h1', '1680.y1', '2520.f1', '2520.o1', '2520.p1', '2520.v1', '2520.w1', '2520.ba1', '2520.bd1'], 'contains': ['10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4884, -1, 4586, -1], 'generators': [12424343, 3639600], 'label': '20160.l.5040.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '5040.l1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.l1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952770
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['560.j1', '1008.i1', '1680.z1', '2520.g1', '2520.h1', '2520.o1', '2520.t1', '2520.bb1', '2520.be1', '2520.be2'], 'contains': ['10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 945, 'diagramx': [4848, -1, 4630, -1], 'generators': [18679680, 23234423], 'label': '20160.l.5040.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.m1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952771
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['560.k1', '1008.j1', '1680.ba1', '2520.g1', '2520.p1', '2520.u1', '2520.bc1', '2520.bf1'], 'contains': ['10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [3562, -1, 3724, -1], 'generators': [18679680, 23234400], 'label': '20160.l.5040.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '315.a1', 'old_label': '5040.n1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952772
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.bd1', '1680.be1', '1680.bf2', '2520.j1', '2520.r1', '2520.w1', '2520.be1', '2520.bf1'], 'contains': ['10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [3163, -1, 3482, -1], 'generators': [8351280, 3714480], 'label': '20160.l.5040.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '5040.o1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952773
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.o2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.bf1', '1680.bg1', '2520.j2', '2520.y1', '2520.bd1', '2520.be2', '2520.bf1'], 'contains': ['10080.c1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [2765, -1, 3374, -1], 'generators': [85800, 3628920], 'label': '20160.l.5040.o2', 'mobius_quo': None, 'mobius_sub': 48, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '5040.o2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.o2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20952774
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.e1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['1680.bh1', '1680.bi1', '2520.e1', '2520.k1', '2520.q1', '2520.s1'], 'contains': ['10080.d1', '10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 3780, 'diagramx': [6948, -1, 6308, -1], 'generators': [3669840, 131767], 'label': '20160.l.5040.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.e1', 'old_label': '5040.p1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.p1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952775
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.bj1', '2520.i1', '2520.s1'], 'contains': ['10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7551, -1, 6493, -1], 'generators': [3714496, 8351287], 'label': '20160.l.5040.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.n1', 'old_label': '5040.q1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.q1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952776
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '5040.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '630.h1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.bk1', '2520.i2', '2520.z1'], 'contains': ['10080.e1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [8173, -1, 6786, -1], 'generators': [3628927, 85823], 'label': '20160.l.5040.q2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '630.h1', 'old_label': '5040.q2', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040.q2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952777
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '6720.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '70.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1680.be1', '2240.a1', '3360.a1', '3360.c1', '3360.d1', '3360.e1', '3360.f1', '3360.i1', '3360.k1', '3360.l1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [4398, -1, 5262, -1], 'generators': [448560], 'label': '20160.l.6720.a1', 'mobius_quo': None, 'mobius_sub': -192, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '6720.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952779
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '6720.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '280.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['960.a1', '1680.bf1', '1680.bf2', '2240.a1', '3360.b1', '3360.g1', '3360.h1', '3360.j1', '3360.m1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [1296, -1, 1444, -1], 'generators': [19968480], 'label': '20160.l.6720.b1', 'mobius_quo': None, 'mobius_sub': -48, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '6720.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6720.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20952780
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '10080.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['2.a1'], 'conjugacy_class_count': 3, 'contained_in': ['1440.a1', '2016.a1', '3360.a1', '3360.b1', '5040.a1', '5040.b1', '5040.c1', '5040.d1', '5040.e1'], 'contains': ['20160.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8776, 8150, 7153, 9181], 'generators': [23], 'label': '20160.l.10080.a1', 'mobius_quo': -1, 'mobius_sub': -5040, 'normal_closure': '10080.a1', 'normal_contained_in': ['4.a1', '5040.a1'], 'normal_contains': ['20160.a1'], 'normalizer': '1.a1', 'old_label': '10080.a1', 'projective_image': '10080.l', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10080.l', 'quotient_action_kernel_order': 10080, 'quotient_fusion': None, 'short_label': '10080.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952781
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '10080.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '21.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2016.b1', '3360.c1', '3360.d1', '5040.b1', '5040.f1', '5040.g1', '5040.h1', '5040.i1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4949, -1, 5348, -1], 'generators': [10800], 'label': '20160.l.10080.b1', 'mobius_quo': None, 'mobius_sub': -240, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '10080.b1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952782
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '10080.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2016.c1', '3360.e1', '3360.f1', '3360.g1', '5040.c1', '5040.f1', '5040.h1', '5040.j1', '5040.k1', '5040.k2', '5040.l1', '5040.m1', '5040.n1', '5040.o1', '5040.o2'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [4472, -1, 4520, -1], 'generators': [8351280], 'label': '20160.l.10080.c1', 'mobius_quo': None, 'mobius_sub': -192, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '10080.c1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952783
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '10080.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1440.b1', '2016.d1', '3360.h1', '3360.i1', '3360.j1', '5040.d1', '5040.f1', '5040.g1', '5040.j1', '5040.p1'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [4914, -1, 5305, -1], 'generators': [3669840], 'label': '20160.l.10080.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '10080.d1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952784
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '10080.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '105.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2016.e1', '3360.k1', '3360.l1', '3360.m1', '5040.c1', '5040.e1', '5040.g1', '5040.i1', '5040.k1', '5040.k2', '5040.p1', '5040.q1', '5040.q2'], 'contains': ['20160.a1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 315, 'diagramx': [7523, -1, 6331, -1], 'generators': [8351296], 'label': '20160.l.10080.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '10080.e1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10080.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952785
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '20160.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2880.a1', '4032.a1', '6720.a1', '6720.b1', '10080.a1', '10080.b1', '10080.c1', '10080.d1', '10080.e1'], 'contains': [], 'core': '20160.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4914, 8150, 5305, 9181], 'generators': [], 'label': '20160.l.20160.a1', 'mobius_quo': 1, 'mobius_sub': 20160, 'normal_closure': '20160.a1', 'normal_contained_in': ['8.a1', '10080.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '20160.a1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20160.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20952786
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '126.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1'], 'contains': ['252.a1', '252.b1', '252.c1', '252.d1', '252.e1', '630.d1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [8693, -1, 8308, -1], 'generators': [23, 23679480, 18230536, 23316480, 7, 40336], 'label': '20160.l.126.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '126.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952787
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.a1', '70.b1', '70.c1'], 'contains': ['280.c1', '280.k1', '420.a1', '420.j1', '560.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7161, -1, 4617, -1], 'generators': [1135560, 11370960, 18593280, 1134007, 51127, 7], 'label': '20160.l.140.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952788
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.a1', '70.b1', '70.d1'], 'contains': ['280.c1', '280.l1', '420.e1', '420.n1', '560.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [7038, -1, 4503, -1], 'generators': [51120, 18593280, 11370976, 1135576, 16, 40343], 'label': '20160.l.140.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.b1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952789
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['14.a1', '70.e1'], 'contains': ['280.a1', '280.d1', '280.e1', '280.m1', '280.n1', '1260.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1854, -1, 1179, -1], 'generators': [11370976, 8356343, 16, 1497623, 15362656, 11743216], 'label': '20160.l.140.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '140.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952790
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.e1'], 'contains': ['280.a1', '280.d1', '280.f1', '280.m1', '1260.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2381, -1, 2064, -1], 'generators': [23, 11743223, 11370983, 1497623, 8356336, 15362663], 'label': '20160.l.140.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '140.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952791
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['70.a1', '70.f1'], 'contains': ['280.c1', '280.o1', '420.r1', '420.s1', '420.t1', '560.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5264, -1, 3691, -1], 'generators': [23679480, 16, 20050576, 45360, 1583303, 18553080], 'label': '20160.l.140.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.e1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952792
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '70.b1', '70.f1'], 'contains': ['280.c1', '280.o1', '280.p1', '420.w1', '420.x1', '420.y2', '560.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [1993, -1, 2504, -1], 'generators': [23, 23679480, 20050583, 45360, 1583303, 18553080], 'label': '20160.l.140.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.f1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952793
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': ['5040.g1', '5040.i1', '5040.d1', '5040.p1', '5040.b1', '5040.e1', '5040.q2', '5040.a1', '5040.q1'], 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.a1', '28.b1', '84.i1', '140.l1', '480.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1062, 5764, 1209, 5499], 'generators': [8156296, 3628816], 'label': '20160.l.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '20160.l', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952794
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['35.a1', '70.e1'], 'contains': ['280.a1', '280.b1', '280.h1', '280.i1', '420.bc1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [6893, -1, 3942, -1], 'generators': [23, 11370983, 1497616, 11743216, 7, 15362663], 'label': '20160.l.140.g1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '140.g1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.g1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952795
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.c1', '70.d1', '70.f1'], 'contains': ['280.c1', '420.bh1', '420.bi1', '420.bj2', '560.e1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7544, -1, 6980, -1], 'generators': [23, 18553087, 23679480, 45367, 20050576, 7], 'label': '20160.l.140.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.h1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.h1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952796
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.e1'], 'contains': ['280.d1', '280.g1', '280.i1', '280.j1', '420.bg1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2475, -1, 2169, -1], 'generators': [23, 11370983, 8356343, 11743216, 7, 15362663], 'label': '20160.l.140.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '140.i1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.i1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952797
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1', '70.e1'], 'contains': ['280.e1', '280.f1', '280.i1', '1260.t1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 70, 'diagramx': [2272, -1, 2260, -1], 'generators': [23, 5126416, 18679696, 23234400, 7, 166440], 'label': '20160.l.140.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '140.j1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.j1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952798
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['70.a1', '70.b1'], 'contains': ['280.k1', '280.l1', '280.o1', '420.bp1', '420.bs1', '560.g1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [3345, -1, 3016, -1], 'generators': [1135560, 51120, 11370960, 18593280, 40343, 1134000], 'label': '20160.l.140.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.k1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.k1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952799
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '140.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '70.b1'], 'contains': ['280.k1', '280.l1', '280.p1', '420.br1', '420.bt1', '560.f1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [1766, -1, 1303, -1], 'generators': [1135560, 51120, 11370960, 1134016, 18593280, 40336], 'label': '20160.l.140.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '140.l1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '140.l1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
id: 20952800
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['28.a1', '84.a1', '84.b1', '84.d1', '84.e1', '84.f1'], 'contains': ['336.a1', '840.q1', '1008.b1', '1680.d1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7428, -1, 7512, -1], 'generators': [9077880, 87256, 16], 'label': '20160.l.168.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952801
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['28.a1', '84.c1', '84.g1'], 'contains': ['336.b1', '840.r1', '1008.b1', '1680.e1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [1159, -1, 1483, -1], 'generators': [23, 18915863, 7259040], 'label': '20160.l.168.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '168.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952802
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['84.a1', '84.h1', '84.i1'], 'contains': ['336.a1', '840.be1', '1008.f1', '1680.n1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3822, -1, 3937, -1], 'generators': [1498320, 40343, 18552240], 'label': '20160.l.168.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.c1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952803
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '84.b1', '84.h1', '84.i1'], 'contains': ['336.a1', '840.bt1', '1008.h1', '1680.t1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2875, -1, 1687, -1], 'generators': [7994160, 3628800], 'label': '20160.l.168.d1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.d1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952804
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '7.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '42.d1', '42.e1', '70.e1', '105.a1', '105.c1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2931, -1, 2953, -1], 'generators': [23, 4037063, 3719527, 7], 'label': '20160.l.7.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '7.a1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952805
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1', '84.c1'], 'contains': ['336.b1', '840.bx1', '1008.h1', '1680.bb1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [544, -1, 453, -1], 'generators': [3719543, 4112663], 'label': '20160.l.168.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '42.e1', 'old_label': '168.e1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952806
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['84.d1', '84.e1', '84.h1'], 'contains': ['336.a1', '840.bz1', '1008.i1', '1680.bc1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [3771, -1, 3874, -1], 'generators': [4803263, 5183], 'label': '20160.l.168.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.f1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952807
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '84.e1', '84.i1'], 'contains': ['336.a1', '840.ce1', '1008.j1', '1680.bg1'], 'core': '20160.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [1013, -1, 886, -1], 'generators': [4803240, 5160], 'label': '20160.l.168.g1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '21.a1', 'old_label': '168.g1', 'projective_image': '20160.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 20952808
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['105.a1'], 'contains': ['420.i1', '420.q1', '420.t2', '420.bl1', '630.b1', '840.u1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [2409, -1, 2373, -1], 'generators': [3714496, 8472960, 90736, 15291360, 16, 3719527], 'label': '20160.l.210.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '210.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952809
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['14.a1', '105.a1'], 'contains': ['420.i1', '420.q1', '420.y1', '420.bl1', '420.bm1', '630.c1', '840.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [1672, -1, 1778, -1], 'generators': [3714487, 8472967, 15291360, 7, 90727, 3719527], 'label': '20160.l.210.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '210.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952810
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['105.b1'], 'contains': ['420.b1', '420.d1', '420.f1', '420.h1', '420.k1', '420.o1', '420.p1', '420.bn1', '420.bo1', '630.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6514, -1, 5813, -1], 'generators': [23, 18593280, 11370976, 1135583, 1134000, 40336], 'label': '20160.l.210.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.c1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952811
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.a1', '105.b1'], 'contains': ['420.c1', '420.e1', '420.g1', '420.j1', '420.k1', '420.o1', '420.r1', '420.bn1', '420.bp1', '630.b2'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6394, -1, 5608, -1], 'generators': [23, 18593280, 11370983, 1135583, 1134000, 40336], 'label': '20160.l.210.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.d1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952812
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['105.b1'], 'contains': ['420.c1', '420.d1', '420.g1', '420.h1', '420.m1', '420.u1', '420.v1', '420.bn1', '420.bq1', '630.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [6125, -1, 5197, -1], 'generators': [23, 18593280, 1134007, 11370976, 1135583, 40336], 'label': '20160.l.210.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.e1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952813
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.b1', '105.b1'], 'contains': ['420.b1', '420.e1', '420.f1', '420.j1', '420.m1', '420.u1', '420.w1', '420.bo1', '420.bp1', '420.bq1', '420.br1', '630.c1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [4625, -1, 4327, -1], 'generators': [18593280, 11370976, 1135576, 16, 1134000, 40336], 'label': '20160.l.210.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.f1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952814
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.a1', '70.a1', '105.c1'], 'contains': ['420.a1', '420.n1', '420.s1', '420.bs1', '630.b2', '840.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [7577, -1, 6282, -1], 'generators': [23, 3760576, 3755536, 3669856, 3719527, 121703], 'label': '20160.l.210.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '210.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.g1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952815
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': ['2520.l1', '2520.n1', '2520.b1', '2520.d1', '2520.k1', '2520.z1', '2520.s1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1'], 'contains': ['56.a1', '120.b1', '168.g1', '280.p1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [896, 4370, 757, 4169], 'generators': [21819000, 7988520], 'label': '20160.l.8.a1', 'mobius_quo': -1, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1'], 'normal_contains': ['20160.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '20160.l', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '5040.w'}
id: 20952816
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['14.a1', '42.b1', '70.b1', '105.c1'], 'contains': ['420.a1', '420.n1', '420.x1', '420.bs1', '420.bt1', '630.c1', '840.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 630, 'diagramx': [2090, -1, 3870, -1], 'generators': [3755527, 3669840, 121687, 3719527, 7, 3760560], 'label': '20160.l.210.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '210.h1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.h1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952817
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.c1', '70.c1', '105.c1'], 'contains': ['420.a1', '420.bi1', '630.e1', '840.w1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [8216, -1, 7815, -1], 'generators': [3760583, 23, 121696, 3669863, 3719527, 7], 'label': '20160.l.210.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '210.i1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.i1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952818
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.b1'], 'contains': ['420.b1', '420.c1', '420.ba1', '420.bd1', '420.bf1', '630.f1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6832, -1, 6616, -1], 'generators': [12096016, 23, 18593280, 1135583, 7, 40336], 'label': '20160.l.210.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.j1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.j1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952819
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.y1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.d1', '105.b1'], 'contains': ['420.d1', '420.e1', '420.ba1', '420.be1', '420.bh1', '630.g1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7444, -1, 7107, -1], 'generators': [23, 18593280, 11370983, 1135583, 7, 40336], 'label': '20160.l.210.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.k1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.k1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 20952820
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.s1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.b1'], 'contains': ['420.f1', '420.g1', '420.bb1', '420.be1', '420.bf1', '630.d1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5899, -1, 6743, -1], 'generators': [23, 18593280, 11260103, 1134007, 1135583, 7], 'label': '20160.l.210.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.l1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952821
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.a1'], 'contains': ['420.i1', '420.bj1', '630.h1', '840.bb1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [2986, -1, 3502, -1], 'generators': [90736, 8472967, 23, 3714496, 7, 3719527], 'label': '20160.l.210.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '210.m1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.m1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952822
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.u1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.c1', '105.b1'], 'contains': ['420.h1', '420.j1', '420.bb1', '420.bd1', '420.bh1', '630.e1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [7339, -1, 7394, -1], 'generators': [23, 18593280, 1134007, 11370983, 1135583, 7], 'label': '20160.l.210.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '210.n1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.n1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952823
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1260.q1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['21.a1', '105.b1'], 'contains': ['420.k1', '420.l1', '420.m1', '420.z1', '420.ba1', '420.bb1', '420.bc1', '420.bk1', '630.h1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7894, -1, 7488, -1], 'generators': [41063, 23, 3669127, 863, 7, 40336], 'label': '20160.l.210.o1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.o1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.o1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20952824
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '840.x1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.d1', '70.d1', '105.c1'], 'contains': ['420.n1', '420.bi1', '630.g1', '840.x1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 35, 'diagramx': [8412, -1, 7721, -1], 'generators': [23, 12419280, 10823, 11300407, 3639623, 7], 'label': '20160.l.210.p1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '210.p1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.p1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952825
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.e1', '105.a1'], 'contains': ['420.q1', '420.bj1', '630.i1', '840.bd1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [3155, -1, 3103, -1], 'generators': [23, 3669863, 3755536, 18990727, 131783, 7], 'label': '20160.l.210.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '210.q1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.q1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952826
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '14.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.a1', '28.b1', '84.b1', '84.c1', '140.c1', '210.b1', '210.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [1919, -1, 2058, -1], 'generators': [23, 3719520, 4037063], 'label': '20160.l.14.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952827
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['105.b1'], 'contains': ['420.o1', '420.u1', '420.bd1', '420.be1', '420.bk1', '630.i1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [6740, -1, 6503, -1], 'generators': [12096016, 23, 18593280, 11260103, 1135583, 7], 'label': '20160.l.210.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.r1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.r1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952828
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.f1', '105.b1'], 'contains': ['420.p1', '420.r1', '420.v1', '420.w1', '420.bf1', '420.bh1', '420.bk1', '630.j1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5593, -1, 4901, -1], 'generators': [23, 23679480, 45367, 20050576, 1583303, 7], 'label': '20160.l.210.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.b1', 'old_label': '210.s1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.s1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 20952829
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1', '42.f1', '70.f1', '105.c1'], 'contains': ['420.s1', '420.x1', '420.bi1', '630.j1', '840.z1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [5416, -1, 5947, -1], 'generators': [23, 1219680, 126000, 363607, 7, 22308623], 'label': '20160.l.210.t1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.c1', 'old_label': '210.t1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.t1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952830
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.n1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1', '30.a1', '105.a1'], 'contains': ['420.t2', '420.y1', '420.bj1', '630.j1', '840.ba1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [2240, -1, 2624, -1], 'generators': [23, 1219680, 22308623, 18276487, 7620600, 7], 'label': '20160.l.210.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '105.a1', 'old_label': '210.u1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.u1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952831
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '210.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1', '70.f1'], 'contains': ['420.t1', '420.y2', '420.bj2', '630.j1', '840.ba1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [2669, -1, 2812, -1], 'generators': [23, 18679696, 19242720, 5167, 7620600, 7], 'label': '20160.l.210.u2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '210.u2', 'old_label': '210.u2', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '210.u2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20952832
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '120.a1'], 'contains': ['480.a1', '480.b1', '720.a1', '1680.f1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 720, 'diagramx': [206, -1, 1857, -1], 'generators': [16497360, 23, 22147343, 18643687], 'label': '20160.l.240.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '240.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952833
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '240.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1', '120.a1'], 'contains': ['480.a1', '720.b1', '1680.m1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 120, 'diagramx': [615, -1, 3479, -1], 'generators': [23, 14596696, 18316096, 7], 'label': '20160.l.240.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '120.a1', 'old_label': '240.b1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
id: 20952834
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '252.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.b1', '126.a1'], 'contains': ['504.a1', '504.c1', '504.d1', '504.i1', '504.j1', '1260.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [4836, -1, 6516, -1], 'generators': [18230543, 23, 23679480, 40343, 23316480], 'label': '20160.l.252.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '252.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952835
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '252.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['42.a1', '126.a1'], 'contains': ['504.a1', '504.c1', '504.e1', '504.i1', '1260.b1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 756, 'diagramx': [8799, -1, 8574, -1], 'generators': [23, 23679480, 18230536, 40343, 23316480], 'label': '20160.l.252.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '252.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952836
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '252.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.c1', '126.a1'], 'contains': ['504.a1', '504.b1', '504.f1', '504.g1', '504.h1', '1260.p1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [9509, -1, 9489, -1], 'generators': [3629527, 23, 23678040, 7, 40336], 'label': '20160.l.252.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '252.c1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952837
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '7.a1'], 'contains': ['28.a1', '84.f1', '84.g1', '140.j1', '210.t1', '210.u1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [2865, -1, 2812, -1], 'generators': [23, 23765056, 22308623, 7], 'label': '20160.l.14.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.b1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '720.763'}
id: 20952838
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '252.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.d1', '42.e1', '126.a1'], 'contains': ['504.c1', '504.g1', '1260.s1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [8720, -1, 8879, -1], 'generators': [23, 5121367, 19319063, 12338647, 7], 'label': '20160.l.252.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '252.d1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952839
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '252.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2520.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['42.f1', '126.a1'], 'contains': ['504.d1', '504.e1', '504.g1', '1260.t1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [8113, -1, 8308, -1], 'generators': [10931880, 23, 15689520, 15321607, 7], 'label': '20160.l.252.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.a1', 'old_label': '252.e1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 20952840
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['70.b1', '140.c1', '140.d1', '140.g1'], 'contains': ['560.a1', '560.b1', '560.f1', '560.g1', '840.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2128, -1, 2153, -1], 'generators': [11370976, 16, 1497616, 15362656, 11743216], 'label': '20160.l.280.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.a1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952841
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['70.a1', '140.g1'], 'contains': ['560.a1', '560.d1', '560.g1', '840.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [6988, -1, 3723, -1], 'generators': [23, 11743223, 11370976, 1497623, 15362663], 'label': '20160.l.280.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.g1', 'old_label': '280.b1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952842
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.a1', '140.b1', '140.e1', '140.f1', '140.h1'], 'contains': ['560.h1', '840.p1', '840.q1', '840.r2', '1120.a1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 105, 'diagramx': [7114, -1, 3811, -1], 'generators': [18553087, 23679480, 20050567, 45367, 7], 'label': '20160.l.280.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '35.a1', 'old_label': '280.c1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.c1', 'subgroup_fusion': None, 'weyl_group': '48.48'}
id: 20952843
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['140.c1', '140.d1', '140.i1'], 'contains': ['560.b1', '560.c1', '560.i1', '560.l1', '840.o1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [1948, -1, 1163, -1], 'generators': [11743207, 11370960, 15362640, 8356343, 7], 'label': '20160.l.280.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.d1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.d1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952844
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['28.a1', '140.c1', '140.j1'], 'contains': ['560.b1', '560.j1', '560.k1', '2520.g1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1349, -1, 804, -1], 'generators': [23, 23234400, 5126423, 18679703, 166440], 'label': '20160.l.280.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.e1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.e1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952845
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.d1', '140.j1'], 'contains': ['560.b1', '560.j1', '2520.h1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 210, 'diagramx': [1861, -1, 1583, -1], 'generators': [23, 5126423, 23234407, 18679703, 166440], 'label': '20160.l.280.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '70.e1', 'old_label': '280.f1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 20952846
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5040.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['140.i1'], 'contains': ['560.c1', '560.d1', '560.l1', '840.u1'], 'core': '10080.a1', 'coset_action_label': None, 'count': 420, 'diagramx': [2278, -1, 1954, -1], 'generators': [11743207, 15362640, 11370983, 8356343, 7], 'label': '20160.l.280.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.i1', 'old_label': '280.g1', 'projective_image': '10080.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.g1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 20952847
{'ambient': '20160.l', 'aut_centralizer_order': None, 'aut_label': '280.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1680.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['70.c1', '70.d1', '140.g1'], 'contains': ['560.a1', '560.e1', '840.w1', '840.x1'], 'core': '5040.a1', 'coset_action_label': None, 'count': 140, 'diagramx': [8462, -1, 8464, -1], 'generators': [23, 1497616, 11743216, 7, 15362663], 'label': '20160.l.280.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '140.g1', 'old_label': '280.h1', 'projective_image': '5040.w', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '280.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}

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.