LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-24T12:35:47.831850

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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 3], 'aut_gens': [[13286, 14809, 13448, 14065, 6664, 9257, 7987], [13286, 1167, 13448, 8735, 6658, 9257, 1943], [13286, 12270, 13448, 3212, 17761, 13307, 18355], [13286, 10753, 13463, 5464, 6664, 9257, 18349]], 'aut_group': '432.734', 'aut_hash': 734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 432, 'aut_permdeg': 32, 'aut_perms': [80394071457668005846009793077884751, 205840237197259922601661378035715798, 8194481426605577989710855998550], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [3, 8, 1, 1], [3, 12, 2, 1], [3, 24, 2, 1], [4, 54, 1, 2], [6, 8, 1, 1], [6, 12, 2, 1], [6, 24, 2, 1], [6, 36, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 2], [3, 8, 1], [3, 12, 2], [3, 24, 2], [4, 54, 2], [6, 8, 1], [6, 12, 2], [6, 24, 2], [6, 36, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '216.153', 'commutator_count': 1, 'commutator_label': '72.41', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 735, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['216.153', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 2], [3, 8, 1, 1], [3, 12, 2, 1], [3, 24, 2, 1], [4, 54, 1, 2], [6, 8, 1, 1], [6, 12, 2, 1], [6, 24, 2, 1], [6, 36, 2, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 192, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 2], [8, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '432.735', 'hash': 735, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [1, 4, 2, 4, 3, 3, 6], 'inner_gens': [[13286, 14809, 13448, 14065, 6664, 9257, 7987], [13286, 14809, 8927, 3956, 17761, 9236, 12278], [13286, 14803, 13448, 14044, 6658, 4715, 7981], [13286, 3212, 8933, 14065, 2857, 13301, 5466], [13286, 6229, 13469, 9994, 6664, 9257, 3187], [13286, 10765, 4877, 5479, 6664, 9257, 7981], [13286, 16077, 4883, 3197, 2851, 13301, 7987]], 'inner_hash': 153, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': '\\PU(3,2)', 'inner_used': [2, 3, 4, 7], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 6], [2, 6], [3, 2], [8, 6]], 'label': '432.735', 'linC_count': 3, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 1, 'linQ_dim': 8, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2*PU(3,2)', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 20, 'number_divisions': 14, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 50, 'number_subgroups': 498, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 19], [3, 80], [4, 108], [6, 224]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [6643], 'outer_gens': [[13286, 1173, 13448, 8729, 6664, 4715, 1922]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 4], [3, 2], [4, 2], [8, 2], [16, 2]], 'representations': {'PC': {'code': 10971436765438046916329389100487499564217936835203003205, 'gens': [1, 2, 3, 5, 6], 'pres': [7, 3, 2, 2, 2, 3, 2, 3, 127, 64, 65, 135, 58, 5044, 3651, 858, 165, 16133, 5388, 1699, 1286, 124, 16470, 5501, 412, 1203]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [13286, 14809, 13448, 14065, 6664, 9257, 7987]}, 'Perm': {'d': 11, 'gens': [1, 937464, 1277688, 737310, 1539408, 5262510, 9155688]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times \\PU(3,2)', 'transitive_degree': 18, '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: 110224257
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 735, 'group_order': 432, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 6643, 'size': 1}
id: 110224268
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 735, 'group_order': 432, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 13286, 'size': 1}
id: 110224270
{'aut_label': '2B', 'centralizer': '9.a1.a1', 'counter': 3, 'group_counter': 735, 'group_order': 432, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 4883, 'size': 9}
id: 110224271
{'aut_label': '2C', 'centralizer': '9.a1.a1', 'counter': 4, 'group_counter': 735, 'group_order': 432, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 17593, 'size': 9}
id: 110224272
{'aut_label': '3A', 'centralizer': '8.a1.a1', 'counter': 5, 'group_counter': 735, 'group_order': 432, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 2836, 'size': 8}
id: 110224273
{'aut_label': '3B1', 'centralizer': '12.b1.a1', 'counter': 6, 'group_counter': 735, 'group_order': 432, 'label': '3B1', 'order': 3, 'powers': [7, 1], 'representative': 6652, 'size': 12}
id: 110224274
{'aut_label': '3B1', 'centralizer': '12.b1.a1', 'counter': 7, 'group_counter': 735, 'group_order': 432, 'label': '3B-1', 'order': 3, 'powers': [6, 1], 'representative': 6661, 'size': 12}
id: 110224275
{'aut_label': '3C1', 'centralizer': '24.e1.a1', 'counter': 8, 'group_counter': 735, 'group_order': 432, 'label': '3C1', 'order': 3, 'powers': [9, 1], 'representative': 17764, 'size': 24}
id: 110224276
{'aut_label': '3C1', 'centralizer': '24.e1.a1', 'counter': 9, 'group_counter': 735, 'group_order': 432, 'label': '3C-1', 'order': 3, 'powers': [8, 1], 'representative': 2854, 'size': 24}
id: 110224258
{'aut_label': '4A', 'centralizer': '54.a1.a1', 'counter': 10, 'group_counter': 735, 'group_order': 432, 'label': '4A', 'order': 4, 'powers': [3, 10], 'representative': 6229, 'size': 54}
id: 110224259
{'aut_label': '4B', 'centralizer': '54.a1.a1', 'counter': 11, 'group_counter': 735, 'group_order': 432, 'label': '4B', 'order': 4, 'powers': [3, 11], 'representative': 8168, 'size': 54}
id: 110224260
{'aut_label': '6A', 'centralizer': '8.a1.a1', 'counter': 12, 'group_counter': 735, 'group_order': 432, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 9236, 'size': 8}
id: 110224261
{'aut_label': '6B1', 'centralizer': '12.b1.a1', 'counter': 13, 'group_counter': 735, 'group_order': 432, 'label': '6B1', 'order': 6, 'powers': [6, 2], 'representative': 13295, 'size': 12}
id: 110224262
{'aut_label': '6B1', 'centralizer': '12.b1.a1', 'counter': 14, 'group_counter': 735, 'group_order': 432, 'label': '6B-1', 'order': 6, 'powers': [7, 2], 'representative': 13304, 'size': 12}
id: 110224263
{'aut_label': '6C1', 'centralizer': '24.e1.a1', 'counter': 15, 'group_counter': 735, 'group_order': 432, 'label': '6C1', 'order': 6, 'powers': [8, 2], 'representative': 4709, 'size': 24}
id: 110224264
{'aut_label': '6C1', 'centralizer': '24.e1.a1', 'counter': 16, 'group_counter': 735, 'group_order': 432, 'label': '6C-1', 'order': 6, 'powers': [9, 2], 'representative': 9248, 'size': 24}
id: 110224265
{'aut_label': '6D1', 'centralizer': '36.a1.a1', 'counter': 17, 'group_counter': 735, 'group_order': 432, 'label': '6D1', 'order': 6, 'powers': [6, 4], 'representative': 10008, 'size': 36}
id: 110224266
{'aut_label': '6D1', 'centralizer': '36.a1.a1', 'counter': 18, 'group_counter': 735, 'group_order': 432, 'label': '6D-1', 'order': 6, 'powers': [7, 4], 'representative': 1922, 'size': 36}
id: 110224267
{'aut_label': '6E1', 'centralizer': '36.a1.a1', 'counter': 19, 'group_counter': 735, 'group_order': 432, 'label': '6E1', 'order': 6, 'powers': [7, 3], 'representative': 18507, 'size': 36}
id: 110224269
{'aut_label': '6E1', 'centralizer': '36.a1.a1', 'counter': 20, 'group_counter': 735, 'group_order': 432, 'label': '6E-1', 'order': 6, 'powers': [6, 3], 'representative': 17236, 'size': 36}

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: 4558244
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.1a', '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], 'schur_index': 1}
id: 4558250
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.1b', '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], 'schur_index': 1}
id: 4558251
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 4558252
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.1d', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -1, -1, -1, -1, -2, 2, -2, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
id: 4558253
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.2a', 'multiplicity': 1, 'nt': [24, 7], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -1, -1, -1, -1, 0, 0, -2, 1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 2}
id: 4558254
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.2b', 'multiplicity': 1, 'nt': [24, 7], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -1, -1, -1, -1, 0, 0, 2, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 2}
id: 4558257
{'cdim': 3, 'counter': 9, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, 0, 0, 0, 0, -1, -1, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4558245
{'cdim': 3, 'counter': 10, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.3b', 'multiplicity': 1, 'nt': [6, 6], 'qdim': 3, 'qvalues': [3, -3, 3, -3, 3, 0, 0, 0, 0, 1, -1, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 4558255
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.2c', 'multiplicity': 2, 'nt': [8, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 1, 1, 1, 1, 0, 0, -4, -1, -1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
id: 4558256
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.2d', 'multiplicity': 2, 'nt': [8, 12], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 1, 1, 1, 1, 0, 0, 4, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 4558246
{'cdim': 8, 'counter': 11, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.8a', 'multiplicity': 1, 'nt': [9, 23], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -1, 2, 2, -1, -1, 0, 0, -1, 2, 2, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
id: 4558247
{'cdim': 8, 'counter': 12, 'faithful': True, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.8b', 'multiplicity': 1, 'nt': [18, 151], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -1, 2, 2, -1, -1, 0, 0, 1, -2, -2, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
id: 4558248
{'cdim': 8, 'counter': 13, 'faithful': False, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.8c', 'multiplicity': 2, 'nt': [24, 569], 'qdim': 16, 'qvalues': [16, 16, 0, 0, -2, -2, -2, 1, 1, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
id: 4558249
{'cdim': 8, 'counter': 14, 'faithful': True, 'group': '432.735', 'group_order': 432, 'image': None, 'label': '432.735.8d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -2, -2, -2, 1, 1, 0, 0, 2, 2, 2, -1, -1, 0, 0, 0, 0], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema

id: 7131716
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 432, 'label': '432.735.1a', '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]]]}
id: 7131727
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 216, 'label': '432.735.1b', '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]]]}
id: 7131729
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.735.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 7131730
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 144, 'label': '432.735.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 7131731
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.735.1d1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
id: 7131732
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 432, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 72, 'label': '432.735.1d2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
id: 7131733
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': -1, 'kernel': '24.c1.a1', 'kernel_order': 18, 'label': '432.735.2a', 'nt': [24, 7], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 7131734
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': -1, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.735.2b', 'nt': [24, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7131735
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 9, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 18, 'label': '432.735.2c1', 'nt': [8, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]]]}
id: 7131717
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 10, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 18, 'label': '432.735.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]]]}
id: 7131718
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 11, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.735.2d1', 'nt': [8, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
id: 7131719
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 12, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.3', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 18, 'label': '432.735.2d2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
id: 7131720
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 13, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 36, 'label': '432.735.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131721
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 36, 'counter': 14, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '24.13', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 18, 'label': '432.735.3b', 'nt': [6, 6], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131722
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 15, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '216.153', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.735.8a', 'nt': [9, 23], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131723
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 16, 'cyclotomic_n': 1, 'dim': 8, 'faithful': True, 'field': [0, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '432.735', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.735.8b', 'nt': [18, 151], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131724
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 17, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '216.153', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.735.8c1', 'nt': [24, 569], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131725
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 18, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '216.153', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 2, 'label': '432.735.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131726
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 19, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '432.735', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.735.8d1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 7131728
{'center': '216.a1.a1', 'center_index': 216, 'center_order': 2, 'counter': 20, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '432.735', 'group_counter': 735, 'group_order': 432, 'image': None, 'image_isoclass': '432.735', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 1, 'label': '432.735.8d2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 66581378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 432, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '432.735.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.735', 'subgroup_hash': 735, 'subgroup_order': 432, 'subgroup_tex': 'C_2\\times \\PU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 66581389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': True, 'core_order': 216, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '432.735.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.153', 'subgroup_hash': 153, 'subgroup_order': 216, 'subgroup_tex': '\\PU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 66581400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 144, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.187', 'subgroup_hash': 187, 'subgroup_order': 144, 'subgroup_tex': 'C_2\\times \\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 66581411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.4.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
id: 66581422
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 72, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 66581424
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 66581425
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 66581426
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
id: 66581427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 66581379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 66581380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 66581381
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 36, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 66581382
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 66581383
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 66581384
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 66581385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '432.735.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 3}
id: 66581386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 66581387
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 18, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,3)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, '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: 66581388
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 18, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': False, '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: 66581390
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 18, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,3)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 66581391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 66581392
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 66581393
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 66581394
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 66581395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '432.735.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 2}
id: 66581396
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': 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: 66581397
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': 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: 66581398
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 9, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '432.735.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.32', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\SL(2,3)', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 66581399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 66581401
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 66581402
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': 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: 66581403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 66581404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 66581405
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581406
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581407
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581408
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581409
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581410
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581412
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 66581413
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '432.735.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': 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: 66581414
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': 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: 66581415
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': 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: 66581416
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 66581417
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 66581418
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 66581419
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 2, 'counter': 47, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '432.735.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.153', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 153, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PU(3,2)', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], '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: 66581420
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 66581421
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '432.735.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 66581423
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '432.735', 'ambient_counter': 735, 'ambient_order': 432, 'ambient_tex': 'C_2\\times \\PU(3,2)', 'central': True, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 1, 'counter': 50, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '432.735.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '432.735', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 735, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\PU(3,2)', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D4', 'C5'], '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: 66581378
{'ambient': '432.735', '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': '216.a1.a1', 'complements': ['432.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '4.a1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8258, 3106, 8958, 6588, 7991, 3371, 7991, 3371], 'generators': [2851, 7210, 6658, 13454, 2082, 13448, 9670], 'label': '432.735.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581379
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '24.g1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3071, -1, 2815, -1, 2978, -1, 2978, -1], 'generators': [2851, 7210, 6658, 6667], 'label': '432.735.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 66581380
{'ambient': '432.735', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 18, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '27.a1.a1', '36.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9797, -1, 9703, -1, 7991, -1, 7991, -1], 'generators': [14212, 7210, 2088, 13448, 13466], 'label': '432.735.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 66581381
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3553, 5093, 3520, 4955, 3860, 5657, 3860, 5657], 'generators': [2851, 7210, 6658, 13448], 'label': '432.735.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581382
{'ambient': '432.735', 'aut_centralizer_order': 3, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.d1.a1', '24.f1.a1', '24.g1.a1', '36.a1.a1', '36.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5713, -1, 5965, -1, 5521, -1, 5521, -1], 'generators': [7210, 6658, 13454, 13448], 'label': '432.735.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581383
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '108.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6770, -1, 7066, -1, 6371, -1, 6371, -1], 'generators': [2851, 6658, 9994, 13448], 'label': '432.735.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 66581384
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '108.c1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7783, -1, 8121, -1, 7174, -1, 7174, -1], 'generators': [2851, 6658, 13448, 9670], 'label': '432.735.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 66581385
{'ambient': '432.735', 'aut_centralizer_order': 3, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2014, -1, 1793, -1, 1970, -1, 1970, -1], 'generators': [2851, 6658, 6667], 'label': '432.735.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 66581386
{'ambient': '432.735', 'aut_centralizer_order': 2, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 18, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '9.a1.a1'], 'contains': ['54.c1.a1', '72.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': '18T151', 'count': 9, 'diagramx': [9056, -1, 9822, -1, 8610, -1, 8610, -1], 'generators': [17229, 13454, 13463, 5626], 'label': '432.735.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 66581387
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 9, 'centralizer': '24.a1.a1', 'complements': ['18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1583, 8447, 1595, 1750, 1285, 8314, 1285, 8314], 'generators': [2851, 6658, 13286], 'label': '432.735.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['12.a1.a1'], 'normal_contains': ['48.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '216.153', 'quotient_action_image': '24.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.3'}
id: 66581388
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '72.e1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5091, 2081, 5248, 7834, 5375, 2457, 5375, 2457], 'generators': [2851, 6658, 13448], 'label': '432.735.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -4, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581389
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': ['216.a1.a1', '216.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '8.b1.a1', '18.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8569, 1553, 9281, 8250, 8215, 1114, 8215, 1114], 'generators': [2851, 6658, 13454, 2082, 13448, 9670], 'label': '432.735.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '432.735', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581390
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': ['18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '72.g1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2546, 4907, 2598, 5133, 3406, 5057, 3406, 5057], 'generators': [2851, 7210, 6658], 'label': '432.735.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '432.735', 'quotient_action_image': '24.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581391
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3268, -1, 3349, -1, 2655, -1, 2655, -1], 'generators': [6658, 6667, 13286], 'label': '432.735.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581392
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '72.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [481, -1, 449, -1, 389, -1, 389, -1], 'generators': [2860, 6658, 13286], 'label': '432.735.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 66581393
{'ambient': '432.735', 'aut_centralizer_order': 3, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.d1.a1', '72.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': '24T1320', 'count': 12, 'diagramx': [6054, -1, 6250, -1, 6120, -1, 6120, -1], 'generators': [6658, 13454, 13448], 'label': '432.735.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581394
{'ambient': '432.735', 'aut_centralizer_order': 3, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.f1.a1', '72.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': '24T1321', 'count': 12, 'diagramx': [4129, -1, 4245, -1, 4150, -1, 4150, -1], 'generators': [7210, 6658, 6667], 'label': '432.735.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581395
{'ambient': '432.735', 'aut_centralizer_order': 2, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 18, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9088, -1, 9249, -1, 9348, -1, 9348, -1], 'generators': [14212, 7210, 2088, 13448], 'label': '432.735.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 66581396
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '12.b1.a1'], 'contains': ['72.b1.a1', '72.d1.a1', '72.f1.a1', '108.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6296, -1, 6500, -1, 7016, -1, 7016, -1], 'generators': [7210, 13448, 13466], 'label': '432.735.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581397
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.g1.a1', '108.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4648, -1, 4786, -1, 4835, -1, 4835, -1], 'generators': [7210, 6658, 13448], 'label': '432.735.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581398
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 9, 'centralizer': '24.a1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['144.a1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1412, 5155, 1417, 4333, 2984, 5571, 2984, 5571], 'generators': [2851, 6658], 'label': '432.735.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.735', 'quotient_action_image': '24.3', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.3'}
id: 66581399
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 36, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.d1.a1', '24.f1.a1', '24.g1.a1'], 'contains': ['144.a1.a1', '144.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3096, -1, 3171, -1, 3524, -1, 3524, -1], 'generators': [6658, 6667], 'label': '432.735.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581400
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': ['144.b1.a1', '144.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '27.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7847, 5093, 8530, 4955, 9262, 5657, 9262, 5657], 'generators': [2851, 7210, 6658, 2082, 13448, 9670], 'label': '432.735.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '216.153', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581401
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.e1.a1'], 'contains': ['144.a1.a1', '144.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [203, -1, 217, -1, 1970, -1, 1970, -1], 'generators': [2860, 6658], 'label': '432.735.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
id: 66581402
{'ambient': '432.735', 'aut_centralizer_order': 8, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7879, -1, 8148, -1, 8412, -1, 8412, -1], 'generators': [14212, 7210, 13448], 'label': '432.735.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66581403
{'ambient': '432.735', 'aut_centralizer_order': 2, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.3', 'aut_weyl_index': 54, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8537, -1, 8834, -1, 9348, -1, 9348, -1], 'generators': [4877, 1920, 9691], 'label': '432.735.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 66581404
{'ambient': '432.735', 'aut_centralizer_order': 2, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 18, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '18.a1.a1', '27.a1.a1'], 'contains': ['108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9581, -1, 9736, -1, 9822, -1, 9822, -1], 'generators': [8912, 12450, 9670], 'label': '432.735.54.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
id: 66581405
{'ambient': '432.735', 'aut_centralizer_order': 54, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '36.b1.a1'], 'contains': ['144.a1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2521, -1, 2551, -1, 2477, -1, 2477, -1], 'generators': [6658, 13286], 'label': '432.735.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66581406
{'ambient': '432.735', 'aut_centralizer_order': 18, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.a1.a1'], 'contains': ['144.b1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5003, -1, 5155, -1, 4032, -1, 4032, -1], 'generators': [6667, 13286], 'label': '432.735.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.b1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581407
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1'], 'contains': ['144.c1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [462, -1, 428, -1, 1462, -1, 1462, -1], 'generators': [2860, 13286], 'label': '432.735.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581408
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '24.f1.a1', '36.a1.a1'], 'contains': ['144.b1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6713, -1, 6935, -1, 6469, -1, 6469, -1], 'generators': [13454, 13463], 'label': '432.735.72.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581409
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.f1.a1', '36.b1.a1'], 'contains': ['144.a1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4547, -1, 4680, -1, 5455, -1, 5455, -1], 'generators': [6658, 13448], 'label': '432.735.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581410
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.a1.a1'], 'contains': ['144.b1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5649, -1, 5828, -1, 4980, -1, 4980, -1], 'generators': [7210, 6652], 'label': '432.735.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581411
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '12.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4066, -1, 4159, -1, 4137, -1, 4137, -1], 'generators': [2851, 7210, 6658, 13454, 13448], 'label': '432.735.4.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
id: 66581412
{'ambient': '432.735', 'aut_centralizer_order': 6, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.g1.a1', '36.b1.a1'], 'contains': ['144.a1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3476, -1, 3566, -1, 4506, -1, 4506, -1], 'generators': [7210, 6658], 'label': '432.735.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 66581413
{'ambient': '432.735', 'aut_centralizer_order': 48, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '54.a1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6175, -1, 6428, -1, 5962, -1, 5962, -1], 'generators': [7210, 13448], 'label': '432.735.108.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581414
{'ambient': '432.735', 'aut_centralizer_order': 8, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '54.a1.a1', '54.b1.a1'], 'contains': ['216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7567, -1, 7607, -1, 8123, -1, 8123, -1], 'generators': [4883, 9994], 'label': '432.735.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66581415
{'ambient': '432.735', 'aut_centralizer_order': 8, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'contains': ['216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8537, -1, 8834, -1, 8985, -1, 8985, -1], 'generators': [8912, 9670], 'label': '432.735.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66581416
{'ambient': '432.735', 'aut_centralizer_order': 54, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1', '72.e1.a1', '72.g1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2938, -1, 2993, -1, 3538, -1, 3538, -1], 'generators': [6658], 'label': '432.735.144.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66581417
{'ambient': '432.735', 'aut_centralizer_order': 18, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.b1.a1', '72.d1.a1', '72.f1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4724, -1, 4851, -1, 4032, -1, 4032, -1], 'generators': [6667], 'label': '432.735.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581418
{'ambient': '432.735', 'aut_centralizer_order': 9, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 216, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '72.c1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [221, -1, 178, -1, 1970, -1, 1970, -1], 'generators': [2860], 'label': '432.735.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581419
{'ambient': '432.735', 'aut_centralizer_order': 432, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '1.a1.a1', 'complements': ['2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '108.a1.a1'], 'contains': ['432.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4135, 7484, 4238, 2611, 3063, 8029, 3063, 8029], 'generators': [13286], 'label': '432.735.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['24.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.153', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.153', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581420
{'ambient': '432.735', 'aut_centralizer_order': 48, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.e1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6472, -1, 6724, -1, 6212, -1, 6212, -1], 'generators': [13448], 'label': '432.735.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581421
{'ambient': '432.735', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 432, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.g1.a1', '108.a1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5009, -1, 5267, -1, 4743, -1, 4743, -1], 'generators': [7210], 'label': '432.735.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581422
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': ['72.f1.a1', '72.b1.a1', '72.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '54.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8626, 1926, 9367, 7982, 9262, 1857, 9262, 1857], 'generators': [2851, 6658, 2082, 13448, 9670], 'label': '432.735.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '432.735', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.153'}
id: 66581423
{'ambient': '432.735', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1'], 'contains': [], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4433, 6397, 4483, 3442, 3788, 6657, 3788, 6657], 'generators': [], 'label': '432.735.432.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['48.a1.a1', '216.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66581424
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '54.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6813, -1, 7384, -1, 6002, -1, 6002, -1], 'generators': [2851, 7210, 6658, 13448, 9670], 'label': '432.735.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 66581425
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.182', 'aut_weyl_index': 3, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '54.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7751, -1, 8372, -1, 6976, -1, 6976, -1], 'generators': [2851, 6658, 1920, 13448, 9670], 'label': '432.735.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 66581426
{'ambient': '432.735', 'aut_centralizer_order': 3, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1704, -1, 1595, -1, 1970, -1, 1970, -1], 'generators': [2851, 6658, 6667, 13286], 'label': '432.735.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '216.153', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
id: 66581427
{'ambient': '432.735', 'aut_centralizer_order': 1, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.a1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.f1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5161, -1, 5392, -1, 4743, -1, 4743, -1], 'generators': [2851, 6658, 13454, 13448], 'label': '432.735.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.735', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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