LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-23T04:40:40.707068

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': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 48, 'aut_gen_orders': [4, 4, 8], 'aut_gens': [[40647600, 133, 1174320, 23, 56, 333, 7660800, 91854000], [160, 167292720, 314, 203661360, 88265520, 84596400, 311, 56], [40647600, 421, 1174320, 94, 676, 56, 203258160, 88265520], [44352000, 377, 90760320, 687, 333, 78, 214104240, 11249280]], 'aut_group': '41472.m', 'aut_hash': 7917341340725978817, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 36, 'aut_perms': [245025168864466323974459964898889443850621, 271798964290846642184411205186584896615008, 129051599181837849020556675003209996555637], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 2, 1], [2, 81, 1, 1], [3, 4, 4, 1], [3, 16, 4, 1], [4, 9, 4, 1], [4, 81, 4, 2], [6, 36, 4, 1], [12, 36, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\SOPlus(4,2)^2.D_4', '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': 48, 'autcentquo_group': '41472.m', 'autcentquo_hash': 7917341340725978817, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)^2.D_4', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [3, 4, 4], [3, 16, 4], [4, 9, 4], [4, 81, 8], [6, 36, 4], [12, 36, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '1296.3496', 'commutator_count': 1, 'commutator_label': '81.15', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3496, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['36.9', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 4, 1, 4], [3, 16, 1, 4], [4, 9, 2, 2], [4, 81, 2, 4], [6, 36, 1, 4], [12, 36, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 12, 'exponent': 12, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1296.3496', 'hash': 3496, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 4, 2, 2, 3, 3, 3, 3], 'inner_gens': [[40647600, 133, 1174320, 23, 56, 333, 84596400, 214104240], [40647600, 133, 1174320, 23, 285, 697, 7660800, 91854000], [40647600, 133, 1174320, 23, 56, 333, 11249280, 210551040], [40647600, 133, 1174320, 23, 78, 676, 7660800, 91854000], [40647600, 462, 1174320, 94, 56, 333, 7660800, 91854000], [40647600, 234, 1174320, 687, 56, 333, 7660800, 91854000], [134628480, 133, 12055680, 23, 56, 333, 7660800, 91854000], [55520640, 133, 211241520, 23, 56, 333, 7660800, 91854000]], 'inner_hash': 3496, 'inner_nilpotent': False, 'inner_order': 1296, 'inner_split': False, 'inner_tex': 'C_3^4:C_4^2', 'inner_used': [1, 2, 5, 7], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [4, 16], [16, 4]], 'label': '1296.3496', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^4:C4^2', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 36, 'number_divisions': 26, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 65, 'number_subgroup_classes': 196, 'number_subgroups': 4956, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 99], [3, 80], [4, 684], [6, 144], [12, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [1174320, 40360320, 0, 1174343], 'outer_gens': [[40647600, 130, 1174320, 23, 627, 333, 203258160, 88265520], [40647600, 130, 1174320, 23, 627, 333, 214104240, 11249280], [40360320, 130, 1174320, 23, 627, 333, 203258160, 91854000], [130, 40647600, 23, 1174320, 7660800, 91854000, 333, 78]], 'outer_group': '32.27', 'outer_hash': 27, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [107, 82, 21821, 34938], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [4, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 8], [8, 4], [16, 4]], 'representations': {'PC': {'code': 332479413123530381969022486350160495931449958063248709927, 'gens': [1, 3, 4, 7, 8], 'pres': [8, 2, 2, 3, 2, 2, 3, 3, 3, 16, 1346, 106, 515, 971, 91, 1284, 2412, 116, 2501, 2317, 3390, 710, 3103, 2343]}, 'GLFq': {'d': 3, 'q': 9, 'gens': [129138492, 189999903, 156849001, 46807135, 86218832, 331826950, 344680685, 157244572]}, 'Perm': {'d': 12, 'gens': [40647600, 133, 1174320, 23, 56, 333, 7660800, 91854000]}}, 'schur_multiplier': [3, 12], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 4], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:C_4^2', 'transitive_degree': 24, '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: 144191630
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3496, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 144191641
{'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 3496, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 23, 'size': 9}
id: 144191652
{'aut_label': '2A', 'centralizer': '9.a1', 'counter': 3, 'group_counter': 3496, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1174320, 'size': 9}
id: 144191660
{'aut_label': '2C', 'centralizer': '81.a1', 'counter': 4, 'group_counter': 3496, 'group_order': 1296, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 211242233, 'size': 81}
id: 144191661
{'aut_label': '3A', 'centralizer': '4.a1', 'counter': 5, 'group_counter': 3496, 'group_order': 1296, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 7660800, 'size': 4}
id: 144191662
{'aut_label': '3A', 'centralizer': '4.a1', 'counter': 6, 'group_counter': 3496, 'group_order': 1296, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 56, 'size': 4}
id: 144191663
{'aut_label': '3A', 'centralizer': '4.a1', 'counter': 7, 'group_counter': 3496, 'group_order': 1296, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 311, 'size': 4}
id: 144191664
{'aut_label': '3A', 'centralizer': '4.a1', 'counter': 8, 'group_counter': 3496, 'group_order': 1296, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 88265520, 'size': 4}
id: 144191665
{'aut_label': '3E', 'centralizer': '16.a1', 'counter': 9, 'group_counter': 3496, 'group_order': 1296, 'label': '3E', 'order': 3, 'powers': [9, 1], 'representative': 7660856, 'size': 16}
id: 144191631
{'aut_label': '3E', 'centralizer': '16.a1', 'counter': 10, 'group_counter': 3496, 'group_order': 1296, 'label': '3F', 'order': 3, 'powers': [10, 1], 'representative': 7661111, 'size': 16}
id: 144191632
{'aut_label': '3E', 'centralizer': '16.a1', 'counter': 11, 'group_counter': 3496, 'group_order': 1296, 'label': '3G', 'order': 3, 'powers': [11, 1], 'representative': 88265576, 'size': 16}
id: 144191633
{'aut_label': '3E', 'centralizer': '16.a1', 'counter': 12, 'group_counter': 3496, 'group_order': 1296, 'label': '3H', 'order': 3, 'powers': [12, 1], 'representative': 88265831, 'size': 16}
id: 144191634
{'aut_label': '4A1', 'centralizer': '9.a1', 'counter': 13, 'group_counter': 3496, 'group_order': 1296, 'label': '4A1', 'order': 4, 'powers': [2, 14], 'representative': 133, 'size': 9}
id: 144191635
{'aut_label': '4A1', 'centralizer': '9.a1', 'counter': 14, 'group_counter': 3496, 'group_order': 1296, 'label': '4A-1', 'order': 4, 'powers': [2, 13], 'representative': 130, 'size': 9}
id: 144191636
{'aut_label': '4A1', 'centralizer': '9.a1', 'counter': 15, 'group_counter': 3496, 'group_order': 1296, 'label': '4B1', 'order': 4, 'powers': [3, 16], 'representative': 40647600, 'size': 9}
id: 144191637
{'aut_label': '4A1', 'centralizer': '9.a1', 'counter': 16, 'group_counter': 3496, 'group_order': 1296, 'label': '4B-1', 'order': 4, 'powers': [3, 15], 'representative': 40360320, 'size': 9}
id: 144191638
{'aut_label': '4C1', 'centralizer': '81.a1', 'counter': 17, 'group_counter': 3496, 'group_order': 1296, 'label': '4C1', 'order': 4, 'powers': [4, 18], 'representative': 55520870, 'size': 81}
id: 144191639
{'aut_label': '4C1', 'centralizer': '81.a1', 'counter': 18, 'group_counter': 3496, 'group_order': 1296, 'label': '4C-1', 'order': 4, 'powers': [4, 17], 'representative': 120562335, 'size': 81}
id: 144191640
{'aut_label': '4D1', 'centralizer': '81.a1', 'counter': 19, 'group_counter': 3496, 'group_order': 1296, 'label': '4D1', 'order': 4, 'powers': [3, 20], 'representative': 134628503, 'size': 81}
id: 144191642
{'aut_label': '4D1', 'centralizer': '81.a1', 'counter': 20, 'group_counter': 3496, 'group_order': 1296, 'label': '4D-1', 'order': 4, 'powers': [3, 19], 'representative': 127738823, 'size': 81}
id: 144191643
{'aut_label': '4D1', 'centralizer': '81.a1', 'counter': 21, 'group_counter': 3496, 'group_order': 1296, 'label': '4E1', 'order': 4, 'powers': [2, 22], 'representative': 12055910, 'size': 81}
id: 144191644
{'aut_label': '4D1', 'centralizer': '81.a1', 'counter': 22, 'group_counter': 3496, 'group_order': 1296, 'label': '4E-1', 'order': 4, 'powers': [2, 21], 'representative': 12056175, 'size': 81}
id: 144191645
{'aut_label': '4C1', 'centralizer': '81.a1', 'counter': 23, 'group_counter': 3496, 'group_order': 1296, 'label': '4F1', 'order': 4, 'powers': [4, 24], 'representative': 127451653, 'size': 81}
id: 144191646
{'aut_label': '4C1', 'centralizer': '81.a1', 'counter': 24, 'group_counter': 3496, 'group_order': 1296, 'label': '4F-1', 'order': 4, 'powers': [4, 23], 'representative': 167292850, 'size': 81}
id: 144191647
{'aut_label': '6A', 'centralizer': '36.b1', 'counter': 25, 'group_counter': 3496, 'group_order': 1296, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 11249303, 'size': 36}
id: 144191648
{'aut_label': '6A', 'centralizer': '36.b1', 'counter': 26, 'group_counter': 3496, 'group_order': 1296, 'label': '6B', 'order': 6, 'powers': [6, 3], 'representative': 1174398, 'size': 36}
id: 144191649
{'aut_label': '6A', 'centralizer': '36.b1', 'counter': 27, 'group_counter': 3496, 'group_order': 1296, 'label': '6C', 'order': 6, 'powers': [7, 3], 'representative': 1175017, 'size': 36}
id: 144191650
{'aut_label': '6A', 'centralizer': '36.b1', 'counter': 28, 'group_counter': 3496, 'group_order': 1296, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 214104263, 'size': 36}
id: 144191651
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 29, 'group_counter': 3496, 'group_order': 1296, 'label': '12A1', 'order': 12, 'powers': [25, 13], 'representative': 7660930, 'size': 36}
id: 144191653
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 30, 'group_counter': 3496, 'group_order': 1296, 'label': '12A-1', 'order': 12, 'powers': [25, 14], 'representative': 7660933, 'size': 36}
id: 144191654
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 31, 'group_counter': 3496, 'group_order': 1296, 'label': '12B1', 'order': 12, 'powers': [26, 15], 'representative': 40360376, 'size': 36}
id: 144191655
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 32, 'group_counter': 3496, 'group_order': 1296, 'label': '12B-1', 'order': 12, 'powers': [26, 16], 'representative': 40647656, 'size': 36}
id: 144191656
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 33, 'group_counter': 3496, 'group_order': 1296, 'label': '12C1', 'order': 12, 'powers': [27, 15], 'representative': 40360631, 'size': 36}
id: 144191657
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 34, 'group_counter': 3496, 'group_order': 1296, 'label': '12C-1', 'order': 12, 'powers': [27, 16], 'representative': 40647911, 'size': 36}
id: 144191658
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 35, 'group_counter': 3496, 'group_order': 1296, 'label': '12D1', 'order': 12, 'powers': [28, 13], 'representative': 88265650, 'size': 36}
id: 144191659
{'aut_label': '12A1', 'centralizer': '36.b1', 'counter': 36, 'group_counter': 3496, 'group_order': 1296, 'label': '12D-1', 'order': 12, 'powers': [28, 14], 'representative': 88265653, '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: 14008237
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 14008248
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 14008256
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1], 'schur_index': 1}
id: 14008257
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
id: 14008258
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008259
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008260
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, -2, 0, 0, -2, -2, 0, 0], 'schur_index': 1}
id: 14008261
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1h', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 2, 2, 0, 0, 2, 2, 0, 0], 'schur_index': 1}
id: 14008262
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 2, 0, 0, -2, -2, 0, 0, -2, -2], 'schur_index': 1}
id: 14008238
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, -2, 2, 0, 0, 2, 2, 0, 0, 2, 2], 'schur_index': 1}
id: 14008239
{'cdim': 4, 'counter': 11, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4a', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 0, 4, 0, -2, 4, 1, 4, -2, 1, -2, 1, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, -2, -2, 0, 0, 1, 1, 0, 0], 'schur_index': 1}
id: 14008240
{'cdim': 4, 'counter': 12, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4b', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 1, 4, -2, 4, 1, -2, 1, -2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 1, 1, 0, 0, -2, -2, 0, 0], 'schur_index': 1}
id: 14008241
{'cdim': 4, 'counter': 13, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4c', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, -2, 4, 1, 1, 1, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, -2, -2, 0, 0, 1, 1], 'schur_index': 1}
id: 14008242
{'cdim': 4, 'counter': 14, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4d', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 1, 4, -2, -2, -2, 1, 1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 1, 1, 0, 0, -2, -2], 'schur_index': 1}
id: 14008243
{'cdim': 4, 'counter': 15, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4e', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 0, 4, 0, -2, 4, 1, 4, -2, 1, -2, 1, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 2, 2, 0, 0, -1, -1, 0, 0], 'schur_index': 1}
id: 14008244
{'cdim': 4, 'counter': 16, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4f', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 0, 4, 0, 1, 4, -2, 4, 1, -2, 1, -2, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, -1, -1, 0, 0, 2, 2, 0, 0], 'schur_index': 1}
id: 14008245
{'cdim': 4, 'counter': 17, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4g', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, -2, 4, 1, 1, 1, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 2, 2, 0, 0, -1, -1], 'schur_index': 1}
id: 14008246
{'cdim': 4, 'counter': 18, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4h', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 1, 4, -2, -2, -2, 1, 1, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, -1, -1, 0, 0, 2, 2], 'schur_index': 1}
id: 14008247
{'cdim': 4, 'counter': 19, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4i', 'multiplicity': 2, 'nt': [24, 240], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, -4, 8, 2, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008249
{'cdim': 4, 'counter': 20, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4j', 'multiplicity': 2, 'nt': [24, 240], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 2, 8, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008250
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4k', 'multiplicity': 2, 'nt': [24, 240], 'qdim': 8, 'qvalues': [8, 0, -8, 0, -4, 8, 2, 8, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008251
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.4l', 'multiplicity': 2, 'nt': [24, 240], 'qdim': 8, 'qvalues': [8, 0, -8, 0, 2, 8, -4, 8, 2, -4, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008252
{'cdim': 16, 'counter': 23, 'faithful': True, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.16a', 'multiplicity': 1, 'nt': [24, 2929], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -8, -8, 4, 4, -2, 1, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008253
{'cdim': 16, 'counter': 24, 'faithful': True, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.16b', 'multiplicity': 1, 'nt': [24, 2929], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -8, 4, 4, -8, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008254
{'cdim': 16, 'counter': 25, 'faithful': True, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.16c', 'multiplicity': 1, 'nt': [24, 2929], 'qdim': 16, 'qvalues': [16, 0, 0, 0, 4, -8, -8, 4, 1, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 14008255
{'cdim': 16, 'counter': 26, 'faithful': True, 'group': '1296.3496', 'group_order': 1296, 'image': None, 'label': '1296.3496.16d', 'multiplicity': 1, 'nt': [24, 2929], 'qdim': 16, 'qvalues': [16, 0, 0, 0, 4, 4, -8, -8, -2, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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: 33247117
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1296, 'label': '1296.3496.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 33247128
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 648, 'label': '1296.3496.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 33247139
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 648, 'label': '1296.3496.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 33247147
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 648, 'label': '1296.3496.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 33247148
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1', 'kernel_order': 324, 'label': '1296.3496.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
id: 33247149
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1', 'kernel_order': 324, 'label': '1296.3496.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
id: 33247150
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1', 'kernel_order': 324, 'label': '1296.3496.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
id: 33247151
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1', 'kernel_order': 324, 'label': '1296.3496.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
id: 33247152
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 324, 'label': '1296.3496.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
id: 33247118
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1', 'kernel_order': 324, 'label': '1296.3496.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
id: 33247119
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 324, 'label': '1296.3496.1h1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]]]}
id: 33247120
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id: 33247121
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id: 33247122
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id: 33247123
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id: 33247124
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id: 33247125
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id: 33247126
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id: 33247127
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id: 33247129
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id: 33247130
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id: 33247131
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id: 33247132
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id: 33247133
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id: 33247134
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id: 33247135
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id: 33247136
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id: 33247137
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id: 33247138
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id: 33247140
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id: 33247141
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id: 33247142
{'center': '36.a1', 'center_index': 36, 'center_order': 36, 'counter': 32, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '144.132', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1', 'kernel_order': 9, 'label': '1296.3496.4l2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
id: 33247143
{'center': '1296.a1', 'center_index': 1296, 'center_order': 1, 'counter': 33, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3496', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.3496.16a', 'nt': [24, 2929], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33247144
{'center': '1296.a1', 'center_index': 1296, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3496', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.3496.16b', 'nt': [24, 2929], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33247145
{'center': '1296.a1', 'center_index': 1296, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3496', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.3496.16c', 'nt': [24, 2929], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 33247146
{'center': '1296.a1', 'center_index': 1296, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1296.3496', 'group_counter': 3496, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3496', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1', 'kernel_order': 1, 'label': '1296.3496.16d', 'nt': [24, 2929], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 115796136
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.3496.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
id: 115796147
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
id: 115796158
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
id: 115796169
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 115796180
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796191
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 115796198
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796199
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
id: 115796200
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 115796137
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796138
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.132', 'subgroup_hash': 132, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': False, 'sylow': 0}
id: 115796139
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 115796140
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796141
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
id: 115796142
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1296.3496.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'S', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
id: 115796143
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796144
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796145
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.45', 'subgroup_hash': 45, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796146
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 115796148
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 115796149
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796150
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796151
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 23, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3496.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 115796152
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 115796153
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 115796154
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 115796155
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796156
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796157
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796159
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 115796160
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 115796161
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 115796162
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 115796163
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 115796164
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 115796165
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 115796166
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796167
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796168
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796170
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796171
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.72.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g2', 'outer_equivalence': True, 'perfect': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 115796172
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.3496.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 2}
id: 115796173
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 115796174
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 115796175
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 115796176
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3496.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.132', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 132, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['C5'], '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: 115796177
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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: 115796178
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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: 115796179
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': 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: 115796181
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.144.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d2', 'outer_equivalence': True, 'perfect': False, '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': 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: 115796182
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 115796183
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 115796184
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': 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: 115796185
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': 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: 115796186
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': 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: 115796187
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': 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: 115796188
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': 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: 115796189
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': 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: 115796190
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3496.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': 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: 115796192
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': 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: 115796193
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 115796194
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 115796195
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 115796196
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3496.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 115796197
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3496', 'ambient_counter': 3496, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:C_4^2', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 1, 'counter': 65, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1296.3496.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1296.3496', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3496, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D2', 'C6'], '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: 115796136
{'ambient': '1296.3496', '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': '1296.a1', 'complements': ['1296.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6127, 3192, 6214, 3688], 'generators': [23, 1174320, 210551040, 133, 40647600, 78, 11249280, 676], 'label': '1296.3496.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796137
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '41472.m', 'aut_weyl_index': 1, 'centralizer': '1296.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.d1'], 'contains': ['16.a1', '24.c1', '24.d1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2994, 2319, 1833, 2861], 'generators': [1174343, 210551040, 11249280, 78, 676], 'label': '1296.3496.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.c1', '4.d1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796138
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['18.a1', '18.b1', '18.c1', '81.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6127, -1, 8428, -1], 'generators': [23, 1174320, 210551040, 133, 40647600, 11249280], 'label': '1296.3496.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796139
{'ambient': '1296.3496', 'aut_centralizer_order': 18, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.a1'], 'contains': ['24.b1', '36.a1', '108.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9841, -1, 6860, -1], 'generators': [1174320, 210551040, 40647600, 11249280, 78], 'label': '1296.3496.12.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
id: 115796140
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.b1', '36.e1', '108.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8481, -1, 5979, -1], 'generators': [40647623, 1174320, 210551040, 11249280, 78], 'label': '1296.3496.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
id: 115796141
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.a1'], 'contains': ['24.a1', '24.b1', '24.d1', '36.d1', '36.f1'], 'core': '72.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5308, -1, 4001, -1], 'generators': [23, 1174320, 11249280, 78, 676], 'label': '1296.3496.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '12.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
id: 115796142
{'ambient': '1296.3496', 'aut_centralizer_order': 81, 'aut_label': '16.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '512.60833', 'aut_weyl_index': 81, 'centralizer': '16.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1'], 'contains': ['48.a1', '48.b1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2994, 3392, 1342, 3865], 'generators': [210551040, 11249280, 78, 676], 'label': '1296.3496.16.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '1296.3496', 'quotient_action_image': '16.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '16.2'}
id: 115796143
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.b1', '36.c1', '36.f1', '54.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7408, -1, 7962, -1], 'generators': [23, 1174320, 40647600, 78, 676], 'label': '1296.3496.18.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796144
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.a1', '36.e1', '36.f1', '162.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9255, -1, 8873, -1], 'generators': [23, 1174320, 210551040, 40647600, 11249280], 'label': '1296.3496.18.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796145
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '9.a1'], 'contains': ['36.f1', '36.g1', '162.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4066, -1, 4907, -1], 'generators': [23, 1174320, 210551040, 40647733, 11249280], 'label': '1296.3496.18.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796146
{'ambient': '1296.3496', 'aut_centralizer_order': 18, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '96.120', 'aut_weyl_index': 432, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.c1'], 'contains': ['48.b1', '72.b1', '72.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4653, -1, 3120, -1], 'generators': [1174320, 11249280, 78, 676], 'label': '1296.3496.24.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
id: 115796147
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '1296.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '6.a1', '18.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6981, 4514, 6214, 4941], 'generators': [23, 1174320, 210551040, 40647600, 78, 11249280, 676], 'label': '1296.3496.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796148
{'ambient': '1296.3496', 'aut_centralizer_order': 18, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.c1'], 'contains': ['48.b1', '72.a1', '72.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6207, -1, 4337, -1], 'generators': [1174320, 210551040, 11249280, 78], 'label': '1296.3496.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
id: 115796149
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '432.741', 'aut_weyl_index': 96, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1'], 'contains': ['48.a1', '72.d1', '72.e1', '72.g1', '72.g2'], 'core': '1296.a1', 'coset_action_label': '24T2929', 'count': 96, 'diagramx': [1450, -1, 851, -1], 'generators': [210551118, 1174343, 11249280, 676], 'label': '1296.3496.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '24.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
id: 115796150
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '12.c1'], 'contains': ['48.b1', '72.d1', '72.e1', '72.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2716, -1, 1833, -1], 'generators': [1174343, 11249280, 78, 676], 'label': '1296.3496.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '24.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
id: 115796151
{'ambient': '1296.3496', 'aut_centralizer_order': 144, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '36.a1', 'complements': ['36.a1', '36.e1', '36.g1', '36.h1'], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '18.b1'], 'contains': ['72.a1', '324.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9673, 7107, 7451, 8534], 'generators': [1174320, 210551040, 40647600, 11249280], 'label': '1296.3496.36.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '1296.3496', 'quotient_action_image': '36.9', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796152
{'ambient': '1296.3496', 'aut_centralizer_order': 72, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '32.40', 'aut_weyl_index': 1296, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '18.a1'], 'contains': ['72.b1', '108.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7791, -1, 8358, -1], 'generators': [1174320, 40647600, 78, 676], 'label': '1296.3496.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 115796153
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 144, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '18.a1'], 'contains': ['72.b1', '108.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6911, -1, 6059, -1], 'generators': [40647623, 1174320, 78, 676], 'label': '1296.3496.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796154
{'ambient': '1296.3496', 'aut_centralizer_order': 4, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.c1'], 'contains': ['72.c1', '72.e1', '108.c1'], 'core': '1296.a1', 'coset_action_label': '36T2264', 'count': 144, 'diagramx': [5224, -1, 3716, -1], 'generators': [23, 1174320, 11249280, 78], 'label': '1296.3496.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '36.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 115796155
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '18.b1'], 'contains': ['72.a1', '324.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8878, -1, 6840, -1], 'generators': [40647623, 1174320, 210551040, 11249280], 'label': '1296.3496.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.e1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796156
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.a1', '18.b1', '18.c1'], 'contains': ['72.a1', '72.b1', '72.f1', '108.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6028, -1, 5168, -1], 'generators': [23, 1174320, 210551040, 11249280], 'label': '1296.3496.36.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.f1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796157
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '18.c1'], 'contains': ['72.f1', '324.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3396, -1, 2424, -1], 'generators': [1174343, 210551040, 40647733, 11249280], 'label': '1296.3496.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.g1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796158
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '41472.m', 'aut_weyl_index': 1, 'centralizer': '1296.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '18.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4280, 1858, 4342, 2423], 'generators': [23, 1174320, 210551040, 40647733, 78, 11249280, 676], 'label': '1296.3496.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796159
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1'], 'contains': ['72.g2', '324.d1'], 'core': '1296.a1', 'coset_action_label': '36T2315', 'count': 144, 'diagramx': [293, -1, 260, -1], 'generators': [203258836, 210551118, 1174343, 40647733], 'label': '1296.3496.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '36.h1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796160
{'ambient': '1296.3496', 'aut_centralizer_order': 81, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.11', 'aut_weyl_index': 2592, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '24.c1'], 'contains': ['144.b1', '144.c1', '144.d1', '144.d2'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1484, -1, 1197, -1], 'generators': [210551118, 11249280, 676], 'label': '1296.3496.48.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '48.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796161
{'ambient': '1296.3496', 'aut_centralizer_order': 162, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '32.40', 'aut_weyl_index': 1296, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.d1'], 'contains': ['144.a1', '144.b1', '144.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3685, -1, 2719, -1], 'generators': [11249280, 78, 676], 'label': '1296.3496.48.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '48.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
id: 115796162
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '18.a1'], 'contains': ['108.a1', '108.b1', '108.c1', '162.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7895, -1, 9104, -1], 'generators': [23, 1174320, 40647600, 78], 'label': '1296.3496.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796163
{'ambient': '1296.3496', 'aut_centralizer_order': 144, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['24.b1', '36.a1', '36.e1', '36.f1'], 'contains': ['144.a1', '216.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6649, 7107, 5168, 8534], 'generators': [1174320, 210551040, 11249280], 'label': '1296.3496.72.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1', '36.a1'], 'normal_contains': ['144.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796164
{'ambient': '1296.3496', 'aut_centralizer_order': 144, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '16.8', 'aut_weyl_index': 2592, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.a1', '36.b1', '36.c1', '36.f1'], 'contains': ['144.a1', '216.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5894, -1, 4597, -1], 'generators': [1174320, 78, 676], 'label': '1296.3496.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 115796165
{'ambient': '1296.3496', 'aut_centralizer_order': 36, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '36.d1'], 'contains': ['144.c1', '216.a1', '216.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [5030, -1, 3916, -1], 'generators': [1174320, 11249280, 78], 'label': '1296.3496.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1', 'old_label': '72.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 115796166
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 576, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1152, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.c1', '24.d1'], 'contains': ['144.b1', '216.c1', '216.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 576, 'diagramx': [1961, -1, 1632, -1], 'generators': [1174343, 11249956, 78], 'label': '1296.3496.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.d1', 'old_label': '72.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
id: 115796167
{'ambient': '1296.3496', 'aut_centralizer_order': 4, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '72.40', 'aut_weyl_index': 576, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.d1', '36.d1'], 'contains': ['144.c1', '216.c1', '216.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [3083, -1, 2283, -1], 'generators': [1174343, 11249280, 78], 'label': '1296.3496.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1', 'old_label': '72.e1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
id: 115796168
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.d1', '36.f1', '36.g1'], 'contains': ['144.a1', '216.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3843, -1, 3155, -1], 'generators': [1174343, 210551040, 11249280], 'label': '1296.3496.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.f1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796169
{'ambient': '1296.3496', 'aut_centralizer_order': 9, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '144.a1', 'complements': ['324.a1', '324.b1', '324.d1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.a1', '36.b1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7761, 4514, 6214, 4941], 'generators': [1174320, 210551040, 40647600, 11249280, 78, 676], 'label': '1296.3496.4.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '1296.3496', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '144.132'}
id: 115796170
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1'], 'contains': ['144.d1', '216.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [879, -1, 761, -1], 'generators': [210551118, 1174343, 11249956], 'label': '1296.3496.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.g1', 'old_label': '72.g1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
id: 115796171
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '72.g2', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '144.182', 'aut_weyl_index': 288, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '36.h1'], 'contains': ['144.d2', '216.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [233, -1, 305, -1], 'generators': [11249613, 210551118, 1174343], 'label': '1296.3496.72.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.h1', 'old_label': '72.g2', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g2', 'subgroup_fusion': None, 'weyl_group': '36.9'}
id: 115796172
{'ambient': '1296.3496', 'aut_centralizer_order': 64, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1'], 'contains': ['162.a1', '162.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4896, -1, 9840, -1], 'generators': [23, 1174320, 133, 40647600], 'label': '1296.3496.81.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796173
{'ambient': '1296.3496', 'aut_centralizer_order': 144, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '36.b1', '54.a1'], 'contains': ['216.a1', '324.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8461, -1, 7852, -1], 'generators': [1174320, 40647600, 78], 'label': '1296.3496.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '108.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796174
{'ambient': '1296.3496', 'aut_centralizer_order': 16, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '12.4', 'aut_weyl_index': 3456, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '36.c1', '54.a1'], 'contains': ['216.a1', '324.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7458, -1, 6670, -1], 'generators': [40647623, 1174320, 78], 'label': '1296.3496.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796175
{'ambient': '1296.3496', 'aut_centralizer_order': 32, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.d1', '36.f1', '54.a1'], 'contains': ['216.a1', '216.b1', '216.c1', '324.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [6137, -1, 5578, -1], 'generators': [23, 1174320, 11249280], 'label': '1296.3496.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796176
{'ambient': '1296.3496', 'aut_centralizer_order': 1296, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '16.8', 'aut_weyl_index': 2592, 'centralizer': '4.a1', 'complements': ['9.a1'], 'conjugacy_class_count': 2, 'contained_in': ['48.b1', '72.a1', '72.b1', '72.f1'], 'contains': ['432.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4707, 7107, 3866, 8534], 'generators': [210551040, 11249280], 'label': '1296.3496.144.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['16.a1', '72.a1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '1296.3496', 'quotient_action_image': '4.1', 'quotient_action_kernel': '36.8', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 115796177
{'ambient': '1296.3496', 'aut_centralizer_order': 162, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '4.2', 'aut_weyl_index': 10368, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.a1', '48.b1', '72.d1'], 'contains': ['432.a1', '432.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [2035, -1, 2018, -1], 'generators': [11249956, 78], 'label': '1296.3496.144.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '144.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796178
{'ambient': '1296.3496', 'aut_centralizer_order': 324, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.a1', '48.b1', '72.c1', '72.e1'], 'contains': ['432.a1', '432.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3371, -1, 2574, -1], 'generators': [11249280, 78], 'label': '1296.3496.144.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '144.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 115796179
{'ambient': '1296.3496', 'aut_centralizer_order': 81, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '16.8', 'aut_weyl_index': 2592, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.a1', '72.g1'], 'contains': ['432.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [755, -1, 1222, -1], 'generators': [210551118, 11249956], 'label': '1296.3496.144.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '144.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796180
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '1296.a1', 'complements': ['324.a1', '324.b1', '324.d1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.b1', '36.c1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6619, 6832, 5283, 7139], 'generators': [40647623, 1174320, 210551040, 11249280, 78, 676], 'label': '1296.3496.4.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '1296.3496', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796181
{'ambient': '1296.3496', 'aut_centralizer_order': 162, 'aut_label': '144.d2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '16.8', 'aut_weyl_index': 2592, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.a1', '72.g2'], 'contains': ['432.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [159, -1, 811, -1], 'generators': [11249613, 210551118], 'label': '1296.3496.144.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '144.d2', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d2', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 115796182
{'ambient': '1296.3496', 'aut_centralizer_order': 128, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '54.a1', '81.a1'], 'contains': ['324.a1', '324.b1', '324.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [8078, -1, 8758, -1], 'generators': [23, 1174320, 40647600], 'label': '1296.3496.162.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796183
{'ambient': '1296.3496', 'aut_centralizer_order': 64, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 5184, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '81.a1'], 'contains': ['324.c1', '324.d1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4275, -1, 6099, -1], 'generators': [23, 1174320, 40647733], 'label': '1296.3496.162.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796184
{'ambient': '1296.3496', 'aut_centralizer_order': 288, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.b1', '72.c1', '108.a1', '108.b1', '108.c1'], 'contains': ['432.a1', '648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5865, -1, 5553, -1], 'generators': [1174320, 78], 'label': '1296.3496.216.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1', 'old_label': '216.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796185
{'ambient': '1296.3496', 'aut_centralizer_order': 288, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.c1', '108.c1'], 'contains': ['432.a1', '648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6569, -1, 5168, -1], 'generators': [1174320, 11249280], 'label': '1296.3496.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796186
{'ambient': '1296.3496', 'aut_centralizer_order': 32, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.e1', '72.f1', '108.c1'], 'contains': ['432.a1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [3371, -1, 3120, -1], 'generators': [1174343, 11249280], 'label': '1296.3496.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '216.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796187
{'ambient': '1296.3496', 'aut_centralizer_order': 8, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '6.1', 'aut_weyl_index': 6912, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.e1', '72.g1', '72.g2'], 'contains': ['432.b1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [1465, -1, 1632, -1], 'generators': [11249358, 1174343], 'label': '1296.3496.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.d1', 'old_label': '216.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 115796188
{'ambient': '1296.3496', 'aut_centralizer_order': 1152, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '108.a1', '162.a1'], 'contains': ['648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8465, -1, 7691, -1], 'generators': [1174320, 40647600], 'label': '1296.3496.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796189
{'ambient': '1296.3496', 'aut_centralizer_order': 128, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.e1', '108.b1', '162.a1'], 'contains': ['648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7741, -1, 6830, -1], 'generators': [40647623, 1174320], 'label': '1296.3496.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796190
{'ambient': '1296.3496', 'aut_centralizer_order': 256, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '162.a1', '162.b1'], 'contains': ['648.a1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6082, -1, 5939, -1], 'generators': [23, 1174320], 'label': '1296.3496.324.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796191
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '41472.m', 'aut_weyl_index': 1, 'centralizer': '1296.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '12.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4493, 2319, 4001, 2861], 'generators': [23, 1174320, 210551040, 11249280, 78, 676], 'label': '1296.3496.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796192
{'ambient': '1296.3496', 'aut_centralizer_order': 128, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.g1', '36.h1', '162.b1'], 'contains': ['648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [2438, -1, 3480, -1], 'generators': [1174343, 40647733], 'label': '1296.3496.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.d1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796193
{'ambient': '1296.3496', 'aut_centralizer_order': 2592, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.a1', '144.b1', '144.c1', '216.a1', '216.b1', '216.c1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3654, -1, 3661, -1], 'generators': [11249280], 'label': '1296.3496.432.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '432.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796194
{'ambient': '1296.3496', 'aut_centralizer_order': 648, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 20736, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.b1', '144.c1', '144.d1', '144.d2', '216.d1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1470, -1, 1828, -1], 'generators': [11249358], 'label': '1296.3496.432.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '432.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 115796195
{'ambient': '1296.3496', 'aut_centralizer_order': 2304, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.a1', '216.b1', '324.a1', '324.b1', '324.c1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6475, -1, 5744, -1], 'generators': [1174320], 'label': '1296.3496.648.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796196
{'ambient': '1296.3496', 'aut_centralizer_order': 512, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 41472, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.d1', '324.c1', '324.d1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3277, -1, 3300, -1], 'generators': [1174343], 'label': '1296.3496.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '648.b1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796197
{'ambient': '1296.3496', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1', '432.b1', '648.a1', '648.b1'], 'contains': [], 'core': '1296.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3466, 9663, 3480, 9681], 'generators': [], 'label': '1296.3496.1296.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1', 'normal_contained_in': ['144.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1296.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 115796198
{'ambient': '1296.3496', 'aut_centralizer_order': 1, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '20736.x', 'aut_weyl_index': 2, 'centralizer': '1296.a1', 'complements': ['324.a1', '324.b1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1'], 'contains': ['8.b1', '36.g1', '36.h1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3237, 337, 2103, 981], 'generators': [210551040, 1174343, 40647733, 78, 11249280, 676], 'label': '1296.3496.4.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '1296.3496', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '1296.3496'}
id: 115796199
{'ambient': '1296.3496', 'aut_centralizer_order': 2, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 48, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '18.b1', '54.a1'], 'core': '36.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8406, -1, 7251, -1], 'generators': [23, 1174320, 210551040, 40647600, 11249280, 78], 'label': '1296.3496.6.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '6.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
id: 115796200
{'ambient': '1296.3496', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 18, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '24.a1', '24.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5169, 4489, 3120, 4905], 'generators': [1174320, 210551040, 11249280, 78, 676], 'label': '1296.3496.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1296.3496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '144.132'}

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.