LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-10-31T15:44:52.268718

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
abelian_quotient	text
all_subgroups_known	boolean
almost_simple	boolean
aut_abelian	boolean
aut_cyclic	boolean
aut_derived_length	smallint
aut_exponent	numeric
aut_gen_orders	numeric[]
aut_gens	numeric[]
aut_group	text
aut_hash	bigint
aut_nilpotency_class	smallint
aut_nilpotent	boolean
aut_order	numeric
aut_permdeg	integer
aut_perms	numeric[]
aut_phi_ratio	double precision
aut_solvable	boolean
aut_stats	numeric[]
aut_supersolvable	boolean
aut_tex	text
autcent_abelian	boolean
autcent_cyclic	boolean
autcent_exponent	numeric
autcent_group	text
autcent_hash	bigint
autcent_nilpotent	boolean
autcent_order	numeric
autcent_solvable	boolean
autcent_split	boolean
autcent_supersolvable	boolean
autcent_tex	text
autcentquo_abelian	boolean
autcentquo_cyclic	boolean
autcentquo_exponent	numeric
autcentquo_group	text
autcentquo_hash	bigint
autcentquo_nilpotent	boolean
autcentquo_order	numeric
autcentquo_solvable	boolean
autcentquo_supersolvable	boolean
autcentquo_tex	text
cc_stats	numeric[]
center_label	text
center_order	numeric
central_product	boolean
central_quotient	text
commutator_count	integer
commutator_label	text
complements_known	boolean
complete	boolean
complex_characters_known	boolean
composition_factors	text[]
composition_length	smallint
conjugacy_classes_known	boolean
counter	integer
cyclic	boolean
derived_length	smallint
dihedral	boolean
direct_factorization	jsonb
direct_product	boolean
div_stats	numeric[]
element_repr_type	text
elementary	integer
eulerian_function	numeric
exponent	numeric
exponents_of_order	smallint[]
factors_of_aut_order	integer[]
factors_of_order	smallint[]
faithful_reps	numeric[]
familial	boolean
frattini_label	text
frattini_quotient	text
hash	bigint
hyperelementary	integer
inner_abelian	boolean
inner_cyclic	boolean
inner_exponent	numeric
inner_gen_orders	numeric[]
inner_gens	numeric[]
inner_hash	bigint
inner_nilpotent	boolean
inner_order	numeric
inner_split	boolean
inner_tex	text
inner_used	smallint[]
irrC_degree	integer
irrQ_degree	integer
irrQ_dim	integer
irrR_degree	integer
irrep_stats	numeric[]
label	text
linC_count	numeric
linC_degree	integer
linFp_degree	integer
linFq_degree	integer
linQ_degree	integer
linQ_degree_count	numeric
linQ_dim	integer
linQ_dim_count	numeric
linR_count	numeric
linR_degree	integer
maximal_subgroups_known	boolean
metabelian	boolean
metacyclic	boolean
monomial	boolean
name	text
ngens	smallint
nilpotency_class	smallint
nilpotent	boolean
normal_counts	integer[]
normal_index_bound	numeric
normal_order_bound	numeric
normal_subgroups_known	boolean
number_autjugacy_classes	integer
number_characteristic_subgroups	integer
number_conjugacy_classes	integer
number_divisions	integer
number_normal_subgroups	integer
number_subgroup_autclasses	integer
number_subgroup_classes	integer
number_subgroups	numeric
old_label	text
order	numeric
order_factorization_type	integer
order_stats	numeric[]
outer_abelian	boolean
outer_cyclic	boolean
outer_equivalence	boolean
outer_exponent	numeric
outer_gen_orders	numeric[]
outer_gen_pows	numeric[]
outer_gens	numeric[]
outer_group	text
outer_hash	bigint
outer_nilpotent	boolean
outer_order	numeric
outer_permdeg	integer
outer_perms	numeric[]
outer_solvable	boolean
outer_supersolvable	boolean
outer_tex	text
pc_rank	smallint
perfect	boolean
permutation_degree	integer
pgroup	smallint
primary_abelian_invariants	integer[]
quasisimple	boolean
rank	smallint
rational	boolean
rational_characters_known	boolean
ratrep_stats	numeric[]
representations	jsonb
schur_multiplier	integer[]
semidirect_product	boolean
simple	boolean
smith_abelian_invariants	integer[]
solvability_type	smallint
solvable	boolean
subgroup_inclusions_known	boolean
subgroup_index_bound	numeric
supersolvable	boolean
sylow_subgroups_known	boolean
tex_name	text
transitive_degree	integer
wreath_data	text[]
wreath_product	boolean

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [2, 2, 2, 2, 3, 2, 2, 3, 3], 'aut_gens': [[40345, 45507, 144, 148, 367920, 806400], [40345, 80884, 144, 148, 806400, 367920], [40345, 45360, 4, 148, 367920, 806400], [40345, 45363, 240, 4, 367920, 806400], [40345, 725907, 144, 148, 367920, 806400], [40586, 45507, 144, 148, 367920, 806400], [40345, 45600, 144, 243, 367920, 806400], [1134025, 1129107, 144, 148, 367920, 806400], [40441, 45507, 144, 148, 367920, 806400], [85802, 45507, 144, 148, 1174320, 367920]], 'aut_group': '93312.jr', 'aut_hash': 7211166090879777373, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 93312, 'aut_permdeg': 31, 'aut_perms': [65758909511913611102344579805, 97710843914081409953165516818560, 29683090601387201498813671237320, 16, 1980733759795531023896470538581920, 1579853970287315571264708862080, 7, 292725590573433126986456181557880, 841865860084755513106525351172523], 'aut_phi_ratio': 1296.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 2, 4, 1], [3, 8, 9, 1], [4, 54, 1, 1], [6, 6, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(S_4\\times \\GL(2,3))', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '93312.jr', 'autcentquo_hash': 7211166090879777373, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(S_4\\times \\GL(2,3))', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 54, 1], [3, 2, 4], [3, 8, 9], [4, 54, 1], [6, 6, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '216.165', 'commutator_count': 1, 'commutator_label': '108.41', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 165, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 2, 1, 4], [3, 8, 1, 9], [4, 54, 1, 1], [6, 6, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 12285, 'exponent': 12, 'exponents_of_order': [3, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '216.165', 'hash': 165, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 3, 3, 2, 2], 'inner_gens': [[40345, 80884, 240, 243, 806400, 367920], [5309, 45507, 144, 148, 806400, 1174320], [40585, 45507, 144, 148, 367920, 806400], [40586, 45507, 144, 148, 367920, 806400], [1134025, 1129107, 144, 148, 367920, 806400], [1134025, 448707, 144, 148, 367920, 806400]], 'inner_hash': 165, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [2, 13], [3, 2], [6, 4]], 'label': '216.165', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:S4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 21, 'number_divisions': 21, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 33, 'number_subgroup_classes': 130, 'number_subgroups': 1060, 'old_label': None, 'order': 216, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 57], [3, 80], [4, 54], [6, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 3, 3], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[40345, 45507, 240, 4, 367920, 806400], [40345, 45507, 3, 148, 367920, 806400], [40345, 45603, 144, 148, 367920, 806400]], 'outer_group': '432.734', 'outer_hash': 734, 'outer_nilpotent': False, 'outer_order': 432, 'outer_permdeg': 9, 'outer_perms': [10829, 35711, 52564], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^2:\\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 13], [3, 2], [6, 4]], 'representations': {'PC': {'code': 8909543178979295278179679509, 'gens': [1, 2, 3, 5], 'pres': [6, 2, 3, 2, 3, 2, 3, 49, 542, 1034, 50, 579, 5944, 2440, 88, 5189]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 909811, 1081075, 502525, 1197949, 70633]}, 'Perm': {'d': 10, 'gens': [40345, 45507, 144, 148, 367920, 806400]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:S_4', 'transitive_degree': 36, '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: 98185775
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 165, 'group_order': 216, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 98185786
{'aut_label': '2A', 'centralizer': '3.b1', 'counter': 2, 'group_counter': 165, 'group_order': 216, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 367920, 'size': 3}
id: 98185789
{'aut_label': '2B', 'centralizer': '54.b1', 'counter': 3, 'group_counter': 165, 'group_order': 216, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1134266, 'size': 54}
id: 98185790
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 4, 'group_counter': 165, 'group_order': 216, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 4, 'size': 2}
id: 98185791
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 165, 'group_order': 216, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 240, 'size': 2}
id: 98185792
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 165, 'group_order': 216, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 244, 'size': 2}
id: 98185793
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 165, 'group_order': 216, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 243, 'size': 2}
id: 98185794
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 8, 'group_counter': 165, 'group_order': 216, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 45360, 'size': 8}
id: 98185795
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 9, 'group_counter': 165, 'group_order': 216, 'label': '3F', 'order': 3, 'powers': [9, 1], 'representative': 45363, 'size': 8}
id: 98185776
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 10, 'group_counter': 165, 'group_order': 216, 'label': '3G', 'order': 3, 'powers': [10, 1], 'representative': 45364, 'size': 8}
id: 98185777
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 11, 'group_counter': 165, 'group_order': 216, 'label': '3H', 'order': 3, 'powers': [11, 1], 'representative': 45504, 'size': 8}
id: 98185778
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 12, 'group_counter': 165, 'group_order': 216, 'label': '3I', 'order': 3, 'powers': [12, 1], 'representative': 45507, 'size': 8}
id: 98185779
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 13, 'group_counter': 165, 'group_order': 216, 'label': '3J', 'order': 3, 'powers': [13, 1], 'representative': 45508, 'size': 8}
id: 98185780
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 14, 'group_counter': 165, 'group_order': 216, 'label': '3K', 'order': 3, 'powers': [14, 1], 'representative': 45600, 'size': 8}
id: 98185781
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 15, 'group_counter': 165, 'group_order': 216, 'label': '3L', 'order': 3, 'powers': [15, 1], 'representative': 45603, 'size': 8}
id: 98185782
{'aut_label': '3E', 'centralizer': '8.a1', 'counter': 16, 'group_counter': 165, 'group_order': 216, 'label': '3M', 'order': 3, 'powers': [16, 1], 'representative': 45604, 'size': 8}
id: 98185783
{'aut_label': '4A', 'centralizer': '54.c1', 'counter': 17, 'group_counter': 165, 'group_order': 216, 'label': '4A', 'order': 4, 'powers': [2, 17], 'representative': 730829, 'size': 54}
id: 98185784
{'aut_label': '6A', 'centralizer': '6.b1', 'counter': 18, 'group_counter': 165, 'group_order': 216, 'label': '6A', 'order': 6, 'powers': [4, 2], 'representative': 367923, 'size': 6}
id: 98185785
{'aut_label': '6A', 'centralizer': '6.b1', 'counter': 19, 'group_counter': 165, 'group_order': 216, 'label': '6B', 'order': 6, 'powers': [5, 2], 'representative': 368064, 'size': 6}
id: 98185787
{'aut_label': '6A', 'centralizer': '6.b1', 'counter': 20, 'group_counter': 165, 'group_order': 216, 'label': '6C', 'order': 6, 'powers': [6, 2], 'representative': 368067, 'size': 6}
id: 98185788
{'aut_label': '6A', 'centralizer': '6.b1', 'counter': 21, 'group_counter': 165, 'group_order': 216, 'label': '6D', 'order': 6, 'powers': [7, 2], 'representative': 368068, 'size': 6}

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: 266360
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.1a', '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], 'schur_index': 1}
id: 266371
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.1b', '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], 'schur_index': 1}
id: 266374
{'cdim': 2, 'counter': 3, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 0, -1, -1, -1, 2], 'schur_index': 1}
id: 266375
{'cdim': 2, 'counter': 4, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, -1, -1, -1, 0, -1, -1, -1, 2], 'schur_index': 1}
id: 266376
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 0, -1, -1, -1, 2], 'schur_index': 1}
id: 266377
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 0, -1, -1, 2, -1], 'schur_index': 1}
id: 266378
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2e', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, 0, -1, -1, 2, -1], 'schur_index': 1}
id: 266379
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2f', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, -1, -1, 2, -1], 'schur_index': 1}
id: 266380
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2g', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 0, -1, 2, -1, -1], 'schur_index': 1}
id: 266361
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2h', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, 0, -1, 2, -1, -1], 'schur_index': 1}
id: 266362
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2i', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 0, -1, 2, -1, -1], 'schur_index': 1}
id: 266363
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2j', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 0, 2, -1, -1, -1], 'schur_index': 1}
id: 266364
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2k', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 0, 2, -1, -1, -1], 'schur_index': 1}
id: 266365
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2l', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 0, 2, -1, -1, -1], 'schur_index': 1}
id: 266366
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.2m', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 2, 2, 2, 2], 'schur_index': 1}
id: 266367
{'cdim': 3, 'counter': 16, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 1, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 266368
{'cdim': 3, 'counter': 17, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, -1, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 266369
{'cdim': 6, 'counter': 18, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.6a', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2], 'schur_index': 1}
id: 266370
{'cdim': 6, 'counter': 19, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.6b', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, 1], 'schur_index': 1}
id: 266372
{'cdim': 6, 'counter': 20, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.6c', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1], 'schur_index': 1}
id: 266373
{'cdim': 6, 'counter': 21, 'faithful': False, 'group': '216.165', 'group_order': 216, 'image': None, 'label': '216.165.6d', 'multiplicity': 1, 'nt': [12, 44], 'qdim': 6, 'qvalues': [6, -2, 0, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1], '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: 378489
{'center': '1.a1', 'center_index': 1, 'center_order': 216, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 216, 'label': '216.165.1a', '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]]]}
id: 378500
{'center': '1.a1', 'center_index': 1, 'center_order': 216, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 108, 'label': '216.165.1b', '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]]]}
id: 378503
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 3, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
id: 378504
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 4, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
id: 378505
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
id: 378506
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
id: 378507
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2e', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
id: 378508
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2f', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
id: 378509
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2g', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378490
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2h', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378491
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2i', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378492
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2j', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378493
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2k', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378494
{'center': '6.a1', 'center_index': 6, 'center_order': 36, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 36, 'label': '216.165.2l', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378495
{'center': '6.b1', 'center_index': 6, 'center_order': 36, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 36, 'label': '216.165.2m', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]]]}
id: 378496
{'center': '24.a1', 'center_index': 24, 'center_order': 9, 'counter': 16, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 9, 'label': '216.165.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378497
{'center': '24.a1', 'center_index': 24, 'center_order': 9, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1', 'kernel_order': 9, 'label': '216.165.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 378498
{'center': '72.a1', 'center_index': 72, 'center_order': 3, 'counter': 18, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '72.43', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 3, 'label': '216.165.6a', 'nt': [12, 44], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
id: 378499
{'center': '72.a1', 'center_index': 72, 'center_order': 3, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '72.43', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 3, 'label': '216.165.6b', 'nt': [12, 44], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
id: 378501
{'center': '72.a1', 'center_index': 72, 'center_order': 3, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '72.43', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 3, 'label': '216.165.6c', 'nt': [12, 44], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
id: 378502
{'center': '72.a1', 'center_index': 72, 'center_order': 3, 'counter': 21, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '216.165', 'group_counter': 165, 'group_order': 216, 'image': None, 'image_isoclass': '72.43', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 3, 'label': '216.165.6d', 'nt': [12, 44], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 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: 20960886
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 216, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '216.165.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.165', 'subgroup_hash': 165, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
id: 20960897
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 108, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.2.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': ['D', 'L1', 'D1', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20960908
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.43', 'subgroup_hash': 43, 'subgroup_order': 72, 'subgroup_tex': 'C_3:S_4', 'supersolvable': False, 'sylow': 0}
id: 20960913
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
id: 20960914
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.4.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
id: 20960915
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
id: 20960916
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
id: 20960917
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
id: 20960918
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 20960887
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '216.165.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
id: 20960888
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 20960889
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
id: 20960890
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 20960891
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.12.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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 20960892
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.12.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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 20960893
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 20960894
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
id: 20960895
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 20960896
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 20960898
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 9, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], '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: 20960899
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 20960900
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '216.165.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
id: 20960901
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '216.165.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 20960902
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20960903
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 20960904
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '216.165.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:S_3', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20960905
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '216.165.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 20960906
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '216.165.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 20960907
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '216.165.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 20960909
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '216.165.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 20960910
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '216.165.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 20960911
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '216.165.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, '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': 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: 20960912
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '216.165', 'ambient_counter': 165, 'ambient_order': 216, 'ambient_tex': 'C_3^2:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 1, 'counter': 33, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '216.165.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '216.165', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 165, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

Column	Type
ambient	text
aut_centralizer_order	numeric
aut_label	text
aut_quo_index	numeric
aut_stab_index	numeric
aut_weyl_group	text
aut_weyl_index	numeric
centralizer	text
complements	text[]
conjugacy_class_count	numeric
contained_in	text[]
contains	text[]
core	text
coset_action_label	text
count	numeric
diagramx	smallint[]
generators	numeric[]
label	text
mobius_quo	bigint
mobius_sub	bigint
normal_closure	text
normal_contained_in	text[]
normal_contains	text[]
normalizer	text
old_label	text
projective_image	text
quotient_action_image	text
quotient_action_kernel	text
quotient_action_kernel_order	numeric
quotient_fusion	jsonb
short_label	text
subgroup_fusion	integer[]
weyl_group	text

gps_subgroup_data • Show schema

id: 20960886
{'ambient': '216.165', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.a1', 'complements': ['216.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '3.a1', '3.b1', '4.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3723, 4471, 6117, 4055], 'generators': [1174320, 80884, 367920, 40345, 240, 243], 'label': '216.165.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '216.165', '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': '216.165'}
id: 20960887
{'ambient': '216.165', 'aut_centralizer_order': 27, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '4.a1'], 'contains': ['24.a1', '24.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5602, -1, 9646, -1], 'generators': [80884, 240, 243], 'label': '216.165.8.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.a1', 'projective_image': '216.165', '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': '2.1'}
id: 20960888
{'ambient': '216.165', 'aut_centralizer_order': 108, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 3888, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.c1', '18.d1', '27.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4547, -1, 2312, -1], 'generators': [1174320, 367920, 40345, 240], 'label': '216.165.9.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '216.165', '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': '12.4'}
id: 20960889
{'ambient': '216.165', 'aut_centralizer_order': 48, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '24.12', 'aut_weyl_index': 3888, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['3.a1'], 'contains': ['18.b1', '27.a1', '36.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 81, 'diagramx': [309, -1, 1305, -1], 'generators': [1174320, 80788, 367920, 40345], 'label': '216.165.9.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20960890
{'ambient': '216.165', 'aut_centralizer_order': 648, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '6.c1', '6.d1'], 'contains': ['24.a1', '36.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9691, -1, 7422, -1], 'generators': [367920, 240, 243], 'label': '216.165.12.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '12.a1', 'projective_image': '216.165', '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': '2.1'}
id: 20960891
{'ambient': '216.165', 'aut_centralizer_order': 6, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '108.17', 'aut_weyl_index': 864, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['3.a1', '4.a1'], 'contains': ['24.b1', '36.b1', '36.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2165, -1, 5741, -1], 'generators': [80884, 40345, 240], 'label': '216.165.12.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '12.b1', 'projective_image': '216.165', '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': '18.4'}
id: 20960892
{'ambient': '216.165', 'aut_centralizer_order': 36, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.734', 'aut_weyl_index': 216, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.c1'], 'contains': ['24.a1', '36.b1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7514, -1, 8683, -1], 'generators': [40345, 240, 243], 'label': '216.165.12.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.c1', 'projective_image': '216.165', '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': '18.4'}
id: 20960893
{'ambient': '216.165', 'aut_centralizer_order': 1944, 'aut_label': '18.a1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '6.b1', 'complements': ['12.b1'], 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '6.b1', '9.a1'], 'contains': ['36.a1', '54.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4903, 2313, 3683, 1799], 'generators': [1174320, 367920, 240], 'label': '216.165.18.a1', 'mobius_quo': 1, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1', '6.b1'], 'normal_contains': ['54.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '216.165', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20960894
{'ambient': '216.165', 'aut_centralizer_order': 432, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '24.12', 'aut_weyl_index': 3888, 'centralizer': '24.a1', 'complements': ['12.b1', '12.c1'], 'conjugacy_class_count': 9, 'contained_in': ['6.a1', '9.b1'], 'contains': ['54.a1', '72.b1'], 'core': '18.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [653, 6392, 1095, 4969], 'generators': [1174320, 80788, 367920], 'label': '216.165.18.b1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['54.a1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '216.165', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20960895
{'ambient': '216.165', 'aut_centralizer_order': 216, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '9.a1'], 'contains': ['36.a1', '36.b1', '54.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [6095, -1, 4834, -1], 'generators': [1174320, 40345, 240], 'label': '216.165.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '216.165', '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': '12.4'}
id: 20960896
{'ambient': '216.165', 'aut_centralizer_order': 216, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.a1', '54.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7514, -1, 2423, -1], 'generators': [1174320, 443545, 240], 'label': '216.165.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20960897
{'ambient': '216.165', 'aut_centralizer_order': 9, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '10368.qn', 'aut_weyl_index': 9, 'centralizer': '24.a1', 'complements': ['108.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '8.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4937, 4471, 6869, 4055], 'generators': [1174320, 80884, 367920, 240, 243], 'label': '216.165.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.a1', '6.b1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '216.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20960898
{'ambient': '216.165', 'aut_centralizer_order': 1944, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1944, 'centralizer': '2.a1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.c1'], 'contains': ['72.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8787, 7883, 8053, 9024], 'generators': [240, 243], 'label': '216.165.24.a1', 'mobius_quo': 3, 'mobius_sub': -12, 'normal_closure': '24.a1', 'normal_contained_in': ['6.b1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '216.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20960899
{'ambient': '216.165', 'aut_centralizer_order': 162, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 7776, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.a1', '8.a1', '12.b1'], 'contains': ['72.a1', '72.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3036, -1, 6460, -1], 'generators': [80884, 240], 'label': '216.165.24.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.b1', 'projective_image': '216.165', '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': '2.1'}
id: 20960900
{'ambient': '216.165', 'aut_centralizer_order': 864, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 23328, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.a1', '54.b1', '54.c1'], 'core': '54.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3093, -1, 299, -1], 'generators': [1174320, 367920, 40345], 'label': '216.165.27.a1', 'mobius_quo': None, 'mobius_sub': -27, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 20960901
{'ambient': '216.165', 'aut_centralizer_order': 3888, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '18.a1', '18.c1', '18.d1'], 'contains': ['72.a1', '108.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7423, -1, 4812, -1], 'generators': [367920, 240], 'label': '216.165.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.a1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20960902
{'ambient': '216.165', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1', '18.c1'], 'contains': ['72.a1', '108.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5727, -1, 5608, -1], 'generators': [40345, 240], 'label': '216.165.36.b1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.b1', 'projective_image': '216.165', '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': '6.1'}
id: 20960903
{'ambient': '216.165', 'aut_centralizer_order': 48, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.b1', '12.b1'], 'contains': ['72.b1', '108.b1'], 'core': '216.a1', 'coset_action_label': '36T303', 'count': 324, 'diagramx': [802, -1, 4015, -1], 'generators': [80788, 40345], 'label': '216.165.36.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1', 'old_label': '36.c1', 'projective_image': '216.165', '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': '6.1'}
id: 20960904
{'ambient': '216.165', 'aut_centralizer_order': 15552, 'aut_label': '54.a1', 'aut_quo_index': 13, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 15552, 'centralizer': '6.b1', 'complements': ['4.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '27.a1'], 'contains': ['108.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3036, 4784, 1836, 3384], 'generators': [1174320, 367920], 'label': '216.165.54.a1', 'mobius_quo': -1, 'mobius_sub': 729, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1', '18.b1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '216.165', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20960905
{'ambient': '216.165', 'aut_centralizer_order': 1728, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1', '27.a1'], 'contains': ['108.a1', '108.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3976, -1, 2743, -1], 'generators': [1174320, 40345], 'label': '216.165.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20960906
{'ambient': '216.165', 'aut_centralizer_order': 1728, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '54.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '27.a1'], 'contains': ['108.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5293, -1, 984, -1], 'generators': [1174320, 443545], 'label': '216.165.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20960907
{'ambient': '216.165', 'aut_centralizer_order': 11664, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '2.a1', 'complements': ['3.a1'], 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.b1', '36.a1', '36.b1'], 'contains': ['216.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6988, 7883, 5608, 9024], 'generators': [240], 'label': '216.165.72.a1', 'mobius_quo': -1, 'mobius_sub': 108, 'normal_closure': '72.a1', 'normal_contained_in': ['18.a1', '24.a1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '216.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20960908
{'ambient': '216.165', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '432.523', 'aut_weyl_index': 216, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['1.a1'], 'contains': ['6.a1', '9.a1', '9.b1', '12.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2234, -1, 3573, -1], 'generators': [1174320, 80884, 367920, 40345, 240], 'label': '216.165.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
id: 20960909
{'ambient': '216.165', 'aut_centralizer_order': 1296, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 46656, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['18.b1', '24.b1', '36.c1'], 'contains': ['216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1260, -1, 4579, -1], 'generators': [80788], 'label': '216.165.72.b1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '72.b1', 'projective_image': '216.165', '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': '2.1'}
id: 20960910
{'ambient': '216.165', 'aut_centralizer_order': 31104, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 93312, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '54.a1', '54.b1', '54.c1'], 'contains': ['216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4971, -1, 2743, -1], 'generators': [367920], 'label': '216.165.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.a1', 'projective_image': '216.165', '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': '1.1'}
id: 20960911
{'ambient': '216.165', 'aut_centralizer_order': 1728, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 93312, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.c1', '54.b1'], 'contains': ['216.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4124, -1, 3783, -1], 'generators': [40345], 'label': '216.165.108.b1', 'mobius_quo': None, 'mobius_sub': 54, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.b1', 'projective_image': '216.165', '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': '1.1'}
id: 20960912
{'ambient': '216.165', 'aut_centralizer_order': None, 'aut_label': '216.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': ['72.a1', '72.b1', '108.a1', '108.b1'], 'contains': [], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4559, 7883, 4181, 9024], 'generators': [], 'label': '216.165.216.a1', 'mobius_quo': 1, 'mobius_sub': -2916, 'normal_closure': '216.a1', 'normal_contained_in': ['54.a1', '72.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '216.165', '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': '1.1'}
id: 20960913
{'ambient': '216.165', 'aut_centralizer_order': 18, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1728.47845', 'aut_weyl_index': 54, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.c1', '6.d1', '9.a1'], 'core': '6.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6851, -1, 5376, -1], 'generators': [1174320, 367920, 40345, 240, 243], 'label': '216.165.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
id: 20960914
{'ambient': '216.165', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '23328.dt', 'aut_weyl_index': 4, 'centralizer': '216.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['8.a1', '12.b1', '12.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4674, -1, 9380, -1], 'generators': [80884, 40345, 240, 243], 'label': '216.165.4.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '4.a1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
id: 20960915
{'ambient': '216.165', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '144.183', 'aut_weyl_index': 648, 'centralizer': '24.a1', 'complements': ['36.b1', '36.c1'], 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '3.a1'], 'contains': ['18.a1', '18.b1', '24.b1'], 'core': '6.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2372, 6392, 3573, 4969], 'generators': [1174320, 80884, 367920, 240], 'label': '216.165.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['18.a1', '18.b1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '216.165', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 20960916
{'ambient': '216.165', 'aut_centralizer_order': 324, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.851', 'aut_weyl_index': 324, 'centralizer': '6.b1', 'complements': ['36.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '18.a1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6667, 2117, 6460, 1646], 'generators': [1174320, 367920, 240, 243], 'label': '216.165.6.b1', 'mobius_quo': -3, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['18.a1', '24.a1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '216.165', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20960917
{'ambient': '216.165', 'aut_centralizer_order': 36, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.a1', '12.c1', '18.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8087, -1, 7832, -1], 'generators': [1174320, 40345, 240, 243], 'label': '216.165.6.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.c1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
id: 20960918
{'ambient': '216.165', 'aut_centralizer_order': 36, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 108, 'centralizer': '108.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.a1', '18.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9691, -1, 5376, -1], 'generators': [1174320, 443545, 240, 243], 'label': '216.165.6.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.d1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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