LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-11-18T07:57:05.531959

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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [2, 10, 22], 'aut_gens': [[1, 10, 20], [11, 10, 20], [1, 10, 260], [241, 10, 30]], 'aut_group': '440.42', 'aut_hash': 42, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 440, 'aut_permdeg': 24, 'aut_perms': [522570481886452470541130, 17548251277974683845823, 121077927107026838559648], 'aut_phi_ratio': 2.75, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 1, 1], [4, 22, 1, 1], [5, 11, 1, 4], [10, 11, 1, 4], [10, 22, 1, 8], [11, 10, 1, 1], [20, 22, 1, 4], [22, 10, 1, 1], [22, 10, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times F_{11}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 22, 1], [4, 22, 1], [5, 11, 4], [10, 11, 4], [10, 22, 8], [11, 10, 1], [20, 22, 4], [22, 10, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '220.7', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 11, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 1, 1], [4, 22, 1, 1], [5, 11, 4, 1], [10, 11, 4, 1], [10, 22, 4, 2], [11, 10, 1, 1], [20, 22, 4, 1], [22, 10, 1, 1], [22, 10, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 220, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '220.7', 'hash': 11, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 1, 22], 'inner_gens': [[1, 10, 270], [1, 10, 20], [211, 10, 20]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 220, 'inner_split': True, 'inner_tex': 'C_2\\times F_{11}', 'inner_used': [1, 3], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 20], [2, 5], [10, 4]], 'label': '440.11', 'linC_count': 2, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D22:C10', 'ngens': 5, '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': 28, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 29, 'number_divisions': 13, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 32, 'number_subgroups': 190, 'old_label': None, 'order': 440, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 25], [4, 22], [5, 44], [10, 220], [11, 10], [20, 88], [22, 30]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[11, 10, 420]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 4], [8, 1], [10, 2], [20, 1]], 'representations': {'PC': {'code': 81489632502225479303009, 'gens': [1, 3, 4], 'pres': [5, -2, -5, -2, 2, -11, 10, 5403, 3008, 58, 2004, 2009]}, 'GLZN': {'d': 2, 'p': 33, 'gens': [35962, 826574, 36037, 1173952, 371834]}, 'Perm': {'d': 15, 'gens': [6267312007, 5, 13499992920, 16, 105871456080]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{22}:C_{10}', 'transitive_degree': 44, '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: 110256227
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 11, 'group_order': 440, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 110256238
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 11, 'group_order': 440, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 10, 'size': 1}
id: 110256249
{'aut_label': '2B', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 11, 'group_order': 440, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 220, 'size': 2}
id: 110256250
{'aut_label': '2C', 'centralizer': '22.b1.a1', 'counter': 4, 'group_counter': 11, 'group_order': 440, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 95, 'size': 22}
id: 110256251
{'aut_label': '4A', 'centralizer': '22.c1.a1', 'counter': 5, 'group_counter': 11, 'group_order': 440, 'label': '4A', 'order': 4, 'powers': [2, 5, 5], 'representative': 145, 'size': 22}
id: 110256252
{'aut_label': '5A1', 'centralizer': '11.a1.a1', 'counter': 6, 'group_counter': 11, 'group_order': 440, 'label': '5A1', 'order': 5, 'powers': [8, 1, 6], 'representative': 126, 'size': 11}
id: 110256253
{'aut_label': '5A-1', 'centralizer': '11.a1.a1', 'counter': 7, 'group_counter': 11, 'group_order': 440, 'label': '5A-1', 'order': 5, 'powers': [9, 1, 7], 'representative': 284, 'size': 11}
id: 110256254
{'aut_label': '5A2', 'centralizer': '11.a1.a1', 'counter': 8, 'group_counter': 11, 'group_order': 440, 'label': '5A2', 'order': 5, 'powers': [7, 1, 8], 'representative': 322, 'size': 11}
id: 110256255
{'aut_label': '5A-2', 'centralizer': '11.a1.a1', 'counter': 9, 'group_counter': 11, 'group_order': 440, 'label': '5A-2', 'order': 5, 'powers': [6, 1, 9], 'representative': 368, 'size': 11}
id: 110256228
{'aut_label': '10A1', 'centralizer': '11.a1.a1', 'counter': 10, 'group_counter': 11, 'group_order': 440, 'label': '10A1', 'order': 10, 'powers': [9, 2, 10], 'representative': 174, 'size': 11}
id: 110256229
{'aut_label': '10A-1', 'centralizer': '11.a1.a1', 'counter': 11, 'group_counter': 11, 'group_order': 440, 'label': '10A-1', 'order': 10, 'powers': [8, 2, 11], 'representative': 336, 'size': 11}
id: 110256230
{'aut_label': '10A3', 'centralizer': '11.a1.a1', 'counter': 12, 'group_counter': 11, 'group_order': 440, 'label': '10A3', 'order': 10, 'powers': [7, 2, 12], 'representative': 132, 'size': 11}
id: 110256231
{'aut_label': '10A-3', 'centralizer': '11.a1.a1', 'counter': 13, 'group_counter': 11, 'group_order': 440, 'label': '10A-3', 'order': 10, 'powers': [6, 2, 13], 'representative': 98, 'size': 11}
id: 110256232
{'aut_label': '10B1', 'centralizer': '22.b1.a1', 'counter': 14, 'group_counter': 11, 'group_order': 440, 'label': '10B1', 'order': 10, 'powers': [6, 4, 14], 'representative': 173, 'size': 22}
id: 110256233
{'aut_label': '10B-1', 'centralizer': '22.b1.a1', 'counter': 15, 'group_counter': 11, 'group_order': 440, 'label': '10B-1', 'order': 10, 'powers': [7, 4, 15], 'representative': 217, 'size': 22}
id: 110256234
{'aut_label': '10B3', 'centralizer': '22.b1.a1', 'counter': 16, 'group_counter': 11, 'group_order': 440, 'label': '10B3', 'order': 10, 'powers': [9, 4, 16], 'representative': 259, 'size': 22}
id: 110256235
{'aut_label': '10B-3', 'centralizer': '22.b1.a1', 'counter': 17, 'group_counter': 11, 'group_order': 440, 'label': '10B-3', 'order': 10, 'powers': [8, 4, 17], 'representative': 411, 'size': 22}
id: 110256236
{'aut_label': '10C1', 'centralizer': '22.a1.a1', 'counter': 18, 'group_counter': 11, 'group_order': 440, 'label': '10C1', 'order': 10, 'powers': [6, 3, 18], 'representative': 198, 'size': 22}
id: 110256237
{'aut_label': '10C-1', 'centralizer': '22.a1.a1', 'counter': 19, 'group_counter': 11, 'group_order': 440, 'label': '10C-1', 'order': 10, 'powers': [7, 3, 19], 'representative': 392, 'size': 22}
id: 110256239
{'aut_label': '10C3', 'centralizer': '22.a1.a1', 'counter': 20, 'group_counter': 11, 'group_order': 440, 'label': '10C3', 'order': 10, 'powers': [9, 3, 20], 'representative': 154, 'size': 22}
id: 110256240
{'aut_label': '10C-3', 'centralizer': '22.a1.a1', 'counter': 21, 'group_counter': 11, 'group_order': 440, 'label': '10C-3', 'order': 10, 'powers': [8, 3, 21], 'representative': 76, 'size': 22}
id: 110256241
{'aut_label': '11A', 'centralizer': '10.a1.a1', 'counter': 22, 'group_counter': 11, 'group_order': 440, 'label': '11A', 'order': 11, 'powers': [22, 22, 1], 'representative': 80, 'size': 10}
id: 110256242
{'aut_label': '20A1', 'centralizer': '22.c1.a1', 'counter': 23, 'group_counter': 11, 'group_order': 440, 'label': '20A1', 'order': 20, 'powers': [10, 5, 23], 'representative': 27, 'size': 22}
id: 110256243
{'aut_label': '20A-1', 'centralizer': '22.c1.a1', 'counter': 24, 'group_counter': 11, 'group_order': 440, 'label': '20A-1', 'order': 20, 'powers': [11, 5, 24], 'representative': 73, 'size': 22}
id: 110256244
{'aut_label': '20A3', 'centralizer': '22.c1.a1', 'counter': 25, 'group_counter': 11, 'group_order': 440, 'label': '20A3', 'order': 20, 'powers': [12, 5, 25], 'representative': 271, 'size': 22}
id: 110256245
{'aut_label': '20A-3', 'centralizer': '22.c1.a1', 'counter': 26, 'group_counter': 11, 'group_order': 440, 'label': '20A-3', 'order': 20, 'powers': [13, 5, 26], 'representative': 429, 'size': 22}
id: 110256246
{'aut_label': '22A', 'centralizer': '10.a1.a1', 'counter': 27, 'group_counter': 11, 'group_order': 440, 'label': '22A', 'order': 22, 'powers': [22, 27, 2], 'representative': 50, 'size': 10}
id: 110256247
{'aut_label': '22B1', 'centralizer': '10.a1.a1', 'counter': 28, 'group_counter': 11, 'group_order': 440, 'label': '22B1', 'order': 22, 'powers': [22, 28, 3], 'representative': 20, 'size': 10}
id: 110256248
{'aut_label': '22B1', 'centralizer': '10.a1.a1', 'counter': 29, 'group_counter': 11, 'group_order': 440, 'label': '22B-1', 'order': 22, 'powers': [22, 29, 3], 'representative': 30, 'size': 10}

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: 4567903
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4567908
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
id: 4567909
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1], 'schur_index': 1}
id: 4567910
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
id: 4567915
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 0, 2, 2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0], 'schur_index': 1}
id: 4567911
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1e', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, -1, -1, 4, 4, 4], 'schur_index': 1}
id: 4567912
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1f', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 4, -1, -1, -1, -1, -4, 4, -4], 'schur_index': 1}
id: 4567913
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1g', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, 4, -4, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 4, 1, 1, 1, 1, -4, 4, -4], 'schur_index': 1}
id: 4567914
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 4, 1, 1, 1, 1, 4, 4, 4], 'schur_index': 1}
id: 4567904
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.2b', 'multiplicity': 4, 'nt': [20, 12], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0], 'schur_index': 1}
id: 4567905
{'cdim': 10, 'counter': 11, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.10a', 'multiplicity': 1, 'nt': [11, 4], 'qdim': 10, 'qvalues': [10, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
id: 4567906
{'cdim': 10, 'counter': 12, 'faithful': False, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.10b', 'multiplicity': 1, 'nt': [22, 6], 'qdim': 10, 'qvalues': [10, 10, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, -1, 1], 'schur_index': 1}
id: 4567907
{'cdim': 10, 'counter': 13, 'faithful': True, 'group': '440.11', 'group_order': 440, 'image': None, 'label': '440.11.10c', 'multiplicity': 2, 'nt': [44, 20], 'qdim': 20, 'qvalues': [20, -20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 7163686
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 440, 'label': '440.11.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163697
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 220, 'label': '440.11.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163708
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 220, 'label': '440.11.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163709
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 220, 'label': '440.11.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163710
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 88, 'label': '440.11.1e1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163711
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 6, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 88, 'label': '440.11.1e2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163712
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 7, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 88, 'label': '440.11.1e3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163713
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 8, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 88, 'label': '440.11.1e4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163714
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 44, 'label': '440.11.1f1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163687
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 44, 'label': '440.11.1f2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163688
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 44, 'label': '440.11.1f3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163689
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.c1.a1', 'kernel_order': 44, 'label': '440.11.1f4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163690
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 44, 'label': '440.11.1g1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, -1]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163691
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 44, 'label': '440.11.1g2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, 1]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163692
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 44, 'label': '440.11.1g3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163693
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 44, 'label': '440.11.1g4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, -2]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 7163694
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 44, 'label': '440.11.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[-1, 2]], [[1, 2]], [[1, -2]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163695
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 44, 'label': '440.11.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[-1, -2]], [[1, -2]], [[1, 2]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163696
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 44, 'label': '440.11.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[1, 2]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163698
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 440, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 44, 'label': '440.11.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[1, -2]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7163699
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 110, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 55, 'label': '440.11.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
id: 7163700
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 110, 'counter': 22, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 11, 'label': '440.11.2b1', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, -1]], [[2, 2]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
id: 7163701
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 110, 'counter': 23, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 11, 'label': '440.11.2b2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, 1]], [[2, -2]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
id: 7163702
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 110, 'counter': 24, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 11, 'label': '440.11.2b3', 'nt': [20, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 2]], [[2, 1]], [[2, -2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
id: 7163703
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 110, 'counter': 25, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '40.10', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 11, 'label': '440.11.2b4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -2]], [[2, -1]], [[2, 2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]]]}
id: 7163704
{'center': '110.a1.a1', 'center_index': 110, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '110.1', 'image_order': 110, 'indicator': 1, 'kernel': '110.a1.a1', 'kernel_order': 4, 'label': '440.11.10a', 'nt': [11, 4], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 7163705
{'center': '110.a1.a1', 'center_index': 110, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 1, 'dim': 10, 'faithful': False, 'field': [0, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '220.7', 'image_order': 220, 'indicator': 1, 'kernel': '220.a1.a1', 'kernel_order': 2, 'label': '440.11.10b', 'nt': [22, 6], 'q_character': None, 'values': [[[10, 0]], [[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 7163706
{'center': '220.a1.a1', 'center_index': 220, 'center_order': 2, 'counter': 28, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [3, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '440.11', 'image_order': 440, 'indicator': 0, 'kernel': '440.a1.a1', 'kernel_order': 1, 'label': '440.11.10c1', 'nt': [44, 20], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]], [[1, 0]], [[1, 0], [2, 1], [2, 3], [2, 4], [2, 5], [2, -2]]]}
id: 7163707
{'center': '220.a1.a1', 'center_index': 220, 'center_order': 2, 'counter': 29, 'cyclotomic_n': 11, 'dim': 10, 'faithful': True, 'field': [3, -1, 1], 'group': '440.11', 'group_counter': 11, 'group_order': 440, 'image': None, 'image_isoclass': '440.11', 'image_order': 440, 'indicator': 0, 'kernel': '440.a1.a1', 'kernel_order': 1, 'label': '440.11.10c2', 'nt': [44, 2], 'q_character': None, 'values': [[[10, 0]], [[-10, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1], [2, 3], [2, 4], [2, 5], [2, -2]], [[1, 0]], [[-1, 0], [-2, 1], [-2, 3], [-2, 4], [-2, 5], [-2, -2]]]}

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: 66662901
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 440, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '440.11.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '440.11', 'subgroup_hash': 11, 'subgroup_order': 440, 'subgroup_tex': 'D_{22}:C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662912
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 220, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '220.8', 'subgroup_hash': 8, 'subgroup_order': 220, 'subgroup_tex': 'C_{22}:C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662923
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 220, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
id: 66662927
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 220, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '220.1', 'subgroup_hash': 1, 'subgroup_order': 220, 'subgroup_tex': 'C_{11}:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 66662928
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 110, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662929
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 55, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662930
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 55, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
id: 66662931
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 88, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '440.11.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '88.7', 'subgroup_hash': 7, 'subgroup_order': 88, 'subgroup_tex': 'C_{11}:D_4', 'supersolvable': True, 'sylow': 0}
id: 66662932
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 55, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '440.11.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
id: 66662902
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 44, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '44.4', 'subgroup_hash': 4, 'subgroup_order': 44, 'subgroup_tex': 'C_2\\times C_{22}', 'supersolvable': True, 'sylow': 0}
id: 66662903
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 44, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
id: 66662904
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 44, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '44.1', 'subgroup_hash': 1, 'subgroup_order': 44, 'subgroup_tex': 'C_{11}:C_4', 'supersolvable': True, 'sylow': 0}
id: 66662905
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '440.11.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '11.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 66662906
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 22, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '440.11.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
id: 66662907
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': False, 'core_order': 11, 'counter': 15, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
id: 66662908
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 11, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
id: 66662909
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.22.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662910
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.22.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662911
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.22.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '22.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 22, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 66662913
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 44, 'characteristic': True, 'core_order': 11, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 11, 'label': '440.11.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 11}
id: 66662914
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662915
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.44.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662916
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.44.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '44.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 66662917
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '440.11.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '55.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 55, 'quotient_simple': 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: 66662918
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '440.11.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '88.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 66662919
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 220, 'characteristic': True, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '440.11.110.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '110.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '110.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 110, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_{11}', 'simple': False, 'solvable': True, 'special_labels': ['U0'], '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: 66662920
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '440.11.110.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': 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: 66662921
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.110.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '110.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 110, 'quotient_simple': 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: 66662922
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 440, 'characteristic': True, 'core_order': 2, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '440.11.220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '220.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '220.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 220, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_{11}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 66662924
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 220, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.220.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, '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: 66662925
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '440.11.220.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '220.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 220, '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: 66662926
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '440.11', 'ambient_counter': 11, 'ambient_order': 440, 'ambient_tex': 'D_{22}:C_{10}', 'central': True, 'central_factor': False, 'centralizer_order': 440, 'characteristic': True, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '440.11.440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '440.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '440.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 440, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{22}:C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', '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: 66662901
{'ambient': '440.11', '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': '220.a1.a1', 'complements': ['440.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '5.a1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7182, 5591, 7231, 3182, 6722, 4826, 4652, 4826], 'generators': [5, 2, 10, 220, 40], 'label': '440.11.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662902
{'ambient': '440.11', 'aut_centralizer_order': 22, 'aut_label': '10.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '20.5', 'aut_weyl_index': 22, 'centralizer': '10.a1.a1', 'complements': ['44.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '110.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5932, 8730, 2067, 1439, 5408, 8879, 6733, 8879], 'generators': [10, 40, 220], 'label': '440.11.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '110.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
id: 66662903
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '10.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 2, 'centralizer': '220.a1.a1', 'complements': ['44.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.c1.a1', '110.b1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3962, 4409, 3368, 3512, 7604, 6930, 930, 6930], 'generators': [5, 40, 10], 'label': '440.11.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '220.7', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662904
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '10.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 2, 'centralizer': '220.a1.a1', 'complements': ['44.b1.a1', '44.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '110.c1.a1'], 'core': '10.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7678, 6243, 6467, 5864, 9616, 5321, 4440, 5321], 'generators': [25, 40, 10], 'label': '440.11.10.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1.a1', 'normal_contained_in': ['2.c1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '220.7', 'quotient_action_image': '10.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662905
{'ambient': '440.11', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 110, 'centralizer': '44.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '22.b1.a1', '22.c1.a1', '55.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9666, -1, 8596, -1, 6722, -1, 5625, -1], 'generators': [5, 2, 10, 220], 'label': '440.11.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 66662906
{'ambient': '440.11', 'aut_centralizer_order': 44, 'aut_label': '20.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 44, 'centralizer': '10.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '220.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5320, 4745, 2985, 4038, 6502, 5878, 4037, 5878], 'generators': [10, 40], 'label': '440.11.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normal_contains': ['40.a1.a1', '220.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '10.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
id: 66662907
{'ambient': '440.11', 'aut_centralizer_order': 22, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '10.2', 'aut_weyl_index': 44, 'centralizer': '10.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '220.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1858, -1, 361, -1, 3190, -1, 6733, -1], 'generators': [220, 40], 'label': '440.11.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '5.1'}
id: 66662908
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 4, 'centralizer': '220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.b1.a1'], 'contains': ['40.a1.a1', '220.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [539, -1, 1281, -1, 4535, -1, 1044, -1], 'generators': [5, 40], 'label': '440.11.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '20.c1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
id: 66662909
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '22.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.b1.a1', '110.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [6911, -1, 5465, -1, 2689, -1, 7972, -1], 'generators': [10, 2, 220], 'label': '440.11.22.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662910
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '22.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '44.c1.a1', '110.b1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3846, -1, 8337, -1, 6646, -1, 1888, -1], 'generators': [5, 2, 10], 'label': '440.11.22.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.b1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662911
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '22.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '22.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '11.a1.a1'], 'contains': ['44.a1.a1', '110.c1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [9055, -1, 9639, -1, 8279, -1, 5230, -1], 'generators': [225, 10, 2], 'label': '440.11.22.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '22.c1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '22.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662912
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 2, 'centralizer': '110.a1.a1', 'complements': ['220.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '10.a1.a1', '22.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5941, 7178, 5207, 1621, 4049, 6295, 6961, 6295], 'generators': [10, 2, 40, 220], 'label': '440.11.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
id: 66662913
{'ambient': '440.11', 'aut_centralizer_order': 44, 'aut_label': '40.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 44, 'centralizer': '10.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['440.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1266, 4198, 1013, 5057, 3927, 5259, 3551, 5259], 'generators': [40], 'label': '440.11.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['440.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '440.11', 'quotient_action_image': '10.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
id: 66662914
{'ambient': '440.11', 'aut_centralizer_order': 40, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '22.a1.a1', '22.b1.a1', '22.c1.a1'], 'contains': ['88.a1.a1', '220.a1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [4826, -1, 9173, -1, 5211, -1, 4706, -1], 'generators': [10, 2], 'label': '440.11.44.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662915
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '44.b1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '22.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '22.a1.a1'], 'contains': ['88.a1.a1', '220.b1.a1'], 'core': '440.a1.a1', 'coset_action_label': '44T20', 'count': 22, 'diagramx': [2740, -1, 4680, -1, 1610, -1, 7683, -1], 'generators': [220, 2], 'label': '440.11.44.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.a1.a1', 'old_label': '44.b1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662916
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '44.c1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '22.b1.a1'], 'contains': ['88.a1.a1', '220.c1.a1'], 'core': '440.a1.a1', 'coset_action_label': '44T22', 'count': 22, 'diagramx': [1460, -1, 7551, -1, 3859, -1, 1834, -1], 'generators': [5, 2], 'label': '440.11.44.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '44.c1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662917
{'ambient': '440.11', 'aut_centralizer_order': 10, 'aut_label': '55.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '4.2', 'aut_weyl_index': 110, 'centralizer': '44.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '11.a1.a1'], 'contains': ['110.a1.a1', '110.b1.a1', '110.c1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8424, -1, 4071, -1, 8887, -1, 5838, -1], 'generators': [5, 220], 'label': '440.11.55.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '55.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 66662918
{'ambient': '440.11', 'aut_centralizer_order': 40, 'aut_label': '88.a1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '11.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1', '44.b1.a1', '44.c1.a1'], 'contains': ['440.a1.a1'], 'core': '440.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [1595, -1, 8739, -1, 2772, -1, 4159, -1], 'generators': [2], 'label': '440.11.88.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662919
{'ambient': '440.11', 'aut_centralizer_order': 220, 'aut_label': '110.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '2.a1.a1', 'complements': ['4.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '22.a1.a1', '55.a1.a1'], 'contains': ['220.a1.a1', '220.b1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6300, 6720, 3069, 3018, 5856, 8306, 6088, 8306], 'generators': [10, 220], 'label': '440.11.110.a1.a1', 'mobius_quo': 0, 'mobius_sub': -11, 'normal_closure': '110.a1.a1', 'normal_contained_in': ['10.a1.a1'], 'normal_contains': ['220.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '110.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '55.1', 'quotient_action_kernel_order': 55, 'quotient_fusion': None, 'short_label': '110.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662920
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '110.b1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '22.b1.a1', '55.a1.a1'], 'contains': ['220.a1.a1', '220.c1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [3720, -1, 4029, -1, 7147, -1, 2480, -1], 'generators': [5, 10], 'label': '440.11.110.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '110.b1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662921
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '110.c1', 'aut_quo_index': None, 'aut_stab_index': 11, 'aut_weyl_group': '2.1', 'aut_weyl_index': 220, 'centralizer': '22.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '22.c1.a1', '55.a1.a1'], 'contains': ['220.a1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [8114, -1, 6426, -1, 8583, -1, 5313, -1], 'generators': [25], 'label': '440.11.110.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '110.c1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '110.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 66662922
{'ambient': '440.11', 'aut_centralizer_order': 440, 'aut_label': '220.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.a1', '110.a1.a1', '110.b1.a1', '110.c1.a1'], 'contains': ['440.a1.a1'], 'core': '220.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5195, 5309, 4784, 4021, 6176, 6496, 4706, 6496], 'generators': [10], 'label': '440.11.220.a1.a1', 'mobius_quo': -1, 'mobius_sub': 22, 'normal_closure': '220.a1.a1', 'normal_contained_in': ['20.a1.a1', '110.a1.a1'], 'normal_contains': ['440.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '220.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '220.7', 'quotient_action_kernel_order': 220, 'quotient_fusion': None, 'short_label': '220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662923
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 2, 'centralizer': '220.a1.a1', 'complements': ['220.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '10.b1.a1', '22.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3691, 1270, 7231, 4729, 5583, 3372, 1888, 3372], 'generators': [5, 2, 40, 10], 'label': '440.11.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '220.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662924
{'ambient': '440.11', 'aut_centralizer_order': 220, 'aut_label': '220.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '44.b1.a1', '110.a1.a1'], 'contains': ['440.a1.a1'], 'core': '440.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2498, -1, 2562, -1, 3319, -1, 6407, -1], 'generators': [220], 'label': '440.11.220.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '110.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '220.b1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662925
{'ambient': '440.11', 'aut_centralizer_order': 20, 'aut_label': '220.c1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '1.1', 'aut_weyl_index': 440, 'centralizer': '22.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '44.c1.a1', '110.b1.a1'], 'contains': ['440.a1.a1'], 'core': '440.a1.a1', 'coset_action_label': None, 'count': 22, 'diagramx': [955, -1, 4029, -1, 4535, -1, 2161, -1], 'generators': [5], 'label': '440.11.220.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '22.b1.a1', 'old_label': '220.c1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662926
{'ambient': '440.11', 'aut_centralizer_order': None, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '88.a1.a1', '220.a1.a1', '220.b1.a1', '220.c1.a1'], 'contains': [], 'core': '440.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1595, 4797, 4029, 4515, 3927, 5878, 4159, 5878], 'generators': [], 'label': '440.11.440.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '440.a1.a1', 'normal_contained_in': ['40.a1.a1', '220.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '440.a1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 66662927
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '220.7', 'aut_weyl_index': 2, 'centralizer': '220.a1.a1', 'complements': ['220.b1.a1', '220.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.c1.a1', '22.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8075, 3986, 8864, 7261, 7801, 990, 3642, 990], 'generators': [25, 10, 40, 2], 'label': '440.11.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '220.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662928
{'ambient': '440.11', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '110.1', 'aut_weyl_index': 4, 'centralizer': '110.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '20.a1.a1', '44.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4816, 3986, 7314, 5353, 4049, 2892, 3247, 2892], 'generators': [10, 40, 2], 'label': '440.11.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '220.7', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
id: 66662929
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 4, 'centralizer': '110.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '20.b1.a1', '44.b1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1741, -1, 4008, -1, 668, -1, 9331, -1], 'generators': [220, 40, 2], 'label': '440.11.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '55.1'}
id: 66662930
{'ambient': '440.11', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '110.1', 'aut_weyl_index': 4, 'centralizer': '220.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '20.c1.a1', '44.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [334, -1, 5857, -1, 1739, -1, 262, -1], 'generators': [5, 40, 2], 'label': '440.11.4.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.c1.a1', 'projective_image': '440.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
id: 66662931
{'ambient': '440.11', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '440.42', 'aut_weyl_index': 1, 'centralizer': '220.a1.a1', 'complements': ['88.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '55.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7309, 8077, 3368, 2146, 8811, 8879, 4652, 8879], 'generators': [5, 10, 40, 220], 'label': '440.11.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '220.7', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
id: 66662932
{'ambient': '440.11', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '110.1', 'aut_weyl_index': 4, 'centralizer': '110.a1.a1', 'complements': ['55.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['40.a1.a1', '88.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1052, 1887, 6415, 8561, 2400, 3867, 3247, 3867], 'generators': [2, 40], 'label': '440.11.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '440.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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