LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-11-18T16:12:27.067891

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

gps_groups • Show schema

{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '55.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 20, 'aut_gen_orders': [2, 20], 'aut_gens': [[1], [21], [42]], 'aut_group': '40.9', 'aut_hash': 9, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 40, 'aut_permdeg': 11, 'aut_perms': [3719520, 46113], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1], [11, 1, 10, 1], [55, 1, 40, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{20}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '40.9', 'autcent_hash': 9, 'autcent_nilpotent': True, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{20}', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [5, 1, 4], [11, 1, 10], [55, 1, 40]], 'center_label': '55.2', 'center_order': 55, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['5.1', '11.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1], [11, 1, 10, 1], [55, 1, 40, 1]], 'element_repr_type': 'PC', 'elementary': 55, 'eulerian_function': 1, 'exponent': 55, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [5, 11], 'faithful_reps': [[1, 0, 40]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '55.2', 'hash': 2, 'hyperelementary': 55, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 2, 'irrep_stats': [[1, 55]], 'label': '55.2', 'linC_count': 40, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 1, 'linQ_dim': 14, 'linQ_dim_count': 1, 'linR_count': 20, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C55', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 55, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 55, 'order_factorization_type': 11, 'order_stats': [[1, 1], [5, 4], [11, 10], [55, 40]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [2, 20], 'outer_gen_pows': [0, 0], 'outer_gens': [[21], [42]], 'outer_group': '40.9', 'outer_hash': 9, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 11, 'outer_perms': [3719520, 46113], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{20}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [5, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [10, 1], [40, 1]], 'representations': {'PC': {'code': 539, 'gens': [1], 'pres': [2, -5, -11, 10]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [1343, 11988]}, 'Perm': {'d': 16, 'gens': [5230697472000, 36288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [55], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{55}', 'transitive_degree': 55, '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: 110604866
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2, 'group_order': 55, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 110604877
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2, 'group_order': 55, 'label': '5A1', 'order': 5, 'powers': [4, 1, 2], 'representative': 11, 'size': 1}
id: 110604888
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 2, 'group_order': 55, 'label': '5A-1', 'order': 5, 'powers': [5, 1, 3], 'representative': 44, 'size': 1}
id: 110604899
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 2, 'group_order': 55, 'label': '5A2', 'order': 5, 'powers': [3, 1, 4], 'representative': 22, 'size': 1}
id: 110604910
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 2, 'group_order': 55, 'label': '5A-2', 'order': 5, 'powers': [2, 1, 5], 'representative': 33, 'size': 1}
id: 110604917
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 2, 'group_order': 55, 'label': '11A1', 'order': 11, 'powers': [8, 14, 1], 'representative': 5, 'size': 1}
id: 110604918
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 2, 'group_order': 55, 'label': '11A-1', 'order': 11, 'powers': [9, 15, 1], 'representative': 50, 'size': 1}
id: 110604919
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 2, 'group_order': 55, 'label': '11A2', 'order': 11, 'powers': [12, 7, 1], 'representative': 10, 'size': 1}
id: 110604920
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 2, 'group_order': 55, 'label': '11A-2', 'order': 11, 'powers': [13, 6, 1], 'representative': 45, 'size': 1}
id: 110604867
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 2, 'group_order': 55, 'label': '11A3', 'order': 11, 'powers': [15, 12, 1], 'representative': 15, 'size': 1}
id: 110604868
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 2, 'group_order': 55, 'label': '11A-3', 'order': 11, 'powers': [14, 13, 1], 'representative': 40, 'size': 1}
id: 110604869
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 2, 'group_order': 55, 'label': '11A4', 'order': 11, 'powers': [11, 9, 1], 'representative': 20, 'size': 1}
id: 110604870
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 2, 'group_order': 55, 'label': '11A-4', 'order': 11, 'powers': [10, 8, 1], 'representative': 35, 'size': 1}
id: 110604871
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 2, 'group_order': 55, 'label': '11A5', 'order': 11, 'powers': [7, 10, 1], 'representative': 25, 'size': 1}
id: 110604872
{'aut_label': '11A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 2, 'group_order': 55, 'label': '11A-5', 'order': 11, 'powers': [6, 11, 1], 'representative': 30, 'size': 1}
id: 110604873
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 2, 'group_order': 55, 'label': '55A1', 'order': 55, 'powers': [18, 6, 2], 'representative': 1, 'size': 1}
id: 110604874
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 2, 'group_order': 55, 'label': '55A-1', 'order': 55, 'powers': [19, 7, 3], 'representative': 54, 'size': 1}
id: 110604875
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 2, 'group_order': 55, 'label': '55A2', 'order': 55, 'powers': [22, 8, 4], 'representative': 2, 'size': 1}
id: 110604876
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 2, 'group_order': 55, 'label': '55A-2', 'order': 55, 'powers': [23, 9, 5], 'representative': 53, 'size': 1}
id: 110604878
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 2, 'group_order': 55, 'label': '55A3', 'order': 55, 'powers': [24, 10, 5], 'representative': 3, 'size': 1}
id: 110604879
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 2, 'group_order': 55, 'label': '55A-3', 'order': 55, 'powers': [25, 11, 4], 'representative': 52, 'size': 1}
id: 110604880
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 2, 'group_order': 55, 'label': '55A4', 'order': 55, 'powers': [28, 12, 3], 'representative': 4, 'size': 1}
id: 110604881
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 2, 'group_order': 55, 'label': '55A-4', 'order': 55, 'powers': [29, 13, 2], 'representative': 51, 'size': 1}
id: 110604882
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 2, 'group_order': 55, 'label': '55A6', 'order': 55, 'powers': [32, 15, 2], 'representative': 6, 'size': 1}
id: 110604883
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 2, 'group_order': 55, 'label': '55A-6', 'order': 55, 'powers': [33, 14, 3], 'representative': 49, 'size': 1}
id: 110604884
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 2, 'group_order': 55, 'label': '55A7', 'order': 55, 'powers': [36, 13, 4], 'representative': 7, 'size': 1}
id: 110604885
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 2, 'group_order': 55, 'label': '55A-7', 'order': 55, 'powers': [37, 12, 5], 'representative': 48, 'size': 1}
id: 110604886
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 2, 'group_order': 55, 'label': '55A8', 'order': 55, 'powers': [38, 11, 5], 'representative': 8, 'size': 1}
id: 110604887
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 29, 'group_counter': 2, 'group_order': 55, 'label': '55A-8', 'order': 55, 'powers': [39, 10, 4], 'representative': 47, 'size': 1}
id: 110604889
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 30, 'group_counter': 2, 'group_order': 55, 'label': '55A9', 'order': 55, 'powers': [42, 9, 3], 'representative': 9, 'size': 1}
id: 110604890
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 31, 'group_counter': 2, 'group_order': 55, 'label': '55A-9', 'order': 55, 'powers': [43, 8, 2], 'representative': 46, 'size': 1}
id: 110604891
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 32, 'group_counter': 2, 'group_order': 55, 'label': '55A12', 'order': 55, 'powers': [50, 6, 4], 'representative': 12, 'size': 1}
id: 110604892
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 33, 'group_counter': 2, 'group_order': 55, 'label': '55A-12', 'order': 55, 'powers': [51, 7, 5], 'representative': 43, 'size': 1}
id: 110604893
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 34, 'group_counter': 2, 'group_order': 55, 'label': '55A13', 'order': 55, 'powers': [52, 8, 5], 'representative': 13, 'size': 1}
id: 110604894
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 35, 'group_counter': 2, 'group_order': 55, 'label': '55A-13', 'order': 55, 'powers': [53, 9, 4], 'representative': 42, 'size': 1}
id: 110604895
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 36, 'group_counter': 2, 'group_order': 55, 'label': '55A14', 'order': 55, 'powers': [55, 10, 3], 'representative': 14, 'size': 1}
id: 110604896
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 37, 'group_counter': 2, 'group_order': 55, 'label': '55A-14', 'order': 55, 'powers': [54, 11, 2], 'representative': 41, 'size': 1}
id: 110604897
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 38, 'group_counter': 2, 'group_order': 55, 'label': '55A16', 'order': 55, 'powers': [49, 14, 2], 'representative': 16, 'size': 1}
id: 110604898
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 39, 'group_counter': 2, 'group_order': 55, 'label': '55A-16', 'order': 55, 'powers': [48, 15, 3], 'representative': 39, 'size': 1}
id: 110604900
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 40, 'group_counter': 2, 'group_order': 55, 'label': '55A17', 'order': 55, 'powers': [47, 15, 4], 'representative': 17, 'size': 1}
id: 110604901
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 41, 'group_counter': 2, 'group_order': 55, 'label': '55A-17', 'order': 55, 'powers': [46, 14, 5], 'representative': 38, 'size': 1}
id: 110604902
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 42, 'group_counter': 2, 'group_order': 55, 'label': '55A18', 'order': 55, 'powers': [45, 13, 5], 'representative': 18, 'size': 1}
id: 110604903
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 43, 'group_counter': 2, 'group_order': 55, 'label': '55A-18', 'order': 55, 'powers': [44, 12, 4], 'representative': 37, 'size': 1}
id: 110604904
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 44, 'group_counter': 2, 'group_order': 55, 'label': '55A19', 'order': 55, 'powers': [41, 11, 3], 'representative': 19, 'size': 1}
id: 110604905
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 45, 'group_counter': 2, 'group_order': 55, 'label': '55A-19', 'order': 55, 'powers': [40, 10, 2], 'representative': 36, 'size': 1}
id: 110604906
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 46, 'group_counter': 2, 'group_order': 55, 'label': '55A21', 'order': 55, 'powers': [35, 7, 2], 'representative': 21, 'size': 1}
id: 110604907
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 47, 'group_counter': 2, 'group_order': 55, 'label': '55A-21', 'order': 55, 'powers': [34, 6, 3], 'representative': 34, 'size': 1}
id: 110604908
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 48, 'group_counter': 2, 'group_order': 55, 'label': '55A23', 'order': 55, 'powers': [31, 6, 5], 'representative': 23, 'size': 1}
id: 110604909
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 49, 'group_counter': 2, 'group_order': 55, 'label': '55A-23', 'order': 55, 'powers': [30, 7, 4], 'representative': 32, 'size': 1}
id: 110604911
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 50, 'group_counter': 2, 'group_order': 55, 'label': '55A24', 'order': 55, 'powers': [27, 8, 3], 'representative': 24, 'size': 1}
id: 110604912
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 51, 'group_counter': 2, 'group_order': 55, 'label': '55A-24', 'order': 55, 'powers': [26, 9, 2], 'representative': 31, 'size': 1}
id: 110604913
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 52, 'group_counter': 2, 'group_order': 55, 'label': '55A26', 'order': 55, 'powers': [21, 12, 2], 'representative': 26, 'size': 1}
id: 110604914
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 2, 'group_order': 55, 'label': '55A-26', 'order': 55, 'powers': [20, 13, 3], 'representative': 29, 'size': 1}
id: 110604915
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 54, 'group_counter': 2, 'group_order': 55, 'label': '55A27', 'order': 55, 'powers': [17, 14, 4], 'representative': 27, 'size': 1}
id: 110604916
{'aut_label': '55A1', 'centralizer': '1.a1.a1', 'counter': 55, 'group_counter': 2, 'group_order': 55, 'label': '55A-27', 'order': 55, 'powers': [16, 15, 5], 'representative': 28, 'size': 1}

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: 4677497
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '55.2', 'group_order': 55, 'image': None, 'label': '55.2.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 4677498
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '55.2', 'group_order': 55, 'image': None, 'label': '55.2.1b', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4677499
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '55.2', 'group_order': 55, 'image': None, 'label': '55.2.1c', 'multiplicity': 10, 'nt': [11, 1], 'qdim': 10, 'qvalues': [10, 10, 10, 10, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4677500
{'cdim': 1, 'counter': 4, 'faithful': True, 'group': '55.2', 'group_order': 55, 'image': None, 'label': '55.2.1d', 'multiplicity': 40, 'nt': [55, 0], 'qdim': 40, 'qvalues': [40, -10, -10, -10, -10, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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}

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: 7512325
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 55, 'label': '55.2.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 7512336
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 2, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 11, 'label': '55.2.1b1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]]]}
id: 7512347
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 3, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 11, 'label': '55.2.1b2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]]]}
id: 7512358
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 4, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 11, 'label': '55.2.1b3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]]]}
id: 7512369
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 5, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 11, 'label': '55.2.1b4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]]]}
id: 7512376
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 6, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c1', 'nt': [11, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -5]], [[1, -3]], [[1, 4]], [[1, -2]], [[1, 5]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -4]], [[1, 2]], [[1, -5]], [[1, -2]], [[1, -4]], [[1, -5]], [[1, 5]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, 5]], [[1, 2]], [[1, 3]], [[1, -5]], [[1, 1]], [[1, 4]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 5]], [[1, -5]], [[1, 3]], [[1, -3]], [[1, 5]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, -4]], [[1, -3]]]}
id: 7512331
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 15, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c10', 'nt': [11, 10], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 5]], [[1, -3]], [[1, -4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -5]], [[1, 3]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, 3]], [[1, 1]], [[1, -1]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, -4]], [[1, -2]], [[1, 3]], [[1, -1]], [[1, 4]], [[1, -5]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -5]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -3]], [[1, 2]], [[1, -3]], [[1, -3]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -5]], [[1, 5]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, 5]]]}
id: 7512377
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 7, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c2', 'nt': [11, 10], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[1, 3]], [[1, -4]], [[1, 2]], [[1, -5]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 4]], [[1, -2]], [[1, 5]], [[1, 2]], [[1, 4]], [[1, 5]], [[1, -5]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, -5]], [[1, -2]], [[1, -3]], [[1, 5]], [[1, -1]], [[1, -4]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -5]], [[1, 5]], [[1, -3]], [[1, 3]], [[1, -5]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, 4]], [[1, 3]]]}
id: 7512378
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 8, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c3', 'nt': [11, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 5]], [[1, 4]], [[1, 3]], [[1, -3]], [[1, -2]], [[1, -1]], [[1, -5]], [[1, -4]], [[1, 5]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, 5]], [[1, -3]], [[1, -1]], [[1, 4]], [[1, -5]], [[1, -2]], [[1, -4]], [[1, 3]], [[1, 1]], [[1, -2]], [[1, 3]], [[1, -5]], [[1, -3]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, -5]], [[1, 3]], [[1, 5]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -5]], [[1, -3]], [[1, 5]], [[1, -1]], [[1, -1]], [[1, 2]]]}
id: 7512379
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 9, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c4', 'nt': [11, 10], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, -5]], [[1, -4]], [[1, -3]], [[1, 3]], [[1, 2]], [[1, 1]], [[1, 5]], [[1, 4]], [[1, -5]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, -5]], [[1, 3]], [[1, 1]], [[1, -4]], [[1, 5]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -1]], [[1, 2]], [[1, -3]], [[1, 5]], [[1, 3]], [[1, -1]], [[1, -3]], [[1, -1]], [[1, -1]], [[1, 5]], [[1, -3]], [[1, -5]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 5]], [[1, 3]], [[1, -5]], [[1, 1]], [[1, 1]], [[1, -2]]]}
id: 7512326
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 10, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c5', 'nt': [11, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, 5]], [[1, -5]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, -5]], [[1, 2]], [[1, 3]], [[1, -1]], [[1, 4]], [[1, -3]], [[1, 5]], [[1, -2]], [[1, 4]], [[1, 5]], [[1, -1]], [[1, -5]], [[1, -2]], [[1, 5]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 5]], [[1, 1]], [[1, -5]], [[1, 3]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, 3]], [[1, -1]], [[1, -5]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -4]]]}
id: 7512327
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 11, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c6', 'nt': [11, 10], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, -5]], [[1, 5]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, 5]], [[1, -2]], [[1, -3]], [[1, 1]], [[1, -4]], [[1, 3]], [[1, -5]], [[1, 2]], [[1, -4]], [[1, -5]], [[1, 1]], [[1, 5]], [[1, 2]], [[1, -5]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -5]], [[1, -1]], [[1, 5]], [[1, -3]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, -3]], [[1, 1]], [[1, 5]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 4]]]}
id: 7512328
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 12, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c7', 'nt': [11, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, -5]], [[1, -3]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, 5]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 5]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -3]], [[1, 4]], [[1, 5]], [[1, 2]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, -5]], [[1, -1]], [[1, -4]], [[1, 3]], [[1, 4]], [[1, -5]], [[1, -4]], [[1, -5]], [[1, -5]], [[1, 3]], [[1, -4]], [[1, -3]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 3]], [[1, 4]], [[1, -3]], [[1, 5]], [[1, 5]], [[1, 1]]]}
id: 7512329
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 13, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c8', 'nt': [11, 10], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, 5]], [[1, 3]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, -5]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -5]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 3]], [[1, -4]], [[1, -5]], [[1, -2]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, 5]], [[1, 1]], [[1, 4]], [[1, -3]], [[1, -4]], [[1, 5]], [[1, 4]], [[1, 5]], [[1, 5]], [[1, -3]], [[1, 4]], [[1, 3]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -3]], [[1, -4]], [[1, 3]], [[1, -5]], [[1, -5]], [[1, -1]]]}
id: 7512330
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 14, 'cyclotomic_n': 11, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '11.1', 'image_order': 11, 'indicator': 0, 'kernel': '11.a1.a1', 'kernel_order': 5, 'label': '55.2.1c9', 'nt': [11, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -5]], [[1, 3]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 5]], [[1, -3]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, -3]], [[1, -1]], [[1, 1]], [[1, -5]], [[1, 5]], [[1, -5]], [[1, 4]], [[1, 2]], [[1, -3]], [[1, 1]], [[1, -4]], [[1, 5]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 5]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 3]], [[1, -2]], [[1, 3]], [[1, 3]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 5]], [[1, -5]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, -3]], [[1, -3]], [[1, -5]]]}
id: 7512332
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id: 7512342
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id: 7512343
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id: 7512344
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 27, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d12', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, -15]], [[1, -20]], [[1, -10]], [[1, 5]], [[1, 15]], [[1, 25]], [[1, -25]], [[1, 20]], [[1, 10]], [[1, -5]], [[1, -4]], [[1, -6]], [[1, -1]], [[1, -26]], [[1, -7]], [[1, 2]], [[1, -13]], [[1, -9]], [[1, 27]], [[1, -3]], [[1, 21]], [[1, -18]], [[1, -16]], [[1, 9]], [[1, 18]], [[1, 3]], [[1, 12]], [[1, -24]], [[1, -19]], [[1, 17]], [[1, 8]], [[1, 23]], [[1, 14]], [[1, 1]], [[1, -21]], [[1, -27]], [[1, -8]], [[1, 16]], [[1, -14]], [[1, 26]], [[1, 7]], [[1, -2]], [[1, 13]], [[1, 4]], [[1, 6]], [[1, 19]], [[1, -17]], [[1, -12]], [[1, -23]], [[1, 24]]]}
id: 7512345
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 28, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d13', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, -10]], [[1, 5]], [[1, -25]], [[1, -15]], [[1, 10]], [[1, -20]], [[1, 20]], [[1, -5]], [[1, 25]], [[1, 15]], [[1, -21]], [[1, -4]], [[1, -19]], [[1, 1]], [[1, -23]], [[1, -17]], [[1, -27]], [[1, -6]], [[1, 18]], [[1, -2]], [[1, 14]], [[1, -12]], [[1, 26]], [[1, 6]], [[1, 12]], [[1, 2]], [[1, 8]], [[1, -16]], [[1, 24]], [[1, -7]], [[1, -13]], [[1, -3]], [[1, -9]], [[1, 19]], [[1, -14]], [[1, -18]], [[1, 13]], [[1, -26]], [[1, 9]], [[1, -1]], [[1, 23]], [[1, 17]], [[1, 27]], [[1, 21]], [[1, 4]], [[1, -24]], [[1, 7]], [[1, -8]], [[1, 3]], [[1, 16]]]}
id: 7512346
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 29, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d14', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, 10]], [[1, -5]], [[1, 25]], [[1, 15]], [[1, -10]], [[1, 20]], [[1, -20]], [[1, 5]], [[1, -25]], [[1, -15]], [[1, 21]], [[1, 4]], [[1, 19]], [[1, -1]], [[1, 23]], [[1, 17]], [[1, 27]], [[1, 6]], [[1, -18]], [[1, 2]], [[1, -14]], [[1, 12]], [[1, -26]], [[1, -6]], [[1, -12]], [[1, -2]], [[1, -8]], [[1, 16]], [[1, -24]], [[1, 7]], [[1, 13]], [[1, 3]], [[1, 9]], [[1, -19]], [[1, 14]], [[1, 18]], [[1, -13]], [[1, 26]], [[1, -9]], [[1, 1]], [[1, -23]], [[1, -17]], [[1, -27]], [[1, -21]], [[1, -4]], [[1, 24]], [[1, -7]], [[1, 8]], [[1, -3]], [[1, -16]]]}
id: 7512348
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 30, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d15', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, 10]], [[1, -5]], [[1, 25]], [[1, 15]], [[1, -10]], [[1, 20]], [[1, -20]], [[1, 5]], [[1, -25]], [[1, -15]], [[1, -1]], [[1, 26]], [[1, -14]], [[1, 21]], [[1, 12]], [[1, -27]], [[1, -17]], [[1, -16]], [[1, -7]], [[1, 13]], [[1, 19]], [[1, 23]], [[1, -4]], [[1, 16]], [[1, -23]], [[1, -13]], [[1, 3]], [[1, -6]], [[1, 9]], [[1, 18]], [[1, 2]], [[1, -8]], [[1, -24]], [[1, 14]], [[1, -19]], [[1, 7]], [[1, -2]], [[1, 4]], [[1, 24]], [[1, -21]], [[1, -12]], [[1, 27]], [[1, 17]], [[1, 1]], [[1, -26]], [[1, -9]], [[1, -18]], [[1, -3]], [[1, 8]], [[1, 6]]]}
id: 7512349
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 31, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d16', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, -10]], [[1, 5]], [[1, -25]], [[1, -15]], [[1, 10]], [[1, -20]], [[1, 20]], [[1, -5]], [[1, 25]], [[1, 15]], [[1, 1]], [[1, -26]], [[1, 14]], [[1, -21]], [[1, -12]], [[1, 27]], [[1, 17]], [[1, 16]], [[1, 7]], [[1, -13]], [[1, -19]], [[1, -23]], [[1, 4]], [[1, -16]], [[1, 23]], [[1, 13]], [[1, -3]], [[1, 6]], [[1, -9]], [[1, -18]], [[1, -2]], [[1, 8]], [[1, 24]], [[1, -14]], [[1, 19]], [[1, -7]], [[1, 2]], [[1, -4]], [[1, -24]], [[1, 21]], [[1, 12]], [[1, -27]], [[1, -17]], [[1, -1]], [[1, 26]], [[1, 9]], [[1, 18]], [[1, 3]], [[1, -8]], [[1, -6]]]}
id: 7512350
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 32, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d17', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, -5]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 5]], [[1, -10]], [[1, 10]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -16]], [[1, -24]], [[1, -4]], [[1, 6]], [[1, 27]], [[1, 8]], [[1, 3]], [[1, 19]], [[1, -2]], [[1, -12]], [[1, -26]], [[1, -17]], [[1, -9]], [[1, -19]], [[1, 17]], [[1, 12]], [[1, -7]], [[1, 14]], [[1, -21]], [[1, 13]], [[1, -23]], [[1, -18]], [[1, 1]], [[1, 4]], [[1, 26]], [[1, 2]], [[1, 23]], [[1, 9]], [[1, -1]], [[1, -6]], [[1, -27]], [[1, -8]], [[1, -3]], [[1, 16]], [[1, 24]], [[1, 21]], [[1, -13]], [[1, 7]], [[1, 18]], [[1, -14]]]}
id: 7512351
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 33, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d18', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, 5]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -5]], [[1, 10]], [[1, -10]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 16]], [[1, 24]], [[1, 4]], [[1, -6]], [[1, -27]], [[1, -8]], [[1, -3]], [[1, -19]], [[1, 2]], [[1, 12]], [[1, 26]], [[1, 17]], [[1, 9]], [[1, 19]], [[1, -17]], [[1, -12]], [[1, 7]], [[1, -14]], [[1, 21]], [[1, -13]], [[1, 23]], [[1, 18]], [[1, -1]], [[1, -4]], [[1, -26]], [[1, -2]], [[1, -23]], [[1, -9]], [[1, 1]], [[1, 6]], [[1, 27]], [[1, 8]], [[1, 3]], [[1, -16]], [[1, -24]], [[1, -21]], [[1, 13]], [[1, -7]], [[1, -18]], [[1, 14]]]}
id: 7512352
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 34, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d19', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, 5]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -5]], [[1, 10]], [[1, -10]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, -6]], [[1, -9]], [[1, 26]], [[1, 16]], [[1, 17]], [[1, 3]], [[1, 8]], [[1, 14]], [[1, 13]], [[1, 23]], [[1, 4]], [[1, -27]], [[1, -24]], [[1, -14]], [[1, 27]], [[1, -23]], [[1, 18]], [[1, 19]], [[1, -1]], [[1, -2]], [[1, 12]], [[1, 7]], [[1, 21]], [[1, -26]], [[1, -4]], [[1, -13]], [[1, -12]], [[1, 24]], [[1, -21]], [[1, -16]], [[1, -17]], [[1, -3]], [[1, -8]], [[1, 6]], [[1, 9]], [[1, 1]], [[1, 2]], [[1, -18]], [[1, -7]], [[1, -19]]]}
id: 7512333
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 17, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d2', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, 25]], [[1, 15]], [[1, -20]], [[1, 10]], [[1, -25]], [[1, -5]], [[1, 5]], [[1, -15]], [[1, 20]], [[1, -10]], [[1, -19]], [[1, -1]], [[1, 9]], [[1, 14]], [[1, 8]], [[1, -18]], [[1, 7]], [[1, 26]], [[1, -23]], [[1, 27]], [[1, -24]], [[1, -3]], [[1, -21]], [[1, -26]], [[1, 3]], [[1, -27]], [[1, 2]], [[1, -4]], [[1, 6]], [[1, 12]], [[1, -17]], [[1, 13]], [[1, -16]], [[1, -9]], [[1, 24]], [[1, 23]], [[1, 17]], [[1, 21]], [[1, 16]], [[1, -14]], [[1, -8]], [[1, 18]], [[1, -7]], [[1, 19]], [[1, 1]], [[1, -6]], [[1, -12]], [[1, -2]], [[1, -13]], [[1, 4]]]}
id: 7512353
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 35, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d20', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, -5]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 5]], [[1, -10]], [[1, 10]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, 6]], [[1, 9]], [[1, -26]], [[1, -16]], [[1, -17]], [[1, -3]], [[1, -8]], [[1, -14]], [[1, -13]], [[1, -23]], [[1, -4]], [[1, 27]], [[1, 24]], [[1, 14]], [[1, -27]], [[1, 23]], [[1, -18]], [[1, -19]], [[1, 1]], [[1, 2]], [[1, -12]], [[1, -7]], [[1, -21]], [[1, 26]], [[1, 4]], [[1, 13]], [[1, 12]], [[1, -24]], [[1, 21]], [[1, 16]], [[1, 17]], [[1, 3]], [[1, 8]], [[1, -6]], [[1, -9]], [[1, -1]], [[1, -2]], [[1, 18]], [[1, 7]], [[1, 19]]]}
id: 7512354
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id: 7512355
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id: 7512356
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id: 7512357
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id: 7512359
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id: 7512360
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id: 7512361
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id: 7512362
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id: 7512363
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id: 7512334
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id: 7512364
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id: 7512365
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id: 7512366
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id: 7512367
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id: 7512368
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id: 7512370
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id: 7512371
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 51, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d36', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 11]], [[1, -11]], [[1, -22]], [[1, 22]], [[1, -10]], [[1, 5]], [[1, -25]], [[1, -15]], [[1, 10]], [[1, -20]], [[1, 20]], [[1, -5]], [[1, 25]], [[1, 15]], [[1, 23]], [[1, 7]], [[1, -8]], [[1, 12]], [[1, -1]], [[1, 16]], [[1, 6]], [[1, -17]], [[1, -4]], [[1, -24]], [[1, 3]], [[1, 21]], [[1, -18]], [[1, 17]], [[1, -21]], [[1, 24]], [[1, -14]], [[1, -27]], [[1, 13]], [[1, 26]], [[1, 9]], [[1, 19]], [[1, 2]], [[1, 8]], [[1, -3]], [[1, 4]], [[1, -9]], [[1, 18]], [[1, -2]], [[1, -12]], [[1, 1]], [[1, -16]], [[1, -6]], [[1, -23]], [[1, -7]], [[1, -13]], [[1, -26]], [[1, 14]], [[1, -19]], [[1, 27]]]}
id: 7512372
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 52, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d37', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -11]], [[1, 11]], [[1, 22]], [[1, -22]], [[1, -5]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 5]], [[1, -10]], [[1, 10]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, 17]], [[1, -2]], [[1, 18]], [[1, -27]], [[1, 16]], [[1, 19]], [[1, 14]], [[1, -3]], [[1, 9]], [[1, -1]], [[1, 7]], [[1, -6]], [[1, 13]], [[1, 3]], [[1, 6]], [[1, 1]], [[1, 4]], [[1, -8]], [[1, 12]], [[1, 24]], [[1, 21]], [[1, 26]], [[1, 23]], [[1, -18]], [[1, -7]], [[1, -9]], [[1, -21]], [[1, -13]], [[1, -23]], [[1, 27]], [[1, -16]], [[1, -19]], [[1, -14]], [[1, -17]], [[1, 2]], [[1, -12]], [[1, -24]], [[1, -4]], [[1, -26]], [[1, 8]]]}
id: 7512373
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 53, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d38', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 11]], [[1, -11]], [[1, -22]], [[1, 22]], [[1, 5]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -5]], [[1, 10]], [[1, -10]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, -17]], [[1, 2]], [[1, -18]], [[1, 27]], [[1, -16]], [[1, -19]], [[1, -14]], [[1, 3]], [[1, -9]], [[1, 1]], [[1, -7]], [[1, 6]], [[1, -13]], [[1, -3]], [[1, -6]], [[1, -1]], [[1, -4]], [[1, 8]], [[1, -12]], [[1, -24]], [[1, -21]], [[1, -26]], [[1, -23]], [[1, 18]], [[1, 7]], [[1, 9]], [[1, 21]], [[1, 13]], [[1, 23]], [[1, -27]], [[1, 16]], [[1, 19]], [[1, 14]], [[1, 17]], [[1, -2]], [[1, 12]], [[1, 24]], [[1, 4]], [[1, 26]], [[1, -8]]]}
id: 7512374
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 54, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d39', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -11]], [[1, 11]], [[1, 22]], [[1, -22]], [[1, 5]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -5]], [[1, 10]], [[1, -10]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 27]], [[1, 13]], [[1, -7]], [[1, -17]], [[1, 6]], [[1, 14]], [[1, 19]], [[1, -8]], [[1, 24]], [[1, -21]], [[1, -18]], [[1, -16]], [[1, -2]], [[1, 8]], [[1, 16]], [[1, 21]], [[1, -26]], [[1, -3]], [[1, -23]], [[1, 9]], [[1, 1]], [[1, -4]], [[1, -12]], [[1, 7]], [[1, 18]], [[1, -24]], [[1, -1]], [[1, 2]], [[1, 12]], [[1, 17]], [[1, -6]], [[1, -14]], [[1, -19]], [[1, -27]], [[1, -13]], [[1, 23]], [[1, -9]], [[1, 26]], [[1, 4]], [[1, 3]]]}
id: 7512335
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 19, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d4', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, -25]], [[1, -15]], [[1, 20]], [[1, -10]], [[1, 25]], [[1, 5]], [[1, -5]], [[1, 15]], [[1, -20]], [[1, 10]], [[1, -14]], [[1, -21]], [[1, 24]], [[1, 19]], [[1, 3]], [[1, 7]], [[1, -18]], [[1, -4]], [[1, 12]], [[1, 17]], [[1, -9]], [[1, -8]], [[1, -1]], [[1, 4]], [[1, 8]], [[1, -17]], [[1, -13]], [[1, 26]], [[1, 16]], [[1, -23]], [[1, -27]], [[1, -2]], [[1, -6]], [[1, -24]], [[1, 9]], [[1, -12]], [[1, 27]], [[1, 1]], [[1, 6]], [[1, -19]], [[1, -3]], [[1, -7]], [[1, 18]], [[1, 14]], [[1, 21]], [[1, -16]], [[1, 23]], [[1, 13]], [[1, 2]], [[1, -26]]]}
id: 7512375
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 55, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d40', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 11]], [[1, -11]], [[1, -22]], [[1, 22]], [[1, -5]], [[1, -25]], [[1, 15]], [[1, 20]], [[1, 5]], [[1, -10]], [[1, 10]], [[1, 25]], [[1, -15]], [[1, -20]], [[1, -27]], [[1, -13]], [[1, 7]], [[1, 17]], [[1, -6]], [[1, -14]], [[1, -19]], [[1, 8]], [[1, -24]], [[1, 21]], [[1, 18]], [[1, 16]], [[1, 2]], [[1, -8]], [[1, -16]], [[1, -21]], [[1, 26]], [[1, 3]], [[1, 23]], [[1, -9]], [[1, -1]], [[1, 4]], [[1, 12]], [[1, -7]], [[1, -18]], [[1, 24]], [[1, 1]], [[1, -2]], [[1, -12]], [[1, -17]], [[1, 6]], [[1, 14]], [[1, 19]], [[1, 27]], [[1, 13]], [[1, -23]], [[1, 9]], [[1, -26]], [[1, -4]], [[1, -3]]]}
id: 7512337
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 20, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d5', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, -20]], [[1, 10]], [[1, 5]], [[1, 25]], [[1, 20]], [[1, 15]], [[1, -15]], [[1, -10]], [[1, -5]], [[1, -25]], [[1, 24]], [[1, -19]], [[1, 6]], [[1, -9]], [[1, -13]], [[1, -12]], [[1, 23]], [[1, -1]], [[1, 3]], [[1, 18]], [[1, -16]], [[1, -2]], [[1, -14]], [[1, 1]], [[1, 2]], [[1, -18]], [[1, -17]], [[1, -21]], [[1, 4]], [[1, 8]], [[1, 7]], [[1, 27]], [[1, 26]], [[1, -6]], [[1, 16]], [[1, -3]], [[1, -7]], [[1, 14]], [[1, -26]], [[1, 9]], [[1, 13]], [[1, 12]], [[1, -23]], [[1, -24]], [[1, 19]], [[1, -4]], [[1, -8]], [[1, 17]], [[1, -27]], [[1, 21]]]}
id: 7512338
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 21, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d6', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, 20]], [[1, -10]], [[1, -5]], [[1, -25]], [[1, -20]], [[1, -15]], [[1, 15]], [[1, 10]], [[1, 5]], [[1, 25]], [[1, -24]], [[1, 19]], [[1, -6]], [[1, 9]], [[1, 13]], [[1, 12]], [[1, -23]], [[1, 1]], [[1, -3]], [[1, -18]], [[1, 16]], [[1, 2]], [[1, 14]], [[1, -1]], [[1, -2]], [[1, 18]], [[1, 17]], [[1, 21]], [[1, -4]], [[1, -8]], [[1, -7]], [[1, -27]], [[1, -26]], [[1, 6]], [[1, -16]], [[1, 3]], [[1, 7]], [[1, -14]], [[1, 26]], [[1, -9]], [[1, -13]], [[1, -12]], [[1, 23]], [[1, 24]], [[1, -19]], [[1, 4]], [[1, 8]], [[1, -17]], [[1, 27]], [[1, -21]]]}
id: 7512339
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 22, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d7', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, 20]], [[1, -10]], [[1, -5]], [[1, -25]], [[1, -20]], [[1, -15]], [[1, 15]], [[1, 10]], [[1, 5]], [[1, 25]], [[1, 9]], [[1, -14]], [[1, 16]], [[1, -24]], [[1, 2]], [[1, 23]], [[1, -12]], [[1, -21]], [[1, 8]], [[1, -7]], [[1, -6]], [[1, 13]], [[1, -19]], [[1, 21]], [[1, -13]], [[1, 7]], [[1, -27]], [[1, -1]], [[1, -26]], [[1, 3]], [[1, -18]], [[1, 17]], [[1, -4]], [[1, -16]], [[1, 6]], [[1, -8]], [[1, 18]], [[1, 19]], [[1, 4]], [[1, 24]], [[1, -2]], [[1, -23]], [[1, 12]], [[1, -9]], [[1, 14]], [[1, 26]], [[1, -3]], [[1, 27]], [[1, -17]], [[1, 1]]]}
id: 7512340
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 23, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d8', 'nt': [55, 40], 'q_character': None, 'values': [[[1, 0]], [[1, 22]], [[1, -22]], [[1, 11]], [[1, -11]], [[1, -20]], [[1, 10]], [[1, 5]], [[1, 25]], [[1, 20]], [[1, 15]], [[1, -15]], [[1, -10]], [[1, -5]], [[1, -25]], [[1, -9]], [[1, 14]], [[1, -16]], [[1, 24]], [[1, -2]], [[1, -23]], [[1, 12]], [[1, 21]], [[1, -8]], [[1, 7]], [[1, 6]], [[1, -13]], [[1, 19]], [[1, -21]], [[1, 13]], [[1, -7]], [[1, 27]], [[1, 1]], [[1, 26]], [[1, -3]], [[1, 18]], [[1, -17]], [[1, 4]], [[1, 16]], [[1, -6]], [[1, 8]], [[1, -18]], [[1, -19]], [[1, -4]], [[1, -24]], [[1, 2]], [[1, 23]], [[1, -12]], [[1, 9]], [[1, -14]], [[1, -26]], [[1, 3]], [[1, -27]], [[1, 17]], [[1, -1]]]}
id: 7512341
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 55, 'counter': 24, 'cyclotomic_n': 55, 'dim': 1, 'faithful': True, 'field': [1, -1, 1, -1, 1], 'group': '55.2', 'group_counter': 2, 'group_order': 55, 'image': None, 'image_isoclass': '55.2', 'image_order': 55, 'indicator': 0, 'kernel': '55.a1.a1', 'kernel_order': 1, 'label': '55.2.1d9', 'nt': [55, 0], 'q_character': None, 'values': [[[1, 0]], [[1, -22]], [[1, 22]], [[1, -11]], [[1, 11]], [[1, -15]], [[1, -20]], [[1, -10]], [[1, 5]], [[1, 15]], [[1, 25]], [[1, -25]], [[1, 20]], [[1, 10]], [[1, -5]], [[1, -26]], [[1, 16]], [[1, 21]], [[1, -4]], [[1, -18]], [[1, 13]], [[1, -2]], [[1, 24]], [[1, -17]], [[1, 8]], [[1, -1]], [[1, -7]], [[1, 6]], [[1, -24]], [[1, 7]], [[1, -8]], [[1, 23]], [[1, 9]], [[1, 14]], [[1, -27]], [[1, -3]], [[1, 12]], [[1, -19]], [[1, -21]], [[1, 1]], [[1, 17]], [[1, 3]], [[1, -6]], [[1, 19]], [[1, 4]], [[1, 18]], [[1, -13]], [[1, 2]], [[1, 26]], [[1, -16]], [[1, -14]], [[1, 27]], [[1, -23]], [[1, -12]], [[1, -9]]]}

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: 67511329
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '55.2', 'ambient_counter': 2, 'ambient_order': 55, 'ambient_tex': 'C_{55}', 'central': True, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 55, 'counter': 1, 'cyclic': True, 'direct': True, 'hall': 55, 'label': '55.2.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['Z', 'F', 'R', 'S', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '55.2', 'subgroup_hash': 2, 'subgroup_order': 55, 'subgroup_tex': 'C_{55}', 'supersolvable': True, 'sylow': 0}
id: 67511330
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '55.2', 'ambient_counter': 2, 'ambient_order': 55, 'ambient_tex': 'C_{55}', 'central': True, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 11, 'counter': 2, 'cyclic': True, 'direct': True, 'hall': 11, 'label': '55.2.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, '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': True, 'solvable': True, 'special_labels': ['C1'], '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: 67511331
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '55.2', 'ambient_counter': 2, 'ambient_order': 55, 'ambient_tex': 'C_{55}', 'central': True, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 5, 'counter': 3, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '55.2.11.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '11.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '11.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 11, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 67511332
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '55.2', 'ambient_counter': 2, 'ambient_order': 55, 'ambient_tex': 'C_{55}', 'central': True, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 1, 'counter': 4, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '55.2.55.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '55.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '55.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 55, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{55}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'Phi', 'PC', 'U1', 'L1', 'D1', 'C2'], '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: 67511329
{'ambient': '55.2', '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': '1.a1.a1', 'complements': ['55.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['5.a1.a1', '11.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4198, 4198, 4869, 4869, 5282, 5282, 4718, 4718], 'generators': [11, 5], 'label': '55.2.1.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['5.a1.a1', '11.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1.1', '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': '1.1'}
id: 67511330
{'ambient': '55.2', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '10.2', 'aut_weyl_index': 4, 'centralizer': '1.a1.a1', 'complements': ['11.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['55.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2672, 2672, 7652, 7652, 2465, 2465, 7535, 7535], 'generators': [5], 'label': '55.2.5.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['55.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '5.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 67511331
{'ambient': '55.2', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 10, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['55.a1.a1'], 'core': '11.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7328, 7328, 2348, 2348, 8099, 8099, 1901, 1901], 'generators': [11], 'label': '55.2.11.a1.a1', 'mobius_quo': -1, 'mobius_sub': -1, 'normal_closure': '11.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['55.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '11.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '11.1', 'quotient_action_kernel_order': 11, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 67511332
{'ambient': '55.2', 'aut_centralizer_order': None, 'aut_label': '55.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': ['5.a1.a1', '11.a1.a1'], 'contains': [], 'core': '55.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6259, 6259, 4869, 4869, 5282, 5282, 4718, 4718], 'generators': [], 'label': '55.2.55.a1.a1', 'mobius_quo': 1, 'mobius_sub': 1, 'normal_closure': '55.a1.a1', 'normal_contained_in': ['5.a1.a1', '11.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '55.a1.a1', 'projective_image': '55.2', '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': '1.1'}

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.