LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-09-21T00:00:48.130559

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

gps_groups • Show schema

{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '54.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 6, 'aut_gen_orders': [3, 3, 2, 2, 6], 'aut_gens': [[1, 3], [1, 22], [1, 39], [2, 51], [2, 5], [20, 15]], 'aut_group': '108.28', 'aut_hash': 28, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 108, 'aut_permdeg': 11, 'aut_perms': [4556304, 11088384, 1, 169567, 26386807], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 1, 6, 1], [6, 1, 2, 1], [6, 1, 6, 1], [9, 1, 18, 1], [18, 1, 18, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^2:D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '108.28', 'autcent_hash': 28, 'autcent_nilpotent': False, 'autcent_order': 108, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^2:D_6', '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], [2, 1, 1], [3, 1, 8], [6, 1, 8], [9, 1, 18], [18, 1, 18]], 'center_label': '54.9', 'center_order': 54, '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': ['2.1', '3.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [6, 1, 2, 4], [9, 1, 6, 3], [18, 1, 6, 3]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 12, 'exponent': 18, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '18.5', 'hash': 9, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 54]], 'label': '54.9', 'linC_count': 648, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 27, 'linQ_dim': 8, 'linQ_dim_count': 27, 'linR_count': 162, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C18', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 54, 'number_divisions': 16, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 20, 'number_subgroups': 20, 'old_label': None, 'order': 54, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 8], [6, 8], [9, 18], [18, 18]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [3, 3, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 22], [1, 39], [2, 51], [2, 5], [20, 15]], 'outer_group': '108.28', 'outer_hash': 28, 'outer_nilpotent': False, 'outer_order': 108, 'outer_permdeg': 11, 'outer_perms': [4556304, 11088384, 1, 169567, 26386807], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2:D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [6, 6]], 'representations': {'PC': {'code': 467051, 'gens': [1, 2], 'pres': [4, -3, -2, -3, -3, 21, 46]}, 'GLFp': {'d': 2, 'p': 19, 'gens': [13719, 75456]}, 'Perm': {'d': 14, 'gens': [6227020800, 357120, 79833600, 80884]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 18], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{18}', 'transitive_degree': 54, '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: 105725653
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 9, 'group_order': 54, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 105725664
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 9, 'group_order': 54, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 27, 'size': 1}
id: 105725675
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 9, 'group_order': 54, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 20, 'size': 1}
id: 105725686
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 9, 'group_order': 54, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 37, 'size': 1}
id: 105725697
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 9, 'group_order': 54, 'label': '3B1', 'order': 3, 'powers': [6, 1], 'representative': 19, 'size': 1}
id: 105725703
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 9, 'group_order': 54, 'label': '3B-1', 'order': 3, 'powers': [5, 1], 'representative': 38, 'size': 1}
id: 105725704
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 9, 'group_order': 54, 'label': '3C1', 'order': 3, 'powers': [8, 1], 'representative': 2, 'size': 1}
id: 105725705
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 9, 'group_order': 54, 'label': '3C-1', 'order': 3, 'powers': [7, 1], 'representative': 1, 'size': 1}
id: 105725706
{'aut_label': '3D1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 9, 'group_order': 54, 'label': '3D1', 'order': 3, 'powers': [10, 1], 'representative': 18, 'size': 1}
id: 105725654
{'aut_label': '3D1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 9, 'group_order': 54, 'label': '3D-1', 'order': 3, 'powers': [9, 1], 'representative': 36, 'size': 1}
id: 105725655
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 9, 'group_order': 54, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 10, 'size': 1}
id: 105725656
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 9, 'group_order': 54, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 47, 'size': 1}
id: 105725657
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 9, 'group_order': 54, 'label': '6B1', 'order': 6, 'powers': [5, 2], 'representative': 11, 'size': 1}
id: 105725658
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 14, 'group_counter': 9, 'group_order': 54, 'label': '6B-1', 'order': 6, 'powers': [6, 2], 'representative': 46, 'size': 1}
id: 105725659
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 9, 'group_order': 54, 'label': '6C1', 'order': 6, 'powers': [7, 2], 'representative': 28, 'size': 1}
id: 105725660
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 9, 'group_order': 54, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 29, 'size': 1}
id: 105725661
{'aut_label': '6D1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 9, 'group_order': 54, 'label': '6D1', 'order': 6, 'powers': [9, 2], 'representative': 9, 'size': 1}
id: 105725662
{'aut_label': '6D1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 9, 'group_order': 54, 'label': '6D-1', 'order': 6, 'powers': [10, 2], 'representative': 45, 'size': 1}
id: 105725663
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 9, 'group_order': 54, 'label': '9A1', 'order': 9, 'powers': [21, 9], 'representative': 6, 'size': 1}
id: 105725665
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 9, 'group_order': 54, 'label': '9A-1', 'order': 9, 'powers': [22, 10], 'representative': 48, 'size': 1}
id: 105725666
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 9, 'group_order': 54, 'label': '9A2', 'order': 9, 'powers': [23, 10], 'representative': 12, 'size': 1}
id: 105725667
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 9, 'group_order': 54, 'label': '9A-2', 'order': 9, 'powers': [24, 9], 'representative': 42, 'size': 1}
id: 105725668
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 9, 'group_order': 54, 'label': '9A4', 'order': 9, 'powers': [20, 9], 'representative': 24, 'size': 1}
id: 105725669
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 9, 'group_order': 54, 'label': '9A-4', 'order': 9, 'powers': [19, 10], 'representative': 30, 'size': 1}
id: 105725670
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 9, 'group_order': 54, 'label': '9B1', 'order': 9, 'powers': [27, 9], 'representative': 8, 'size': 1}
id: 105725671
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 9, 'group_order': 54, 'label': '9B-1', 'order': 9, 'powers': [28, 10], 'representative': 49, 'size': 1}
id: 105725672
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 9, 'group_order': 54, 'label': '9B2', 'order': 9, 'powers': [29, 10], 'representative': 13, 'size': 1}
id: 105725673
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 9, 'group_order': 54, 'label': '9B-2', 'order': 9, 'powers': [30, 9], 'representative': 44, 'size': 1}
id: 105725674
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 29, 'group_counter': 9, 'group_order': 54, 'label': '9B4', 'order': 9, 'powers': [26, 9], 'representative': 26, 'size': 1}
id: 105725676
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 30, 'group_counter': 9, 'group_order': 54, 'label': '9B-4', 'order': 9, 'powers': [25, 10], 'representative': 31, 'size': 1}
id: 105725677
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 31, 'group_counter': 9, 'group_order': 54, 'label': '9C1', 'order': 9, 'powers': [33, 9], 'representative': 7, 'size': 1}
id: 105725678
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 32, 'group_counter': 9, 'group_order': 54, 'label': '9C-1', 'order': 9, 'powers': [34, 10], 'representative': 50, 'size': 1}
id: 105725679
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 33, 'group_counter': 9, 'group_order': 54, 'label': '9C2', 'order': 9, 'powers': [35, 10], 'representative': 14, 'size': 1}
id: 105725680
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 34, 'group_counter': 9, 'group_order': 54, 'label': '9C-2', 'order': 9, 'powers': [36, 9], 'representative': 43, 'size': 1}
id: 105725681
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 35, 'group_counter': 9, 'group_order': 54, 'label': '9C4', 'order': 9, 'powers': [32, 9], 'representative': 25, 'size': 1}
id: 105725682
{'aut_label': '9A1', 'centralizer': '1.a1.a1', 'counter': 36, 'group_counter': 9, 'group_order': 54, 'label': '9C-4', 'order': 9, 'powers': [31, 10], 'representative': 32, 'size': 1}
id: 105725683
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 37, 'group_counter': 9, 'group_order': 54, 'label': '18A1', 'order': 18, 'powers': [19, 17], 'representative': 3, 'size': 1}
id: 105725684
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 38, 'group_counter': 9, 'group_order': 54, 'label': '18A-1', 'order': 18, 'powers': [20, 18], 'representative': 51, 'size': 1}
id: 105725685
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 39, 'group_counter': 9, 'group_order': 54, 'label': '18A5', 'order': 18, 'powers': [24, 18], 'representative': 15, 'size': 1}
id: 105725687
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 40, 'group_counter': 9, 'group_order': 54, 'label': '18A-5', 'order': 18, 'powers': [23, 17], 'representative': 39, 'size': 1}
id: 105725688
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 41, 'group_counter': 9, 'group_order': 54, 'label': '18A7', 'order': 18, 'powers': [22, 17], 'representative': 21, 'size': 1}
id: 105725689
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 42, 'group_counter': 9, 'group_order': 54, 'label': '18A-7', 'order': 18, 'powers': [21, 18], 'representative': 33, 'size': 1}
id: 105725690
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 43, 'group_counter': 9, 'group_order': 54, 'label': '18B1', 'order': 18, 'powers': [25, 17], 'representative': 4, 'size': 1}
id: 105725691
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 44, 'group_counter': 9, 'group_order': 54, 'label': '18B-1', 'order': 18, 'powers': [26, 18], 'representative': 53, 'size': 1}
id: 105725692
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 45, 'group_counter': 9, 'group_order': 54, 'label': '18B5', 'order': 18, 'powers': [30, 18], 'representative': 17, 'size': 1}
id: 105725693
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 46, 'group_counter': 9, 'group_order': 54, 'label': '18B-5', 'order': 18, 'powers': [29, 17], 'representative': 40, 'size': 1}
id: 105725694
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 47, 'group_counter': 9, 'group_order': 54, 'label': '18B7', 'order': 18, 'powers': [28, 17], 'representative': 22, 'size': 1}
id: 105725695
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 48, 'group_counter': 9, 'group_order': 54, 'label': '18B-7', 'order': 18, 'powers': [27, 18], 'representative': 35, 'size': 1}
id: 105725696
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 49, 'group_counter': 9, 'group_order': 54, 'label': '18C1', 'order': 18, 'powers': [31, 17], 'representative': 5, 'size': 1}
id: 105725698
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 50, 'group_counter': 9, 'group_order': 54, 'label': '18C-1', 'order': 18, 'powers': [32, 18], 'representative': 52, 'size': 1}
id: 105725699
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 51, 'group_counter': 9, 'group_order': 54, 'label': '18C5', 'order': 18, 'powers': [36, 18], 'representative': 16, 'size': 1}
id: 105725700
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 52, 'group_counter': 9, 'group_order': 54, 'label': '18C-5', 'order': 18, 'powers': [35, 17], 'representative': 41, 'size': 1}
id: 105725701
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 53, 'group_counter': 9, 'group_order': 54, 'label': '18C7', 'order': 18, 'powers': [34, 17], 'representative': 23, 'size': 1}
id: 105725702
{'aut_label': '18A1', 'centralizer': '1.a1.a1', 'counter': 54, 'group_counter': 9, 'group_order': 54, 'label': '18C-7', 'order': 18, 'powers': [33, 18], 'representative': 34, '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: 3566724
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1a', '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], 'schur_index': 1}
id: 3566732
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 3566733
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1], 'schur_index': 1}
id: 3566734
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2], 'schur_index': 1}
id: 3566735
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1], 'schur_index': 1}
id: 3566736
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -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: 3566737
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, -1, -1, 2, -1, -1, 2, 1, -2, 1, 1, 1, -2, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, -2, 1, -2, 1, -2, 1], 'schur_index': 1}
id: 3566738
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, -1, -1, 2, -1, -1, 2, 1, -2, 1, 1, 1, -2, 1, 1, -1, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, -2], 'schur_index': 1}
id: 3566739
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -1, -1, -1, -1, 2, -1, -1, 2, 1, -2, 1, 1, 1, -2, 1, 1, 2, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -2, 1, 1, -2, 1, 1, -2, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1], 'schur_index': 1}
id: 3566725
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -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: 3566726
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1k', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, 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], 'schur_index': 1}
id: 3566727
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1l', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, -3, 6, -3, -3, -3, 6, -3, -3, -3, -3, -3, -3, 6, -3, -3, 6, 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], 'schur_index': 1}
id: 3566728
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1m', 'multiplicity': 6, 'nt': [9, 1], 'qdim': 6, 'qvalues': [6, 6, 6, -3, -3, -3, -3, -3, 6, -3, 6, -3, -3, -3, -3, -3, 6, -3, 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], 'schur_index': 1}
id: 3566729
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1n', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, -6, -3, -3, 6, 6, -3, -3, -3, -3, 3, 3, -6, -6, 3, 3, 3, 3, 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], 'schur_index': 1}
id: 3566730
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1o', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, -6, -3, 6, -3, -3, -3, 6, -3, -3, 3, 3, 3, 3, -6, 3, 3, -6, 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], 'schur_index': 1}
id: 3566731
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '54.9', 'group_order': 54, 'image': None, 'label': '54.9.1p', 'multiplicity': 6, 'nt': [18, 1], 'qdim': 6, 'qvalues': [6, -6, 6, -3, -3, -3, -3, -3, 6, -3, -6, 3, 3, 3, 3, 3, -6, 3, 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], '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: 5130403
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 54, 'label': '54.9.1a', '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]]]}
id: 5130414
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 27, 'label': '54.9.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-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: 5130425
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 18, 'label': '54.9.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]]]}
id: 5130436
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.c1', 'kernel_order': 18, 'label': '54.9.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]]]}
id: 5130447
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 18, 'label': '54.9.1d1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]]]}
id: 5130453
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.b1', 'kernel_order': 18, 'label': '54.9.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]]]}
id: 5130454
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 18, 'label': '54.9.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
id: 5130455
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1.a1', 'kernel_order': 18, 'label': '54.9.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
id: 5130456
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 18, 'label': '54.9.1f1', 'nt': [3, 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, -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]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
id: 5130404
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id: 5130405
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 9, 'label': '54.9.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]]]}
id: 5130406
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.c1', 'kernel_order': 9, 'label': '54.9.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-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, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]]]}
id: 5130407
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 9, 'label': '54.9.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]]]}
id: 5130408
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.b1', 'kernel_order': 9, 'label': '54.9.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]]]}
id: 5130409
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 9, 'label': '54.9.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
id: 5130410
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 9, 'label': '54.9.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
id: 5130411
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 9, 'label': '54.9.1j1', 'nt': [6, 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, -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]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
id: 5130412
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 9, 'label': '54.9.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
id: 5130413
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 19, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k1', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 2]]]}
id: 5130415
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 20, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k2', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, -2]]]}
id: 5130416
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 21, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k3', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -1]]]}
id: 5130417
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 22, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k4', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 1]]]}
id: 5130418
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 23, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k5', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -4]]]}
id: 5130419
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 24, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.c1', 'kernel_order': 6, 'label': '54.9.1k6', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, 4]]]}
id: 5130420
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 25, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l1', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]]]}
id: 5130421
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 26, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l2', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 4]], [[1, -4]]]}
id: 5130422
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 27, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l3', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -2]]]}
id: 5130423
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 28, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l4', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 2]]]}
id: 5130424
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 29, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l5', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 4]], [[1, -1]], [[1, 1]]]}
id: 5130426
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 30, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.a1', 'kernel_order': 6, 'label': '54.9.1l6', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -4]], [[1, 1]], [[1, -1]]]}
id: 5130427
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m1', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, 4]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -4]], [[1, -1]], [[1, -4]], [[1, -4]], [[1, -2]], [[1, -2]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]]]}
id: 5130428
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m2', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 4]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, 2]], [[1, 2]], [[1, -4]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]]]}
id: 5130429
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m3', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -2]], [[1, -1]], [[1, -4]], [[1, 4]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, 4]]]}
id: 5130430
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m4', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 2]], [[1, 1]], [[1, 4]], [[1, -4]], [[1, 4]], [[1, -2]], [[1, 4]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, -4]]]}
id: 5130431
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m5', 'nt': [9, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 4]], [[1, 4]], [[1, 1]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, -2]]]}
id: 5130432
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '9.1', 'image_order': 9, 'indicator': 0, 'kernel': '9.a1.b1', 'kernel_order': 6, 'label': '54.9.1m6', 'nt': [9, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 4]], [[1, -2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -4]], [[1, -4]], [[1, -1]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, 2]]]}
id: 5130433
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 37, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 1]], [[-1, 2]]]}
id: 5130434
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 38, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, -1]], [[-1, -2]]]}
id: 5130435
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 39, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, 4]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 4]], [[-1, -1]]]}
id: 5130437
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 40, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, -4]], [[-1, -4]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 1]]]}
id: 5130438
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 41, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, -2]], [[-1, -4]]]}
id: 5130439
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 42, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.c1', 'kernel_order': 3, 'label': '54.9.1n6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, -3]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, 4]]]}
id: 5130440
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 43, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, -4]], [[-1, 4]]]}
id: 5130441
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 44, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[-1, -4]]]}
id: 5130442
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 45, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 4]], [[-1, -1]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, 4]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -2]]]}
id: 5130443
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 46, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, 1]], [[-1, 4]], [[-1, 4]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, -4]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 2]]]}
id: 5130444
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 47, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 4]], [[-1, -2]], [[-1, -4]], [[-1, 4]], [[-1, 4]], [[-1, -1]], [[-1, 1]]]}
id: 5130445
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 48, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 3, 'label': '54.9.1o6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 3]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, -3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 0]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, 2]], [[-1, 4]], [[-1, -4]], [[-1, -4]], [[-1, 1]], [[-1, -1]]]}
id: 5130446
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 49, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p1', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, -4]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, -4]], [[1, 2]], [[1, 4]], [[1, 1]], [[-1, 4]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -4]], [[-1, -1]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, -2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, 1]]]}
id: 5130448
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 50, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p2', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, 4]], [[1, -4]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -1]], [[-1, -4]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 4]], [[-1, 1]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[-1, 2]], [[-1, -4]], [[-1, -4]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, -1]]]}
id: 5130449
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 51, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p3', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 4]], [[1, -4]], [[1, -4]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 4]], [[-1, -2]], [[-1, -1]], [[-1, -4]], [[-1, 4]], [[-1, -4]], [[-1, 2]], [[-1, -4]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, 4]]]}
id: 5130450
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 52, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p4', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, 4]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -4]], [[-1, 2]], [[-1, 1]], [[-1, 4]], [[-1, -4]], [[-1, 4]], [[-1, -2]], [[-1, 4]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -4]], [[-1, -1]], [[-1, 1]], [[-1, -4]]]}
id: 5130451
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 53, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p5', 'nt': [18, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, 3]], [[1, 0]], [[1, -3]], [[-1, 0]], [[-1, -3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, 0]], [[-1, 3]], [[1, -1]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, -1]], [[1, -4]], [[1, 1]], [[1, -2]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, 4]], [[-1, 1]], [[-1, 1]], [[-1, -4]], [[-1, -2]], [[-1, 4]], [[-1, -4]], [[-1, -2]]]}
id: 5130452
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 54, 'counter': 54, 'cyclotomic_n': 9, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, -1, 0, 0, 1], 'group': '54.9', 'group_counter': 9, 'group_order': 54, 'image': None, 'image_isoclass': '18.2', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.b1', 'kernel_order': 3, 'label': '54.9.1p6', 'nt': [18, 6], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, -3]], [[1, 0]], [[1, 3]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, -3]], [[-1, 3]], [[-1, -3]], [[-1, 0]], [[-1, -3]], [[1, 1]], [[1, -1]], [[1, 4]], [[1, 1]], [[1, -4]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, -4]], [[1, 1]], [[1, 4]], [[1, -1]], [[1, 2]], [[-1, -1]], [[-1, 4]], [[-1, -2]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, -1]], [[-1, 4]], [[-1, 2]], [[-1, -4]], [[-1, 4]], [[-1, 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: 59409262
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '54.9.1.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', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
id: 59409273
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 3, 'label': '54.9.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 3}
id: 59409275
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 18, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '54.9.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 59409276
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 4, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.3.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 59409277
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 5, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.3.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 59409278
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 6, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.3.b1.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
id: 59409279
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 9, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '54.9.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 59409280
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 8, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 59409281
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 9, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 59409263
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 10, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.6.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
id: 59409264
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 11, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 59409265
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 12, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.9.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 59409266
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 13, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.9.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 59409267
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 6, 'counter': 14, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '54.9.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 59409268
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 15, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 59409269
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 16, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 59409270
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 17, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '54.9.18.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '18.a1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 59409271
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 3, 'counter': 18, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '54.9.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 59409272
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 2, 'counter': 19, 'cyclic': True, 'direct': True, 'hall': 2, 'label': '54.9.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '27.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_9', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 2}
id: 59409274
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '54.9', 'ambient_counter': 9, 'ambient_order': 54, 'ambient_tex': 'C_3\\times C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 1, 'counter': 20, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '54.9.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '54.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_{18}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'PC', 'U1', 'L1', 'D1', 'C4'], '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: 59409262
{'ambient': '54.9', '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': ['54.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5234, 5234, 3799, 3799, 5000, 5000, 4390, 4390], 'generators': [27, 1, 6, 18], 'label': '54.9.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '3.a1.a1', '3.b1.c1', '3.b1.a1', '3.b1.b1'], '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: 59409263
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['9.a1.c1', '9.a1.b1', '9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.c1'], 'contains': ['18.b1.a1'], 'core': '6.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1182, 1182, 2082, 2082, 1725, 1725, 2051, 2051], 'generators': [7], 'label': '54.9.6.b1.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.c1', 'normal_contained_in': ['2.a1.a1', '3.b1.c1'], 'normal_contains': ['18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.c1', 'projective_image': '6.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409264
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['6.b1.a1', '6.b1.c1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.a1', '27.a1.a1'], 'core': '9.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8746, 8746, 8496, 8496, 8333, 8333, 8322, 8322], 'generators': [27, 37], 'label': '54.9.9.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '9.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.a1.a1', '27.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '9.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409265
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['6.b1.a1', '6.b1.c1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.b1', '27.a1.a1'], 'core': '9.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8746, 8746, 9590, 9590, 8333, 8333, 9542, 9542], 'generators': [27, 19], 'label': '54.9.9.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '9.a1.b1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.a1.b1', '27.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.b1', 'projective_image': '9.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409266
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['6.b1.a1', '6.b1.c1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.a1.c1', '27.a1.a1'], 'core': '9.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8746, 8746, 7401, 7401, 8333, 8333, 7102, 7102], 'generators': [27, 1], 'label': '54.9.9.a1.c1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '9.a1.c1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['18.a1.c1', '27.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.a1.c1', 'projective_image': '9.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409267
{'ambient': '54.9', 'aut_centralizer_order': 54, 'aut_label': '9.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1'], 'contains': ['18.b1.a1', '27.a1.a1'], 'core': '9.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6165, 6165, 3997, 3997, 6228, 6228, 5881, 5881], 'generators': [27, 18], 'label': '54.9.9.b1.a1', 'mobius_quo': 1, 'mobius_sub': 3, 'normal_closure': '9.b1.a1', 'normal_contained_in': ['3.a1.a1', '3.b1.c1', '3.b1.a1', '3.b1.b1'], 'normal_contains': ['18.b1.a1', '27.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9.b1.a1', 'projective_image': '9.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409268
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5412, 5412, 5988, 5988, 6082, 6082, 5797, 5797], 'generators': [37], 'label': '54.9.18.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '9.a1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '18.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409269
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.b1'], 'contains': ['54.a1.a1'], 'core': '18.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5412, 5412, 7082, 7082, 6082, 6082, 7017, 7017], 'generators': [19], 'label': '54.9.18.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '18.a1.b1', 'normal_contained_in': ['6.a1.a1', '9.a1.b1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.b1', 'projective_image': '18.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409270
{'ambient': '54.9', 'aut_centralizer_order': 18, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': ['3.b1.a1', '3.b1.b1', '3.b1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.a1.c1'], 'contains': ['54.a1.a1'], 'core': '18.a1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5412, 5412, 4893, 4893, 6082, 6082, 4576, 4576], 'generators': [1], 'label': '54.9.18.a1.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '18.a1.c1', 'normal_contained_in': ['6.a1.a1', '9.a1.c1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.c1', 'projective_image': '18.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409271
{'ambient': '54.9', 'aut_centralizer_order': 54, 'aut_label': '18.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 54, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1', '9.b1.a1'], 'contains': ['54.a1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2832, 2832, 3191, 3191, 3977, 3977, 3322, 3322], 'generators': [18], 'label': '54.9.18.b1.a1', 'mobius_quo': -1, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.c1', '6.b1.a1', '6.b1.b1', '9.b1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '18.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409272
{'ambient': '54.9', 'aut_centralizer_order': 108, 'aut_label': '27.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 108, 'centralizer': '1.a1.a1', 'complements': ['2.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.a1.b1', '9.a1.c1', '9.b1.a1'], 'contains': ['54.a1.a1'], 'core': '27.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7383, 7383, 7918, 7918, 8187, 8187, 8237, 8237], 'generators': [27], 'label': '54.9.27.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '27.a1.a1', 'normal_contained_in': ['9.a1.a1', '9.a1.c1', '9.a1.b1', '9.b1.a1'], 'normal_contains': ['54.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '27.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '27.2', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409273
{'ambient': '54.9', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '108.28', 'aut_weyl_index': 1, 'centralizer': '1.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '6.b1.c1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2115, 2115, 2478, 2478, 1725, 1725, 1000, 1000], 'generators': [1, 6], 'label': '54.9.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.c1', '6.b1.a1', '6.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '2.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409274
{'ambient': '54.9', 'aut_centralizer_order': None, 'aut_label': '54.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': ['18.a1.a1', '18.a1.b1', '18.a1.c1', '18.b1.a1', '27.a1.a1'], 'contains': [], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5412, 5412, 5988, 5988, 6082, 6082, 5797, 5797], 'generators': [], 'label': '54.9.54.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1', '18.a1.c1', '18.a1.b1', '18.b1.a1', '27.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '54.9', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409275
{'ambient': '54.9', 'aut_centralizer_order': 9, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 9, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '9.a1.a1', '9.a1.b1', '9.a1.c1', '9.b1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8818, 8818, 7356, 7356, 8275, 8275, 7780, 7780], 'generators': [27, 1, 18], 'label': '54.9.3.a1.a1', 'mobius_quo': -3, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '9.a1.a1', '9.a1.c1', '9.a1.b1', '9.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '3.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409276
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['18.a1.c1', '18.a1.b1', '18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.b1.a1'], 'core': '3.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4802, 4802, 4954, 4954, 5000, 5000, 5881, 5881], 'generators': [27, 6, 18], 'label': '54.9.3.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1', '9.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.a1', 'projective_image': '3.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409277
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['18.a1.c1', '18.a1.b1', '18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.b1', '9.b1.a1'], 'core': '3.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4802, 4802, 547, 547, 5000, 5000, 2898, 2898], 'generators': [27, 13, 18], 'label': '54.9.3.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.b1', '9.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.b1', 'projective_image': '3.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409278
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['18.a1.c1', '18.a1.b1', '18.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.c1', '9.b1.a1'], 'core': '3.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4802, 4802, 3617, 3617, 5000, 5000, 4390, 4390], 'generators': [27, 7, 18], 'label': '54.9.3.b1.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1.c1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.c1', '9.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.b1.c1', 'projective_image': '3.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.b1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409279
{'ambient': '54.9', 'aut_centralizer_order': 9, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 9, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.a1.c1', '18.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3943, 3943, 6079, 6079, 3977, 3977, 4576, 4576], 'generators': [1, 18], 'label': '54.9.6.a1.a1', 'mobius_quo': 3, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['18.a1.a1', '18.a1.c1', '18.a1.b1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '6.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409280
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['9.a1.c1', '9.a1.b1', '9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1182, 1182, 3176, 3176, 1725, 1725, 3271, 3271], 'generators': [6], 'label': '54.9.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.b1.a1'], 'normal_contains': ['18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '6.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 59409281
{'ambient': '54.9', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 18, 'centralizer': '1.a1.a1', 'complements': ['9.a1.c1', '9.a1.b1', '9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.b1'], 'contains': ['18.b1.a1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1182, 1182, 410, 410, 1725, 1725, 831, 831], 'generators': [13], 'label': '54.9.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.a1.a1', '3.b1.b1'], 'normal_contains': ['18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '6.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.b1', '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.