LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-10-22T13:09:39.808073

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

gps_groups • Show schema

{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 4, 12], 'aut_gens': [[1, 4], [1, 44], [1, 78], [1, 52], [21, 78]], 'aut_group': '192.1103', 'aut_hash': 1103, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 11, 'aut_perms': [368047, 6, 11640, 3991702], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 1, 1], [4, 3, 4, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 1, 4, 1], [10, 1, 8, 1], [15, 2, 4, 1], [20, 3, 16, 1], [30, 2, 4, 1], [30, 2, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.25', 'autcent_hash': 25, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 3, 4], [5, 1, 4], [6, 2, 3], [10, 1, 12], [15, 2, 4], [20, 3, 16], [30, 2, 12]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 24, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 3, 2, 2], [5, 1, 4, 1], [6, 2, 1, 3], [10, 1, 4, 3], [15, 2, 4, 1], [20, 3, 8, 2], [30, 2, 4, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 60, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '60.11', 'hash': 24, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 44], [81, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 20]], 'label': '120.24', 'linC_count': 288, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 16, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6:C20', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 60, 'number_divisions': 20, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 32, 'number_subgroups': 44, 'old_label': None, 'order': 120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 12], [5, 4], [6, 6], [10, 12], [15, 8], [20, 48], [30, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 6], [1, 52], [61, 78]], 'outer_group': '32.25', 'outer_hash': 25, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [120, 9, 11640], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 4], [8, 6]], 'representations': {'PC': {'code': 28150541561476103, 'gens': [1, 3], 'pres': [5, -2, -2, -2, -3, -5, 10, 662, 42, 1763, 78]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1209169791, 418186983, 2143735230, 676010852, 1612184451]}, 'Perm': {'d': 14, 'gens': [483033600, 1, 870, 7983360, 6706022400]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6:C_{20}', 'transitive_degree': 120, '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: 39103312
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 24, 'group_order': 120, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 39103323
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 24, 'group_order': 120, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 2, 'size': 1}
id: 39103334
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 24, 'group_order': 120, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 60, 'size': 1}
id: 39103345
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 24, 'group_order': 120, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 62, 'size': 1}
id: 39103356
{'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 5, 'group_counter': 24, 'group_order': 120, 'label': '3A', 'order': 3, 'powers': [5, 1, 5], 'representative': 40, 'size': 2}
id: 39103367
{'aut_label': '4A1', 'centralizer': '3.a1.a1', 'counter': 6, 'group_counter': 24, 'group_order': 120, 'label': '4A1', 'order': 4, 'powers': [2, 7, 6], 'representative': 1, 'size': 3}
id: 39103369
{'aut_label': '4A1', 'centralizer': '3.a1.a1', 'counter': 7, 'group_counter': 24, 'group_order': 120, 'label': '4A-1', 'order': 4, 'powers': [2, 6, 7], 'representative': 3, 'size': 3}
id: 39103370
{'aut_label': '4A1', 'centralizer': '3.a1.a1', 'counter': 8, 'group_counter': 24, 'group_order': 120, 'label': '4B1', 'order': 4, 'powers': [2, 9, 8], 'representative': 101, 'size': 3}
id: 39103371
{'aut_label': '4A1', 'centralizer': '3.a1.a1', 'counter': 9, 'group_counter': 24, 'group_order': 120, 'label': '4B-1', 'order': 4, 'powers': [2, 8, 9], 'representative': 103, 'size': 3}
id: 39103313
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 24, 'group_order': 120, 'label': '5A1', 'order': 5, 'powers': [12, 13, 1], 'representative': 96, 'size': 1}
id: 39103314
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 11, 'group_counter': 24, 'group_order': 120, 'label': '5A-1', 'order': 5, 'powers': [13, 12, 1], 'representative': 24, 'size': 1}
id: 39103315
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 12, 'group_counter': 24, 'group_order': 120, 'label': '5A2', 'order': 5, 'powers': [11, 10, 1], 'representative': 72, 'size': 1}
id: 39103316
{'aut_label': '5A1', 'centralizer': '1.a1.a1', 'counter': 13, 'group_counter': 24, 'group_order': 120, 'label': '5A-2', 'order': 5, 'powers': [10, 11, 1], 'representative': 48, 'size': 1}
id: 39103317
{'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 24, 'group_order': 120, 'label': '6A', 'order': 6, 'powers': [5, 3, 14], 'representative': 20, 'size': 2}
id: 39103318
{'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 24, 'group_order': 120, 'label': '6B', 'order': 6, 'powers': [5, 2, 15], 'representative': 42, 'size': 2}
id: 39103319
{'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 16, 'group_counter': 24, 'group_order': 120, 'label': '6C', 'order': 6, 'powers': [5, 4, 16], 'representative': 22, 'size': 2}
id: 39103320
{'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 24, 'group_order': 120, 'label': '10A1', 'order': 10, 'powers': [10, 19, 2], 'representative': 50, 'size': 1}
id: 39103321
{'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 24, 'group_order': 120, 'label': '10A-1', 'order': 10, 'powers': [11, 20, 2], 'representative': 74, 'size': 1}
id: 39103322
{'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 24, 'group_order': 120, 'label': '10A3', 'order': 10, 'powers': [13, 18, 2], 'representative': 26, 'size': 1}
id: 39103324
{'aut_label': '10A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 24, 'group_order': 120, 'label': '10A-3', 'order': 10, 'powers': [12, 17, 2], 'representative': 98, 'size': 1}
id: 39103325
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 24, 'group_order': 120, 'label': '10B1', 'order': 10, 'powers': [11, 23, 3], 'representative': 12, 'size': 1}
id: 39103326
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 24, 'group_order': 120, 'label': '10B-1', 'order': 10, 'powers': [10, 24, 3], 'representative': 108, 'size': 1}
id: 39103327
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 24, 'group_order': 120, 'label': '10B3', 'order': 10, 'powers': [12, 22, 3], 'representative': 36, 'size': 1}
id: 39103328
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 24, 'group_order': 120, 'label': '10B-3', 'order': 10, 'powers': [13, 21, 3], 'representative': 84, 'size': 1}
id: 39103329
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 25, 'group_counter': 24, 'group_order': 120, 'label': '10C1', 'order': 10, 'powers': [11, 27, 4], 'representative': 14, 'size': 1}
id: 39103330
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 26, 'group_counter': 24, 'group_order': 120, 'label': '10C-1', 'order': 10, 'powers': [10, 28, 4], 'representative': 110, 'size': 1}
id: 39103331
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 27, 'group_counter': 24, 'group_order': 120, 'label': '10C3', 'order': 10, 'powers': [12, 26, 4], 'representative': 38, 'size': 1}
id: 39103332
{'aut_label': '10B1', 'centralizer': '1.a1.a1', 'counter': 28, 'group_counter': 24, 'group_order': 120, 'label': '10C-3', 'order': 10, 'powers': [13, 25, 4], 'representative': 86, 'size': 1}
id: 39103333
{'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 24, 'group_order': 120, 'label': '15A1', 'order': 15, 'powers': [31, 11, 5], 'representative': 8, 'size': 2}
id: 39103335
{'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 24, 'group_order': 120, 'label': '15A-1', 'order': 15, 'powers': [32, 10, 5], 'representative': 112, 'size': 2}
id: 39103336
{'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 31, 'group_counter': 24, 'group_order': 120, 'label': '15A2', 'order': 15, 'powers': [30, 13, 5], 'representative': 16, 'size': 2}
id: 39103337
{'aut_label': '15A1', 'centralizer': '2.a1.a1', 'counter': 32, 'group_counter': 24, 'group_order': 120, 'label': '15A-2', 'order': 15, 'powers': [29, 12, 5], 'representative': 104, 'size': 2}
id: 39103338
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 33, 'group_counter': 24, 'group_order': 120, 'label': '20A1', 'order': 20, 'powers': [17, 35, 6], 'representative': 25, 'size': 3}
id: 39103339
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 34, 'group_counter': 24, 'group_order': 120, 'label': '20A-1', 'order': 20, 'powers': [18, 36, 7], 'representative': 19, 'size': 3}
id: 39103340
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 35, 'group_counter': 24, 'group_order': 120, 'label': '20A3', 'order': 20, 'powers': [19, 39, 7], 'representative': 75, 'size': 3}
id: 39103341
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 36, 'group_counter': 24, 'group_order': 120, 'label': '20A-3', 'order': 20, 'powers': [20, 40, 6], 'representative': 9, 'size': 3}
id: 39103342
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 37, 'group_counter': 24, 'group_order': 120, 'label': '20A7', 'order': 20, 'powers': [20, 33, 7], 'representative': 11, 'size': 3}
id: 39103343
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 38, 'group_counter': 24, 'group_order': 120, 'label': '20A-7', 'order': 20, 'powers': [19, 34, 6], 'representative': 73, 'size': 3}
id: 39103344
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 39, 'group_counter': 24, 'group_order': 120, 'label': '20A9', 'order': 20, 'powers': [18, 37, 6], 'representative': 17, 'size': 3}
id: 39103346
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 40, 'group_counter': 24, 'group_order': 120, 'label': '20A-9', 'order': 20, 'powers': [17, 38, 7], 'representative': 27, 'size': 3}
id: 39103347
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 41, 'group_counter': 24, 'group_order': 120, 'label': '20B1', 'order': 20, 'powers': [17, 43, 8], 'representative': 5, 'size': 3}
id: 39103348
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 42, 'group_counter': 24, 'group_order': 120, 'label': '20B-1', 'order': 20, 'powers': [18, 44, 9], 'representative': 79, 'size': 3}
id: 39103349
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 43, 'group_counter': 24, 'group_order': 120, 'label': '20B3', 'order': 20, 'powers': [19, 47, 9], 'representative': 15, 'size': 3}
id: 39103350
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 44, 'group_counter': 24, 'group_order': 120, 'label': '20B-3', 'order': 20, 'powers': [20, 48, 8], 'representative': 29, 'size': 3}
id: 39103351
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 45, 'group_counter': 24, 'group_order': 120, 'label': '20B7', 'order': 20, 'powers': [20, 41, 9], 'representative': 31, 'size': 3}
id: 39103352
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 46, 'group_counter': 24, 'group_order': 120, 'label': '20B-7', 'order': 20, 'powers': [19, 42, 8], 'representative': 13, 'size': 3}
id: 39103353
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 47, 'group_counter': 24, 'group_order': 120, 'label': '20B9', 'order': 20, 'powers': [18, 45, 8], 'representative': 77, 'size': 3}
id: 39103354
{'aut_label': '20A1', 'centralizer': '3.a1.a1', 'counter': 48, 'group_counter': 24, 'group_order': 120, 'label': '20B-9', 'order': 20, 'powers': [17, 46, 9], 'representative': 7, 'size': 3}
id: 39103355
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 49, 'group_counter': 24, 'group_order': 120, 'label': '30A1', 'order': 30, 'powers': [29, 21, 14], 'representative': 4, 'size': 2}
id: 39103357
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 50, 'group_counter': 24, 'group_order': 120, 'label': '30A-1', 'order': 30, 'powers': [30, 22, 14], 'representative': 76, 'size': 2}
id: 39103358
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 51, 'group_counter': 24, 'group_order': 120, 'label': '30A7', 'order': 30, 'powers': [31, 24, 14], 'representative': 28, 'size': 2}
id: 39103359
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 52, 'group_counter': 24, 'group_order': 120, 'label': '30A-7', 'order': 30, 'powers': [32, 23, 14], 'representative': 52, 'size': 2}
id: 39103360
{'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 53, 'group_counter': 24, 'group_order': 120, 'label': '30B1', 'order': 30, 'powers': [31, 19, 15], 'representative': 10, 'size': 2}
id: 39103361
{'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 54, 'group_counter': 24, 'group_order': 120, 'label': '30B-1', 'order': 30, 'powers': [32, 20, 15], 'representative': 34, 'size': 2}
id: 39103362
{'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 55, 'group_counter': 24, 'group_order': 120, 'label': '30B7', 'order': 30, 'powers': [30, 17, 15], 'representative': 18, 'size': 2}
id: 39103363
{'aut_label': '30B1', 'centralizer': '2.a1.a1', 'counter': 56, 'group_counter': 24, 'group_order': 120, 'label': '30B-7', 'order': 30, 'powers': [29, 18, 15], 'representative': 66, 'size': 2}
id: 39103364
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 57, 'group_counter': 24, 'group_order': 120, 'label': '30C1', 'order': 30, 'powers': [29, 25, 16], 'representative': 6, 'size': 2}
id: 39103365
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 58, 'group_counter': 24, 'group_order': 120, 'label': '30C-1', 'order': 30, 'powers': [30, 26, 16], 'representative': 78, 'size': 2}
id: 39103366
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 59, 'group_counter': 24, 'group_order': 120, 'label': '30C7', 'order': 30, 'powers': [31, 28, 16], 'representative': 30, 'size': 2}
id: 39103368
{'aut_label': '30A1', 'centralizer': '2.a1.a1', 'counter': 60, 'group_counter': 24, 'group_order': 120, 'label': '30C-7', 'order': 30, 'powers': [32, 27, 16], 'representative': 54, 'size': 2}

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: 60722
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 60733
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1b', '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, -1, -1, -1, -1, -1, 1], 'schur_index': 1}
id: 60735
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 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: 60736
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -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: 60737
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2], 'schur_index': 1}
id: 60738
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, -2, -2, 2, 2, -2, -2, 2, -2, -2], 'schur_index': 1}
id: 60726
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 60727
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, 1, 1, 2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1], 'schur_index': 1}
id: 60728
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2c', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 1, -1, 1, -2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 2}
id: 60729
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2d', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, -1, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1], 'schur_index': 2}
id: 60739
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1g', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 60740
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1h', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, -1, -1, -1, -1, 4, -4, -4, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1], 'schur_index': 1}
id: 60741
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1i', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, 4, -4, -4, -1, -1, -1, -1, 4, -4, -4, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1], 'schur_index': 1}
id: 60723
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1j', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, -4, -4, -4, -4, -1, -1, -1, -1, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 60724
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1k', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 8, 0, 0, 0, 0, -2, -2, -2, -2, -8, 8, -8, 2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2], 'schur_index': 1}
id: 60725
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.1l', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 8, 0, 0, 0, 0, -2, -2, -2, -2, -8, -8, 8, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, -2, 2, 2, -2, 2, 2], 'schur_index': 1}
id: 60730
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2e', 'multiplicity': 4, 'nt': [15, 4], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, 0, 0, 0, 0, -2, -2, -2, -2, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 60731
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2f', 'multiplicity': 4, 'nt': [30, 12], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -4, 0, 0, 0, 0, -2, -2, -2, -2, -4, 4, 4, -2, 2, -2, 2, 2, 2, -2, 2, 2, 2, 2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1], 'schur_index': 1}
id: 60732
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2g', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -4, 0, 0, 0, 0, -2, -2, -2, -2, 4, -4, 4, 2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
id: 60734
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '120.24', 'group_order': 120, 'image': None, 'label': '120.24.2h', 'multiplicity': 4, 'nt': [60, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -4, 0, 0, 0, 0, -2, -2, -2, -2, 4, 4, -4, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1], 'schur_index': 1}

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

gps_char • Show schema

id: 40693
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 120, 'label': '120.24.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 40704
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 60, 'label': '120.24.1b', '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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
id: 40715
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 60, 'label': '120.24.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 40726
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 60, 'label': '120.24.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 40737
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 30, 'label': '120.24.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 40748
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 30, 'label': '120.24.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 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, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 40750
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 30, 'label': '120.24.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 40751
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 30, 'label': '120.24.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 40752
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 9, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.24.1g1', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]]]}
id: 40694
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 10, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.24.1g2', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]]]}
id: 40695
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 11, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.24.1g3', 'nt': [5, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]]]}
id: 40696
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 12, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '5.1', 'image_order': 5, 'indicator': 0, 'kernel': '5.a1.a1', 'kernel_order': 24, 'label': '120.24.1g4', 'nt': [5, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]]]}
id: 40697
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 13, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 12, 'label': '120.24.1h1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[-1, -2]], [[-1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, -2]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[1, 2]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, -1]]]}
id: 40698
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 14, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 12, 'label': '120.24.1h2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[-1, -2]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[-1, 2]], [[-1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 2]], [[-1, -1]], [[-1, -2]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[1, -2]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, 1]]]}
id: 40699
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 15, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 12, 'label': '120.24.1h3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[-1, -1]], [[-1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[1, -1]], [[-1, -2]], [[-1, 1]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[1, 1]], [[-1, -2]], [[-1, 1]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, 2]]]}
id: 40700
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 16, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.b1', 'kernel_order': 12, 'label': '120.24.1h4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[-1, 1]], [[-1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[1, 1]], [[-1, 2]], [[-1, -1]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[1, -1]], [[-1, 2]], [[-1, -1]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, -2]]]}
id: 40701
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 17, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.24.1i1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 2]], [[-1, 1]], [[1, -2]], [[1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, -2]], [[1, 1]], [[1, 2]], [[-1, 2]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[1, -1]]]}
id: 40702
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 18, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.24.1i2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[-1, -2]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -2]], [[-1, -1]], [[1, 2]], [[1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[-1, 2]], [[1, -1]], [[1, -2]], [[-1, -2]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[1, 1]]]}
id: 40703
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 19, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.24.1i3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, 2]], [[-1, 1]], [[-1, -2]], [[1, -1]], [[1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[1, 2]], [[-1, -1]], [[1, -2]], [[1, 1]], [[-1, 1]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, -2]], [[-1, 1]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[1, 2]]]}
id: 40705
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 20, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.b1.a1', 'kernel_order': 12, 'label': '120.24.1i4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, -2]], [[-1, -1]], [[-1, 2]], [[1, 1]], [[1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[1, -2]], [[-1, 1]], [[1, 2]], [[1, -1]], [[-1, -1]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, 2]], [[-1, -1]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[1, -2]]]}
id: 40706
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 21, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.24.1j1', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]]]}
id: 40707
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 22, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.24.1j2', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]]]}
id: 40708
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 23, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.24.1j3', 'nt': [10, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, 2]], [[1, -2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -2]], [[1, 2]], [[-1, 2]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 1]], [[-1, -2]], [[-1, -1]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]]]}
id: 40709
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 24, 'cyclotomic_n': 5, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '10.2', 'image_order': 10, 'indicator': 0, 'kernel': '10.a1.a1', 'kernel_order': 12, 'label': '120.24.1j4', 'nt': [10, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, -2]], [[1, 2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 2]], [[1, -2]], [[-1, -2]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, 2]], [[-1, 1]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]]]}
id: 40710
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 25, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k1', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 4]], [[1, 8]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 6]], [[1, 1]], [[-1, 3]], [[1, 9]], [[1, 7]], [[-1, 3]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[1, 1]], [[-1, 1]], [[-1, 7]], [[-1, 9]], [[1, 3]], [[1, 3]], [[1, 9]], [[-1, 7]], [[-1, 8]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[-1, 4]], [[1, 8]], [[1, 6]]]}
id: 40711
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 26, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k2', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 2]], [[1, 4]], [[-1, 8]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[-1, 3]], [[1, 7]], [[1, 9]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[1, 9]], [[1, 3]], [[1, 1]], [[-1, 7]], [[-1, 7]], [[-1, 1]], [[1, 3]], [[1, 2]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 4]], [[1, 8]], [[1, 6]], [[-1, 2]], [[-1, 4]]]}
id: 40712
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 27, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 6]], [[-1, 2]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[1, 8]], [[1, 2]], [[1, 4]], [[-1, 8]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 9]], [[-1, 7]], [[1, 1]], [[1, 3]], [[-1, 7]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[1, 9]], [[-1, 9]], [[-1, 3]], [[-1, 1]], [[1, 7]], [[1, 7]], [[1, 1]], [[-1, 3]], [[1, 2]], [[-1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 4]], [[1, 8]], [[1, 6]], [[-1, 2]], [[-1, 4]]]}
id: 40713
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 28, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k4', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 4]], [[1, 8]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 6]], [[1, 4]], [[-1, 2]], [[-1, 8]], [[-1, 6]], [[1, 2]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 6]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[-1, 7]], [[1, 3]], [[1, 1]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[1, 1]], [[1, 7]], [[1, 9]], [[-1, 3]], [[-1, 3]], [[-1, 9]], [[1, 7]], [[-1, 8]], [[1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 6]], [[-1, 2]], [[-1, 4]], [[1, 8]], [[1, 6]]]}
id: 40714
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 29, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k5', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 4]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[1, 6]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[-1, 1]], [[1, 9]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 7]], [[-1, 9]], [[-1, 9]], [[-1, 7]], [[1, 1]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[1, 8]], [[-1, 6]], [[1, 2]], [[1, 4]], [[-1, 8]]]}
id: 40716
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 30, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k6', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 8]], [[-1, 6]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 2]], [[1, 8]], [[1, 4]], [[1, 6]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 7]], [[-1, 1]], [[1, 3]], [[1, 9]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[1, 7]], [[-1, 7]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 9]], [[1, 6]], [[1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 8]], [[-1, 6]], [[1, 2]]]}
id: 40717
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 31, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k7', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 8]], [[-1, 6]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[1, 2]], [[1, 8]], [[1, 4]], [[1, 6]], [[-1, 2]], [[-1, 4]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[-1, 9]], [[1, 1]], [[1, 7]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[1, 7]], [[1, 9]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 9]], [[1, 6]], [[1, 8]], [[1, 6]], [[-1, 4]], [[-1, 8]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 8]], [[-1, 6]], [[1, 2]]]}
id: 40718
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 32, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.b1', 'kernel_order': 6, 'label': '120.24.1k8', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 4]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 8]], [[-1, 8]], [[-1, 2]], [[-1, 6]], [[-1, 4]], [[1, 8]], [[1, 6]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[1, 8]], [[1, 3]], [[-1, 9]], [[1, 7]], [[1, 1]], [[-1, 9]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 7]], [[1, 9]], [[1, 9]], [[1, 7]], [[-1, 1]], [[-1, 4]], [[-1, 2]], [[-1, 4]], [[1, 6]], [[1, 2]], [[-1, 8]], [[1, 6]], [[1, 8]], [[-1, 6]], [[1, 2]], [[1, 4]], [[-1, 8]]]}
id: 40719
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 33, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l1', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 8]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 6]], [[1, 2]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 6]], [[1, 1]], [[1, 3]], [[-1, 9]], [[1, 7]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 9]], [[-1, 1]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[1, 3]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[-1, 8]], [[-1, 4]], [[1, 8]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 4]], [[-1, 8]], [[1, 6]]]}
id: 40720
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 34, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l2', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 6]], [[1, 2]], [[1, 2]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 4]], [[-1, 8]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[-1, 9]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[1, 7]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[1, 9]], [[1, 9]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 7]], [[-1, 1]], [[1, 3]], [[1, 2]], [[1, 6]], [[-1, 2]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 6]], [[1, 2]], [[-1, 4]]]}
id: 40721
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 35, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l3', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 6]], [[1, 2]], [[1, 2]], [[1, 8]], [[-1, 6]], [[1, 4]], [[-1, 4]], [[1, 6]], [[-1, 8]], [[-1, 2]], [[-1, 4]], [[-1, 8]], [[1, 8]], [[-1, 2]], [[-1, 6]], [[1, 4]], [[1, 9]], [[1, 7]], [[-1, 1]], [[1, 3]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[1, 1]], [[-1, 9]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 7]], [[1, 1]], [[-1, 3]], [[1, 2]], [[1, 6]], [[-1, 2]], [[-1, 8]], [[1, 6]], [[1, 4]], [[1, 8]], [[-1, 4]], [[-1, 8]], [[-1, 6]], [[1, 2]], [[-1, 4]]]}
id: 40722
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 36, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l4', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[-1, 8]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[-1, 6]], [[1, 6]], [[-1, 4]], [[1, 2]], [[1, 8]], [[1, 6]], [[1, 2]], [[-1, 2]], [[1, 8]], [[1, 4]], [[-1, 6]], [[-1, 1]], [[-1, 3]], [[1, 9]], [[-1, 7]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[1, 1]], [[1, 1]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[1, 3]], [[-1, 9]], [[1, 7]], [[-1, 8]], [[-1, 4]], [[1, 8]], [[1, 2]], [[-1, 4]], [[-1, 6]], [[-1, 2]], [[1, 6]], [[1, 2]], [[1, 4]], [[-1, 8]], [[1, 6]]]}
id: 40723
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 37, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l5', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 8]], [[1, 6]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[1, 8]], [[-1, 3]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[1, 9]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 3]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[1, 9]], [[-1, 7]], [[1, 1]], [[-1, 4]], [[1, 2]], [[1, 4]], [[1, 6]], [[1, 2]], [[1, 8]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 2]], [[-1, 4]], [[-1, 8]]]}
id: 40724
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 38, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l6', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 8]], [[1, 6]], [[1, 6]], [[1, 4]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[1, 7]], [[1, 1]], [[-1, 3]], [[1, 9]], [[-1, 1]], [[1, 7]], [[-1, 9]], [[1, 3]], [[-1, 7]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[1, 6]], [[-1, 8]], [[-1, 6]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 8]], [[1, 6]], [[1, 2]]]}
id: 40725
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 39, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l7', 'nt': [20, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[1, 4]], [[1, 8]], [[-1, 6]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 8]], [[1, 6]], [[1, 6]], [[1, 4]], [[1, 8]], [[-1, 2]], [[1, 2]], [[-1, 8]], [[-1, 4]], [[-1, 6]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 6]], [[1, 8]], [[-1, 2]], [[-1, 7]], [[-1, 1]], [[1, 3]], [[-1, 9]], [[1, 1]], [[-1, 7]], [[1, 9]], [[-1, 3]], [[1, 7]], [[1, 7]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 9]], [[1, 6]], [[-1, 8]], [[-1, 6]], [[-1, 4]], [[-1, 8]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[1, 8]], [[1, 6]], [[1, 2]]]}
id: 40727
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 120, 'counter': 40, 'cyclotomic_n': 20, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '20.2', 'image_order': 20, 'indicator': 0, 'kernel': '20.b1.a1', 'kernel_order': 6, 'label': '120.24.1l8', 'nt': [20, 8], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[-1, 6]], [[-1, 2]], [[1, 4]], [[1, 8]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 6]], [[-1, 2]], [[1, 8]], [[-1, 8]], [[1, 2]], [[1, 6]], [[1, 4]], [[-1, 8]], [[1, 6]], [[-1, 6]], [[1, 4]], [[-1, 2]], [[1, 8]], [[1, 3]], [[1, 9]], [[-1, 7]], [[1, 1]], [[-1, 9]], [[1, 3]], [[-1, 1]], [[1, 7]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[-1, 7]], [[1, 9]], [[-1, 9]], [[1, 7]], [[-1, 1]], [[-1, 4]], [[1, 2]], [[1, 4]], [[1, 6]], [[1, 2]], [[1, 8]], [[-1, 6]], [[-1, 8]], [[1, 6]], [[-1, 2]], [[-1, 4]], [[-1, 8]]]}
id: 40728
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 41, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 20, 'label': '120.24.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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: 40729
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 42, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 10, 'label': '120.24.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-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: 40730
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 43, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.b1', 'kernel_order': 10, 'label': '120.24.2c', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 40731
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 44, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.a1', 'kernel_order': 10, 'label': '120.24.2d', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 40732
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 45, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.24.2e1', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]]]}
id: 40733
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 46, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.24.2e2', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 2]], [[2, -2]], [[2, 1]], [[2, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]]]}
id: 40734
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 47, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.24.2e3', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -2]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[2, 2]], [[2, -2]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, -1]], [[-1, -2]], [[-1, 2]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, -2]], [[-1, 1]], [[-1, 2]]]}
id: 40735
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 48, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '30.1', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 4, 'label': '120.24.2e4', 'nt': [15, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 2]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[2, -2]], [[2, 2]], [[2, 1]], [[2, -1]], [[2, -2]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 2]], [[-1, -1]], [[-1, 1]], [[-1, 2]], [[-1, -2]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -2]]]}
id: 40736
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 49, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.24.2f1', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[-2, 2]], [[2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[2, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[1, -1]], [[1, -2]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 2]], [[-1, -1]]]}
id: 40738
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 50, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.24.2f2', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, -1]], [[-2, -2]], [[2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[2, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -2]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[1, 1]], [[1, 2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -2]], [[-1, 1]]]}
id: 40739
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 51, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.24.2f3', 'nt': [30, 12], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, -2]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[2, 2]], [[-2, -2]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[1, 2]], [[1, -1]], [[1, 2]], [[1, -1]], [[1, -2]], [[1, 1]], [[-1, 2]]]}
id: 40740
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 52, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.11', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 2, 'label': '120.24.2f4', 'nt': [30, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 2]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[2, -2]], [[-2, 2]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[1, -2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[-1, -2]]]}
id: 40741
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 53, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.b1', 'kernel_order': 2, 'label': '120.24.2g1', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 1]], [[2, 2]], [[-2, 2]], [[-2, -2]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[2, -2]], [[-2, 2]], [[2, -1]], [[-2, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[-1, -1]], [[-1, -2]], [[1, 1]], [[-1, 2]], [[1, -1]]]}
id: 40742
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 54, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.b1', 'kernel_order': 2, 'label': '120.24.2g2', 'nt': [60, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, -1]], [[2, -2]], [[-2, -2]], [[-2, 2]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[2, 2]], [[-2, -2]], [[2, 1]], [[-2, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[-1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[-1, 1]], [[-1, 2]], [[1, -1]], [[-1, -2]], [[1, 1]]]}
id: 40743
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 55, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.b1', 'kernel_order': 2, 'label': '120.24.2g3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, -2]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -2]], [[-2, 2]], [[-2, 2]], [[2, -2]], [[2, -1]], [[-2, 1]], [[2, 2]], [[-2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, -2]], [[1, 1]], [[1, -1]], [[1, -2]], [[1, 2]], [[1, -1]], [[-1, 2]], [[-1, -1]], [[1, -2]], [[-1, 1]], [[1, 2]]]}
id: 40744
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 56, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.b1', 'kernel_order': 2, 'label': '120.24.2g4', 'nt': [60, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 2]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 2]], [[-2, -2]], [[-2, -2]], [[2, 2]], [[2, 1]], [[-2, -1]], [[2, -2]], [[-2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[-1, 2]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -2]], [[1, 1]], [[-1, -2]], [[-1, 1]], [[1, 2]], [[-1, -1]], [[1, -2]]]}
id: 40745
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 57, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 2, 'label': '120.24.2h1', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -2]], [[2, 1]], [[2, 2]], [[2, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 1]], [[-2, 2]], [[-2, 2]], [[2, -2]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -2]], [[2, 2]], [[-2, -1]], [[-2, -2]], [[-1, -2]], [[-1, 2]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[1, 1]], [[-1, 2]], [[1, -2]], [[1, 1]], [[-1, -1]], [[-1, -2]], [[1, -1]], [[1, -2]], [[-1, 1]], [[1, 2]], [[1, -1]]]}
id: 40746
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 58, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 2, 'label': '120.24.2h2', 'nt': [60, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[2, -1]], [[2, -2]], [[2, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, -1]], [[-2, -2]], [[-2, -2]], [[2, 2]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 2]], [[2, -2]], [[-2, 1]], [[-2, 2]], [[-1, 2]], [[-1, -2]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -2]], [[1, -1]], [[-1, -2]], [[1, 2]], [[1, -1]], [[-1, 1]], [[-1, 2]], [[1, 1]], [[1, 2]], [[-1, -1]], [[1, -2]], [[1, 1]]]}
id: 40747
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 59, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 2, 'label': '120.24.2h3', 'nt': [60, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -2]], [[2, 1]], [[2, 2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, -2]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[2, -2]], [[2, 2]], [[-2, 2]], [[-2, -2]], [[-2, -1]], [[2, 1]], [[-2, 2]], [[-2, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -2]], [[-1, 1]], [[1, -1]], [[1, -2]], [[-1, 2]], [[-1, -1]], [[1, 2]], [[1, -1]], [[-1, -2]], [[1, 1]], [[1, 2]]]}
id: 40749
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 20, 'counter': 60, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '120.24', 'group_counter': 24, 'group_order': 120, 'image': None, 'image_isoclass': '60.1', 'image_order': 60, 'indicator': 0, 'kernel': '60.b1.a1', 'kernel_order': 2, 'label': '120.24.2h4', 'nt': [60, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 2]], [[2, -1]], [[2, -2]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 2]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[2, 2]], [[2, -2]], [[-2, -2]], [[-2, 2]], [[-2, 1]], [[2, -1]], [[-2, -2]], [[-2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 2]], [[-1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 2]], [[-1, -1]], [[1, 1]], [[1, 2]], [[-1, -2]], [[-1, 1]], [[1, -2]], [[1, 1]], [[-1, 2]], [[1, -1]], [[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: 6580652
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 120, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '120.24.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.24', 'subgroup_hash': 24, 'subgroup_order': 120, 'subgroup_tex': 'C_6:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580663
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 60, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.24.2.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': ['F', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
id: 6580674
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 60, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '120.24.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580678
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 60, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '120.24.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', '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': '60.1', 'subgroup_hash': 1, 'subgroup_order': 60, 'subgroup_tex': 'C_3:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '120.24.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580680
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 30, 'counter': 6, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
id: 6580681
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 30, 'counter': 7, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
id: 6580682
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 30, 'counter': 8, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
id: 6580683
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': True, 'core_order': 24, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '120.24.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 6580653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 20, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.24.6.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': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 6580654
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 11, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.24.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580655
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 12, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.24.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 6580656
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 15, 'counter': 13, 'cyclic': True, 'direct': False, 'hall': 15, 'label': '120.24.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
id: 6580657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 12, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.24.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 6580658
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 12, 'counter': 15, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '120.24.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 6580659
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': True, 'centralizer_order': 20, 'characteristic': False, 'core_order': 12, 'counter': 16, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '120.24.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 6580660
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 10, 'counter': 17, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 6580661
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 10, 'counter': 18, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '120.24.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 6580662
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 10, 'counter': 19, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '120.24.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 6580664
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '120.24.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 2}
id: 6580665
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 6, 'counter': 21, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 6580666
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', '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: 6580667
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 6, 'counter': 23, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', '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: 6580668
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 5, 'counter': 24, 'cyclic': True, 'direct': True, 'hall': 5, 'label': '120.24.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_4', 'simple': True, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 6580669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '120.24.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 6580670
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.24.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 6580671
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '120.24.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 6580672
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': True, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '120.24.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 6580673
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 2, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '120.24.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{10}', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 6580675
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '120.24.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{20}', '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': 0}
id: 6580676
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '120.24.60.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '60.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_{20}', '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': 0}
id: 6580677
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '120.24', 'ambient_counter': 24, 'ambient_order': 120, 'ambient_tex': 'C_6:C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 120, 'characteristic': True, 'core_order': 1, 'counter': 32, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '120.24.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '120.24', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:C_{20}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 6580652
{'ambient': '120.24', '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': '6.a1.a1', 'complements': ['120.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7012, 2642, 7040, 7744, 5530, 5818, 5557, 4110], 'generators': [1, 24, 2, 60, 80], 'label': '120.24.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '6.1', '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': '6.1'}
id: 6580653
{'ambient': '120.24', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '30.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2753, 8885, 3416, 1141, 3217, 2788, 2390, 8924], 'generators': [2, 24, 60], 'label': '120.24.6.a1.a1', 'mobius_quo': -2, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.b1', '12.b1.a1', '12.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '6.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580654
{'ambient': '120.24', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6363, -1, 6027, -1, 6602, -1, 5749, -1], 'generators': [1, 2, 24], 'label': '120.24.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580655
{'ambient': '120.24', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '30.b1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6363, -1, 7418, -1, 6602, -1, 6593, -1], 'generators': [101, 2, 24], 'label': '120.24.6.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580656
{'ambient': '120.24', 'aut_centralizer_order': 24, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': ['15.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['24.a1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [454, 5861, 348, 4179, 685, 2130, 1363, 6213], 'generators': [80, 24], 'label': '120.24.8.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.b1.b1', '4.b1.a1', '4.a1.a1'], 'normal_contains': ['24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580657
{'ambient': '120.24', 'aut_centralizer_order': 48, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 48, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.b1.b1', '30.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5364, 3047, 5878, 6135, 5155, 6909, 4674, 3680], 'generators': [2, 60, 80], 'label': '120.24.10.a1.a1', 'mobius_quo': -2, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.b1.b1', '20.b1.a1', '20.a1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '30.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580658
{'ambient': '120.24', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 16, 'centralizer': '6.a1.a1', 'complements': ['12.b1.a1', '12.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.b1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9597, 1340, 7765, 7960, 7765, 8883, 7457, 2236], 'generators': [1, 2, 80], 'label': '120.24.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '60.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 6580659
{'ambient': '120.24', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 16, 'centralizer': '6.a1.a1', 'complements': ['12.b1.a1', '12.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.a1.a1', '30.b1.b1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9597, 1340, 9057, 9065, 7765, 8883, 9645, 1070], 'generators': [101, 2, 80], 'label': '120.24.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.b1.b1', '5.a1.a1'], 'normal_contains': ['20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '60.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 6580660
{'ambient': '120.24', 'aut_centralizer_order': 48, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 48, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1'], 'contains': ['24.a1.a1', '60.a1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3701, 6998, 4558, 2990, 3889, 4901, 4434, 7328], 'generators': [2, 24], 'label': '120.24.12.a1.a1', 'mobius_quo': 1, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580661
{'ambient': '120.24', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 48, 'centralizer': '1.a1.a1', 'complements': ['10.b1.a1', '10.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '60.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [948, 8315, 526, 1477, 1822, 606, 2207, 9557], 'generators': [60, 24], 'label': '120.24.12.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '12.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580662
{'ambient': '120.24', 'aut_centralizer_order': 24, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 48, 'centralizer': '1.a1.a1', 'complements': ['10.b1.a1', '10.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1'], 'contains': ['24.a1.a1', '60.b1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [948, 8315, 2343, 420, 1822, 606, 518, 8442], 'generators': [62, 24], 'label': '120.24.12.b1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '60.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '12.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580663
{'ambient': '120.24', 'aut_centralizer_order': 12, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 12, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.a1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4065, 5112, 3733, 4851, 2339, 2961, 2390, 7264], 'generators': [2, 80, 24, 60], 'label': '120.24.2.a1.a1', 'mobius_quo': 2, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.b1.a1', '4.a1.a1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '6.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580664
{'ambient': '120.24', 'aut_centralizer_order': 8, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 24, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.b1.b1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8610, -1, 9115, -1, 9238, -1, 8551, -1], 'generators': [1, 60], 'label': '120.24.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '30.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580665
{'ambient': '120.24', 'aut_centralizer_order': 96, 'aut_label': '20.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['40.a1.a1', '60.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6493, 3016, 6653, 7132, 4923, 7706, 5989, 2337], 'generators': [2, 80], 'label': '120.24.20.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580666
{'ambient': '120.24', 'aut_centralizer_order': 48, 'aut_label': '20.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': ['6.b1.a1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.b1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2818, 4095, 2205, 5907, 2855, 3515, 3666, 4161], 'generators': [60, 80], 'label': '120.24.20.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.b1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '60.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580667
{'ambient': '120.24', 'aut_centralizer_order': 48, 'aut_label': '20.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': ['6.b1.a1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.b1.b1'], 'core': '20.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2818, 4095, 3316, 4454, 2855, 3515, 2975, 3249], 'generators': [62, 80], 'label': '120.24.20.b1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': ['4.b1.b1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '60.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.b1', 'projective_image': '60.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580668
{'ambient': '120.24', 'aut_centralizer_order': 48, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 48, 'centralizer': '1.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1'], 'contains': ['120.a1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [403, 8016, 357, 2437, 1848, 2199, 2207, 7328], 'generators': [24], 'label': '120.24.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.b1', '12.b1.a1', '12.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.7', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.7', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580669
{'ambient': '120.24', 'aut_centralizer_order': 96, 'aut_label': '30.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.b1.b1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4727, 7582, 4678, 3026, 5917, 6372, 5250, 5136], 'generators': [2, 60], 'label': '120.24.30.a1.a1', 'mobius_quo': 2, 'mobius_sub': -3, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1'], 'normal_contains': ['60.b1.b1', '60.b1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '30.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '30.1', 'quotient_action_kernel_order': 30, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580670
{'ambient': '120.24', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8130, -1, 7904, -1, 7339, -1, 7063, -1], 'generators': [1], 'label': '120.24.30.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '60.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580671
{'ambient': '120.24', 'aut_centralizer_order': 16, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8130, -1, 9652, -1, 7339, -1, 8148, -1], 'generators': [101], 'label': '120.24.30.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '30.b1.b1', 'projective_image': '60.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580672
{'ambient': '120.24', 'aut_centralizer_order': 96, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 96, 'centralizer': '2.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.b1.b1'], 'contains': ['120.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2558, 4962, 2691, 5763, 2804, 4727, 3628, 3490], 'generators': [80], 'label': '120.24.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.b1.b1', '20.b1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '120.24', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580673
{'ambient': '120.24', 'aut_centralizer_order': 192, 'aut_label': '60.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1', '30.b1.a1', '30.b1.b1'], 'contains': ['120.a1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5507, 6340, 6018, 4754, 4923, 6164, 5614, 4402], 'generators': [2], 'label': '120.24.60.a1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '60.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.11', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580674
{'ambient': '120.24', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 4, 'centralizer': '6.a1.a1', 'complements': ['60.b1.a1', '60.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7675, 2642, 5700, 7132, 4470, 5818, 3973, 5174], 'generators': [1, 2, 80, 24], 'label': '120.24.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 6580675
{'ambient': '120.24', 'aut_centralizer_order': 96, 'aut_label': '60.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1650, 7582, 2045, 3386, 3734, 3481, 4319, 6226], 'generators': [60], 'label': '120.24.60.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '60.b1.a1', 'normal_contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '60.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.1', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580676
{'ambient': '120.24', 'aut_centralizer_order': 96, 'aut_label': '60.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '20.b1.b1', '30.a1.a1'], 'contains': ['120.a1.a1'], 'core': '60.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1650, 7582, 3694, 2521, 3734, 3481, 2937, 5314], 'generators': [62], 'label': '120.24.60.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '60.b1.b1', 'normal_contained_in': ['12.b1.b1', '20.b1.b1', '30.a1.a1'], 'normal_contains': ['120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.b1', 'projective_image': '60.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '60.1', 'quotient_action_kernel_order': 60, 'quotient_fusion': None, 'short_label': '60.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580677
{'ambient': '120.24', 'aut_centralizer_order': None, 'aut_label': '120.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': ['24.a1.a1', '40.a1.a1', '60.a1.a1', '60.b1.a1', '60.b1.b1'], 'contains': [], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2039, 7013, 2691, 3386, 3269, 4104, 3628, 5314], 'generators': [], 'label': '120.24.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.b1.b1', '60.b1.a1', '60.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.24', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580678
{'ambient': '120.24', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 4, 'centralizer': '6.a1.a1', 'complements': ['60.b1.a1', '60.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.b1', '10.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7675, 2642, 8054, 9580, 4470, 5818, 7140, 3059], 'generators': [101, 2, 80, 24], 'label': '120.24.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 6580679
{'ambient': '120.24', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.25', 'aut_weyl_index': 6, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '15.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6363, -1, 7050, -1, 6602, -1, 5557, -1], 'generators': [1, 24, 2, 60], 'label': '120.24.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 6580680
{'ambient': '120.24', 'aut_centralizer_order': 24, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4065, 5098, 4667, 6760, 1589, 4970, 3599, 5098], 'generators': [2, 24, 80], 'label': '120.24.4.a1.a1', 'mobius_quo': -1, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580681
{'ambient': '120.24', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': ['30.b1.a1', '30.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '20.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [792, 6609, 655, 4323, 452, 606, 1180, 7328], 'generators': [60, 24, 80], 'label': '120.24.4.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '12.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580682
{'ambient': '120.24', 'aut_centralizer_order': 12, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 24, 'centralizer': '2.a1.a1', 'complements': ['30.b1.a1', '30.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.b1.b1', '20.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [792, 6609, 2225, 3109, 452, 606, 336, 6213], 'generators': [62, 24, 80], 'label': '120.24.4.b1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.b1', '20.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '12.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 6580683
{'ambient': '120.24', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.38', 'aut_weyl_index': 4, 'centralizer': '6.a1.a1', 'complements': ['24.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9298, 1115, 9066, 8741, 8734, 8710, 8743, 944], 'generators': [1, 60, 2, 80], 'label': '120.24.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '30.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}

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.