LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.3', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 6, 4, 2, 2, 2, 2], 'aut_gens': [[1, 4], [97, 68], [179, 4], [1, 148], [3, 6], [99, 6], [99, 124], [3, 4]], 'aut_group': '768.1076219', 'aut_hash': 1076219, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 768, 'aut_permdeg': 17, 'aut_perms': [39916800, 88137834535, 1271166, 65470897065606, 44460928512000, 1, 44460928522807], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 2, 1, 1], [4, 1, 2, 2], [4, 6, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [8, 1, 4, 2], [8, 6, 4, 1], [12, 2, 2, 2], [16, 2, 8, 1], [16, 6, 8, 1], [24, 2, 4, 2], [48, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:C_2^2\\times D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.2167', 'autcent_hash': 2167, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4^2:C_2^3', '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, 1, 4], [4, 6, 4], [6, 2, 3], [8, 1, 8], [8, 6, 4], [12, 2, 4], [16, 2, 8], [16, 6, 8], [24, 2, 8], [48, 2, 16]], 'center_label': '16.5', 'center_order': 16, 'central_product': False, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 61, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [4, 6, 2, 2], [6, 2, 1, 3], [8, 1, 4, 2], [8, 6, 2, 2], [12, 2, 2, 2], [16, 2, 4, 2], [16, 6, 4, 2], [24, 2, 4, 2], [48, 2, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 48, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.5', 'frattini_quotient': '12.4', 'hash': 61, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6], 'inner_gens': [[1, 164], [33, 4]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 40]], 'label': '192.61', 'linC_count': 256, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 12, 'linQ_dim_count': 22, 'linR_count': 64, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C48:C4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 19, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 72, 'number_divisions': 26, 'number_normal_subgroups': 39, 'number_subgroup_autclasses': 42, 'number_subgroup_classes': 54, 'number_subgroups': 88, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [6, 6], [8, 32], [12, 8], [16, 64], [24, 16], [48, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 12, 0], 'outer_gens': [[3, 100], [3, 28], [1, 102], [147, 174], [1, 148]], 'outer_group': '64.263', 'outer_hash': 263, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [16, 41141527, 295915087, 40043527, 139754880], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [4, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 6], [8, 4], [16, 2]], 'representations': {'PC': {'code': 6155214535520528566357290638977, 'gens': [1, 3], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 14, 3446, 58, 3811, 80, 2804, 102, 6725, 124, 6278]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [110905, 3263857, 831619, 2764825, 111745, 111361, 111169]}, 'GLZq': {'d': 2, 'q': 64, 'gens': [7370083, 14026773, 2363831, 2359305, 4456465, 11405323, 8650785]}, 'Perm': {'d': 23, 'gens': [206924829509219633409, 1185330512248724217616, 16, 2508964433657547989760, 3693551238530158037760, 4718248621232758536960, 840]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 8], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{48}:C_4', 'transitive_degree': 192, '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: 96386126
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 61, 'group_order': 192, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 96386137
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 61, 'group_order': 192, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2, 'size': 1}
id: 96386148
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 61, 'group_order': 192, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 98, 'size': 1}
id: 96386159
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 61, 'group_order': 192, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 96, 'size': 1}
id: 96386170
{'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 61, 'group_order': 192, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 128, 'size': 2}
id: 96386181
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 61, 'group_order': 192, 'label': '4A1', 'order': 4, 'powers': [4, 7], 'representative': 146, 'size': 1}
id: 96386192
{'aut_label': '4A1', 'centralizer': '1.a1.a1', 'counter': 7, 'group_counter': 61, 'group_order': 192, 'label': '4A-1', 'order': 4, 'powers': [4, 6], 'representative': 50, 'size': 1}
id: 96386196
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 8, 'group_counter': 61, 'group_order': 192, 'label': '4B1', 'order': 4, 'powers': [4, 9], 'representative': 144, 'size': 1}
id: 96386197
{'aut_label': '4B1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 61, 'group_order': 192, 'label': '4B-1', 'order': 4, 'powers': [4, 8], 'representative': 48, 'size': 1}
id: 96386127
{'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 10, 'group_counter': 61, 'group_order': 192, 'label': '4C1', 'order': 4, 'powers': [2, 11], 'representative': 1, 'size': 6}
id: 96386128
{'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 11, 'group_counter': 61, 'group_order': 192, 'label': '4C-1', 'order': 4, 'powers': [2, 10], 'representative': 3, 'size': 6}
id: 96386129
{'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 12, 'group_counter': 61, 'group_order': 192, 'label': '4D1', 'order': 4, 'powers': [3, 13], 'representative': 17, 'size': 6}
id: 96386130
{'aut_label': '4C1', 'centralizer': '6.b1.a1', 'counter': 13, 'group_counter': 61, 'group_order': 192, 'label': '4D-1', 'order': 4, 'powers': [3, 12], 'representative': 19, 'size': 6}
id: 96386131
{'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 14, 'group_counter': 61, 'group_order': 192, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 66, 'size': 2}
id: 96386132
{'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 61, 'group_order': 192, 'label': '6B', 'order': 6, 'powers': [5, 3], 'representative': 34, 'size': 2}
id: 96386133
{'aut_label': '6C', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 61, 'group_order': 192, 'label': '6C', 'order': 6, 'powers': [5, 4], 'representative': 32, 'size': 2}
id: 96386134
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 17, 'group_counter': 61, 'group_order': 192, 'label': '8A1', 'order': 8, 'powers': [8, 19], 'representative': 170, 'size': 1}
id: 96386135
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 18, 'group_counter': 61, 'group_order': 192, 'label': '8A-1', 'order': 8, 'powers': [9, 20], 'representative': 26, 'size': 1}
id: 96386136
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 19, 'group_counter': 61, 'group_order': 192, 'label': '8A3', 'order': 8, 'powers': [9, 17], 'representative': 122, 'size': 1}
id: 96386138
{'aut_label': '8A1', 'centralizer': '1.a1.a1', 'counter': 20, 'group_counter': 61, 'group_order': 192, 'label': '8A-3', 'order': 8, 'powers': [8, 18], 'representative': 74, 'size': 1}
id: 96386139
{'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 21, 'group_counter': 61, 'group_order': 192, 'label': '8B1', 'order': 8, 'powers': [9, 23], 'representative': 24, 'size': 1}
id: 96386140
{'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 22, 'group_counter': 61, 'group_order': 192, 'label': '8B-1', 'order': 8, 'powers': [8, 24], 'representative': 168, 'size': 1}
id: 96386141
{'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 23, 'group_counter': 61, 'group_order': 192, 'label': '8B3', 'order': 8, 'powers': [8, 21], 'representative': 72, 'size': 1}
id: 96386142
{'aut_label': '8B1', 'centralizer': '1.a1.a1', 'counter': 24, 'group_counter': 61, 'group_order': 192, 'label': '8B-3', 'order': 8, 'powers': [9, 22], 'representative': 120, 'size': 1}
id: 96386143
{'aut_label': '8C1', 'centralizer': '6.b1.a1', 'counter': 25, 'group_counter': 61, 'group_order': 192, 'label': '8C1', 'order': 8, 'powers': [6, 26], 'representative': 9, 'size': 6}
id: 96386144
{'aut_label': '8C1', 'centralizer': '6.b1.a1', 'counter': 26, 'group_counter': 61, 'group_order': 192, 'label': '8C-1', 'order': 8, 'powers': [7, 25], 'representative': 27, 'size': 6}
id: 96386145
{'aut_label': '8C1', 'centralizer': '6.b1.a1', 'counter': 27, 'group_counter': 61, 'group_order': 192, 'label': '8D1', 'order': 8, 'powers': [7, 28], 'representative': 25, 'size': 6}
id: 96386146
{'aut_label': '8C1', 'centralizer': '6.b1.a1', 'counter': 28, 'group_counter': 61, 'group_order': 192, 'label': '8D-1', 'order': 8, 'powers': [6, 27], 'representative': 11, 'size': 6}
id: 96386147
{'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 29, 'group_counter': 61, 'group_order': 192, 'label': '12A1', 'order': 12, 'powers': [16, 7], 'representative': 18, 'size': 2}
id: 96386149
{'aut_label': '12A1', 'centralizer': '2.b1.a1', 'counter': 30, 'group_counter': 61, 'group_order': 192, 'label': '12A-1', 'order': 12, 'powers': [16, 6], 'representative': 114, 'size': 2}
id: 96386150
{'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 31, 'group_counter': 61, 'group_order': 192, 'label': '12B1', 'order': 12, 'powers': [16, 9], 'representative': 16, 'size': 2}
id: 96386151
{'aut_label': '12B1', 'centralizer': '2.b1.a1', 'counter': 32, 'group_counter': 61, 'group_order': 192, 'label': '12B-1', 'order': 12, 'powers': [16, 8], 'representative': 176, 'size': 2}
id: 96386152
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 33, 'group_counter': 61, 'group_order': 192, 'label': '16A1', 'order': 16, 'powers': [21, 35], 'representative': 12, 'size': 2}
id: 96386153
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 34, 'group_counter': 61, 'group_order': 192, 'label': '16A-1', 'order': 16, 'powers': [22, 36], 'representative': 180, 'size': 2}
id: 96386154
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 35, 'group_counter': 61, 'group_order': 192, 'label': '16A3', 'order': 16, 'powers': [23, 33], 'representative': 36, 'size': 2}
id: 96386155
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 36, 'group_counter': 61, 'group_order': 192, 'label': '16A-3', 'order': 16, 'powers': [24, 34], 'representative': 156, 'size': 2}
id: 96386156
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 37, 'group_counter': 61, 'group_order': 192, 'label': '16B1', 'order': 16, 'powers': [21, 39], 'representative': 14, 'size': 2}
id: 96386157
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 38, 'group_counter': 61, 'group_order': 192, 'label': '16B-1', 'order': 16, 'powers': [22, 40], 'representative': 182, 'size': 2}
id: 96386158
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 39, 'group_counter': 61, 'group_order': 192, 'label': '16B3', 'order': 16, 'powers': [23, 37], 'representative': 38, 'size': 2}
id: 96386160
{'aut_label': '16A1', 'centralizer': '2.b1.a1', 'counter': 40, 'group_counter': 61, 'group_order': 192, 'label': '16B-3', 'order': 16, 'powers': [24, 38], 'representative': 158, 'size': 2}
id: 96386161
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 41, 'group_counter': 61, 'group_order': 192, 'label': '16C1', 'order': 16, 'powers': [17, 43], 'representative': 5, 'size': 6}
id: 96386162
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 42, 'group_counter': 61, 'group_order': 192, 'label': '16C-1', 'order': 16, 'powers': [18, 44], 'representative': 31, 'size': 6}
id: 96386163
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 43, 'group_counter': 61, 'group_order': 192, 'label': '16C3', 'order': 16, 'powers': [19, 41], 'representative': 15, 'size': 6}
id: 96386164
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 44, 'group_counter': 61, 'group_order': 192, 'label': '16C-3', 'order': 16, 'powers': [20, 42], 'representative': 21, 'size': 6}
id: 96386165
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 45, 'group_counter': 61, 'group_order': 192, 'label': '16D1', 'order': 16, 'powers': [19, 47], 'representative': 13, 'size': 6}
id: 96386166
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 46, 'group_counter': 61, 'group_order': 192, 'label': '16D-1', 'order': 16, 'powers': [20, 48], 'representative': 23, 'size': 6}
id: 96386167
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 47, 'group_counter': 61, 'group_order': 192, 'label': '16D3', 'order': 16, 'powers': [17, 45], 'representative': 7, 'size': 6}
id: 96386168
{'aut_label': '16C1', 'centralizer': '6.c1.a1', 'counter': 48, 'group_counter': 61, 'group_order': 192, 'label': '16D-3', 'order': 16, 'powers': [18, 46], 'representative': 29, 'size': 6}
id: 96386169
{'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 49, 'group_counter': 61, 'group_order': 192, 'label': '24A1', 'order': 24, 'powers': [31, 18], 'representative': 10, 'size': 2}
id: 96386171
{'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 50, 'group_counter': 61, 'group_order': 192, 'label': '24A-1', 'order': 24, 'powers': [32, 17], 'representative': 58, 'size': 2}
id: 96386172
{'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 51, 'group_counter': 61, 'group_order': 192, 'label': '24A5', 'order': 24, 'powers': [31, 19], 'representative': 42, 'size': 2}
id: 96386173
{'aut_label': '24A1', 'centralizer': '2.b1.a1', 'counter': 52, 'group_counter': 61, 'group_order': 192, 'label': '24A-5', 'order': 24, 'powers': [32, 20], 'representative': 90, 'size': 2}
id: 96386174
{'aut_label': '24B1', 'centralizer': '2.b1.a1', 'counter': 53, 'group_counter': 61, 'group_order': 192, 'label': '24B1', 'order': 24, 'powers': [31, 21], 'representative': 8, 'size': 2}
id: 96386175
{'aut_label': '24B1', 'centralizer': '2.b1.a1', 'counter': 54, 'group_counter': 61, 'group_order': 192, 'label': '24B-1', 'order': 24, 'powers': [32, 22], 'representative': 184, 'size': 2}
id: 96386176
{'aut_label': '24B1', 'centralizer': '2.b1.a1', 'counter': 55, 'group_counter': 61, 'group_order': 192, 'label': '24B5', 'order': 24, 'powers': [31, 24], 'representative': 40, 'size': 2}
id: 96386177
{'aut_label': '24B1', 'centralizer': '2.b1.a1', 'counter': 56, 'group_counter': 61, 'group_order': 192, 'label': '24B-5', 'order': 24, 'powers': [32, 23], 'representative': 152, 'size': 2}
id: 96386178
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 57, 'group_counter': 61, 'group_order': 192, 'label': '48A1', 'order': 48, 'powers': [53, 33], 'representative': 4, 'size': 2}
id: 96386179
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 58, 'group_counter': 61, 'group_order': 192, 'label': '48A-1', 'order': 48, 'powers': [54, 34], 'representative': 28, 'size': 2}
id: 96386180
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 59, 'group_counter': 61, 'group_order': 192, 'label': '48A5', 'order': 48, 'powers': [55, 36], 'representative': 20, 'size': 2}
id: 96386182
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 60, 'group_counter': 61, 'group_order': 192, 'label': '48A-5', 'order': 48, 'powers': [56, 35], 'representative': 140, 'size': 2}
id: 96386183
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 61, 'group_counter': 61, 'group_order': 192, 'label': '48A11', 'order': 48, 'powers': [56, 35], 'representative': 76, 'size': 2}
id: 96386184
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 62, 'group_counter': 61, 'group_order': 192, 'label': '48A-11', 'order': 48, 'powers': [55, 36], 'representative': 148, 'size': 2}
id: 96386185
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 63, 'group_counter': 61, 'group_order': 192, 'label': '48A17', 'order': 48, 'powers': [53, 33], 'representative': 68, 'size': 2}
id: 96386186
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 64, 'group_counter': 61, 'group_order': 192, 'label': '48A-17', 'order': 48, 'powers': [54, 34], 'representative': 92, 'size': 2}
id: 96386187
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 65, 'group_counter': 61, 'group_order': 192, 'label': '48B1', 'order': 48, 'powers': [53, 37], 'representative': 6, 'size': 2}
id: 96386188
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 66, 'group_counter': 61, 'group_order': 192, 'label': '48B-1', 'order': 48, 'powers': [54, 38], 'representative': 30, 'size': 2}
id: 96386189
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 67, 'group_counter': 61, 'group_order': 192, 'label': '48B5', 'order': 48, 'powers': [55, 40], 'representative': 22, 'size': 2}
id: 96386190
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 68, 'group_counter': 61, 'group_order': 192, 'label': '48B-5', 'order': 48, 'powers': [56, 39], 'representative': 142, 'size': 2}
id: 96386191
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 69, 'group_counter': 61, 'group_order': 192, 'label': '48B11', 'order': 48, 'powers': [56, 39], 'representative': 78, 'size': 2}
id: 96386193
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 70, 'group_counter': 61, 'group_order': 192, 'label': '48B-11', 'order': 48, 'powers': [55, 40], 'representative': 150, 'size': 2}
id: 96386194
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 71, 'group_counter': 61, 'group_order': 192, 'label': '48B17', 'order': 48, 'powers': [53, 37], 'representative': 70, 'size': 2}
id: 96386195
{'aut_label': '48A1', 'centralizer': '2.b1.a1', 'counter': 72, 'group_counter': 61, 'group_order': 192, 'label': '48B-17', 'order': 48, 'powers': [54, 38], 'representative': 94, '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: 237606
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1a', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 237617
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1b', '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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 237625
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1c', '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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 237626
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1d', '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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 237627
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 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, -2], 'schur_index': 1}
id: 237628
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 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, 2], 'schur_index': 1}
id: 237629
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -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], 'schur_index': 1}
id: 237630
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1h', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 237631
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237607
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237612
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 237613
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
id: 237614
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2c', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -1, 2, 2, -2, -2, 0, 0, 0, 0, -1, 1, 1, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, -1, -1, 1, 1, -2, 2, 2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 2}
id: 237615
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2d', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -1, 2, 2, -2, -2, 0, 0, 0, 0, -1, 1, 1, -2, -2, 2, 2, -2, 2, 2, -2, 0, 0, 0, 0, -1, -1, 1, 1, 2, -2, -2, -2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 2}
id: 237608
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1k', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237609
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1l', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237610
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237611
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.1n', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237616
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2e', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, 4, 4, -4, -4, 0, 0, 0, 0, -2, 2, 2, 4, 4, -4, -4, 4, -4, -4, 4, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237618
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2f', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237619
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2g', 'multiplicity': 4, 'nt': [16, 22], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237620
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2h', 'multiplicity': 4, 'nt': [16, 22], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237621
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2i', 'multiplicity': 4, 'nt': [24, 32], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -4, -8, -8, 8, 8, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237622
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2j', 'multiplicity': 4, 'nt': [24, 32], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, -8, -8, -8, -8, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237623
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2k', 'multiplicity': 8, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 237624
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '192.61', 'group_order': 192, 'image': None, 'label': '192.61.2l', 'multiplicity': 8, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

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

gps_char • Show schema

id: 319040
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 192, 'label': '192.61.1a', '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]], [[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: 319051
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 96, 'label': '192.61.1b', '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]], [[-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: 319062
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 96, 'label': '192.61.1c', '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]], [[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: 319073
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 96, 'label': '192.61.1d', '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]], [[-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: 319084
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 48, 'label': '192.61.1e1', 'nt': [4, 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, 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, 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, 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]], [[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: 319095
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.b1', 'kernel_order': 48, 'label': '192.61.1e2', 'nt': [4, 2], '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, 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, 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, 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]], [[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: 319106
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 48, 'label': '192.61.1f1', 'nt': [4, 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, 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, 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, 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]], [[-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: 319110
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.e1.a1', 'kernel_order': 48, 'label': '192.61.1f2', 'nt': [4, 2], '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, 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, 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, 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]], [[-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: 319111
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.b1', 'kernel_order': 48, 'label': '192.61.1g1', 'nt': [4, 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, 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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 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]]]}
id: 319041
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.b1', 'kernel_order': 48, 'label': '192.61.1g2', 'nt': [4, 2], '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, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 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]]]}
id: 319042
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 48, 'label': '192.61.1h1', 'nt': [4, 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, 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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[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, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 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]]]}
id: 319043
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.d1.a1', 'kernel_order': 48, 'label': '192.61.1h2', 'nt': [4, 2], '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, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[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, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 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]]]}
id: 319044
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1.a1', 'kernel_order': 48, 'label': '192.61.1i1', 'nt': [4, 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, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 319045
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id: 319046
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id: 319047
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id: 319048
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id: 319049
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id: 319050
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id: 319052
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id: 319053
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id: 319054
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id: 319055
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id: 319056
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id: 319057
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id: 319058
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id: 319059
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id: 319060
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id: 319061
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id: 319063
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 30, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.61.1n2', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
id: 319064
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 31, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.61.1n3', 'nt': [8, 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, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]]]}
id: 319065
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 192, 'counter': 32, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 24, 'label': '192.61.1n4', 'nt': [8, 4], '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, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 3]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
id: 319066
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 32, 'label': '192.61.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 319067
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 16, 'label': '192.61.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 319068
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.b1', 'kernel_order': 16, 'label': '192.61.2c', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 319069
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.b1.a1', 'kernel_order': 16, 'label': '192.61.2d', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[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: 319070
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 37, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 8, 'label': '192.61.2e1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[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, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
id: 319071
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 38, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 8, 'label': '192.61.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[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, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 319072
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 39, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 8, 'label': '192.61.2f1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]]]}
id: 319074
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 40, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 8, 'label': '192.61.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]]]}
id: 319075
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 41, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 6, 'label': '192.61.2g1', 'nt': [16, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[2, 3]], [[2, 3]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 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]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 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]]]}
id: 319076
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 42, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 6, 'label': '192.61.2g2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 3]], [[-2, 1]], [[-2, 1]], [[-2, 3]], [[-2, 3]], [[2, 3]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 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]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 319077
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 43, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 6, 'label': '192.61.2g3', 'nt': [16, 22], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-2, 3]], [[-2, 3]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 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]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 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]]]}
id: 319078
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 44, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.a1', 'kernel_order': 6, 'label': '192.61.2g4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 3]], [[2, 1]], [[2, 1]], [[2, 3]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 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]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 319079
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 45, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.b1', 'kernel_order': 6, 'label': '192.61.2h1', 'nt': [16, 22], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 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]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 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]]]}
id: 319080
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 46, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.b1', 'kernel_order': 6, 'label': '192.61.2h2', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 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]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 319081
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 47, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.b1', 'kernel_order': 6, 'label': '192.61.2h3', 'nt': [16, 22], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 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]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[-2, 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]]]}
id: 319082
{'center': '4.b1.a1', 'center_index': 4, 'center_order': 48, 'counter': 48, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '32.17', 'image_order': 32, 'indicator': 0, 'kernel': '32.a1.b1', 'kernel_order': 6, 'label': '192.61.2h4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 2]], [[-2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[2, 3]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[2, 2]], [[-2, 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]], [[2, 3]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 319083
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 49, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '48.4', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.61.2i1', 'nt': [24, 32], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[2, 3]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
id: 319085
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 50, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '48.4', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.61.2i2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 3]], [[-2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 3]]]}
id: 319086
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 32, 'counter': 51, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '48.4', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 4, 'label': '192.61.2i3', 'nt': [24, 32], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
id: 319087
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id: 319088
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id: 319089
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id: 319090
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id: 319091
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id: 319092
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id: 319093
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id: 319094
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id: 319096
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id: 319097
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 61, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 2, 'label': '192.61.2k5', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 6]], [[-2, 18]], [[-2, 18]], [[-2, 6]], [[-2, 6]], [[2, 6]], [[2, 18]], [[2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[-2, 1], [1, 9]], [[-1, 5], [-1, 13]], [[-2, 7], [1, 15]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[1, 5], [1, 13]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[-2, 1], [1, 9]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[2, 7], [-1, 15]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[2, 7], [-1, 15]], [[-1, 3], [2, 11]]]}
id: 319098
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id: 319099
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 63, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 2, 'label': '192.61.2k7', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 6]], [[-2, 18]], [[-2, 18]], [[-2, 6]], [[-2, 6]], [[2, 6]], [[2, 18]], [[2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[2, 1], [-1, 9]], [[1, 5], [1, 13]], [[2, 7], [-1, 15]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[-1, 5], [-1, 13]], [[-2, 1], [1, 9]], [[-1, 3], [2, 11]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[-2, 7], [1, 15]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[-2, 7], [1, 15]], [[1, 3], [-2, 11]]]}
id: 319100
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 64, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 2, 'label': '192.61.2k8', 'nt': [48, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 12]], [[-2, 12]], [[2, 12]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 18]], [[2, 6]], [[2, 6]], [[2, 18]], [[2, 18]], [[-2, 18]], [[-2, 6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12]], [[-1, 12]], [[1, 12]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[2, 7], [-1, 15]], [[1, 3], [-2, 11]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[-1, 3], [2, 11]], [[-2, 7], [1, 15]], [[-1, 5], [-1, 13]], [[2, 7], [-1, 15]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[-2, 1], [1, 9]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[-2, 1], [1, 9]], [[1, 5], [1, 13]]]}
id: 319101
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 65, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l1', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[2, 12]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 6]], [[2, 18]], [[-2, 18]], [[-2, 6]], [[2, 6]], [[2, 6]], [[2, 18]], [[-2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[1, 12]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[-1, 18]], [[1, 18]], [[1, 6]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[-2, 1], [1, 9]], [[1, 5], [1, 13]], [[-2, 7], [1, 15]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[2, 1], [-1, 9]], [[-1, 3], [2, 11]], [[2, 1], [-1, 9]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[2, 7], [-1, 15]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[-2, 7], [1, 15]], [[1, 3], [-2, 11]]]}
id: 319102
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 66, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l2', 'nt': [48, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 12]], [[-2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 18]], [[-2, 6]], [[2, 6]], [[2, 18]], [[-2, 18]], [[-2, 18]], [[-2, 6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12]], [[-1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18]], [[1, 6]], [[-1, 6]], [[-1, 18]], [[-1, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[-2, 7], [1, 15]], [[1, 3], [-2, 11]], [[-2, 1], [1, 9]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[2, 7], [-1, 15]], [[-1, 5], [-1, 13]], [[2, 7], [-1, 15]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[-2, 1], [1, 9]], [[1, 5], [1, 13]]]}
id: 319103
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 67, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l3', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[2, 12]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 6]], [[2, 18]], [[-2, 18]], [[-2, 6]], [[2, 6]], [[2, 6]], [[2, 18]], [[-2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[1, 12]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[-1, 18]], [[1, 18]], [[1, 6]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[2, 1], [-1, 9]], [[-1, 5], [-1, 13]], [[2, 7], [-1, 15]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[-2, 1], [1, 9]], [[1, 3], [-2, 11]], [[-2, 1], [1, 9]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[2, 7], [-1, 15]], [[-1, 3], [2, 11]]]}
id: 319104
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 68, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l4', 'nt': [48, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 12]], [[-2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 18]], [[-2, 6]], [[2, 6]], [[2, 18]], [[-2, 18]], [[-2, 18]], [[-2, 6]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12]], [[-1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18]], [[1, 6]], [[-1, 6]], [[-1, 18]], [[-1, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[2, 7], [-1, 15]], [[-1, 3], [2, 11]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[-2, 7], [1, 15]], [[1, 5], [1, 13]], [[-2, 7], [1, 15]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[-2, 1], [1, 9]], [[2, 1], [-1, 9]], [[-1, 5], [-1, 13]]]}
id: 319105
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 69, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l5', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[2, 12]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 6]], [[-2, 18]], [[2, 18]], [[2, 6]], [[-2, 6]], [[-2, 6]], [[-2, 18]], [[2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[1, 12]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[-1, 6]], [[-1, 18]], [[1, 18]], [[1, 6]], [[-1, 5], [-1, 13]], [[-2, 1], [1, 9]], [[-1, 3], [2, 11]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[1, 5], [1, 13]], [[2, 7], [-1, 15]], [[1, 5], [1, 13]], [[2, 7], [-1, 15]], [[-2, 1], [1, 9]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[-1, 3], [2, 11]], [[-2, 7], [1, 15]]]}
id: 319107
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 70, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l6', 'nt': [48, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 12]], [[-2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 18]], [[2, 6]], [[-2, 6]], [[-2, 18]], [[2, 18]], [[2, 18]], [[2, 6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12]], [[-1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[1, 18]], [[1, 6]], [[-1, 6]], [[-1, 18]], [[-1, 3], [2, 11]], [[-2, 7], [1, 15]], [[-1, 5], [-1, 13]], [[2, 7], [-1, 15]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[1, 3], [-2, 11]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[-1, 5], [-1, 13]], [[-2, 1], [1, 9]]]}
id: 319108
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 71, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l7', 'nt': [48, 0], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-2, 12]], [[2, 12]], [[2, 12]], [[-2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 6]], [[-2, 18]], [[2, 18]], [[2, 6]], [[-2, 6]], [[-2, 6]], [[-2, 18]], [[2, 18]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 12]], [[1, 12]], [[1, 12]], [[-1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 6]], [[1, 18]], [[-1, 18]], [[-1, 6]], [[-1, 6]], [[-1, 18]], [[1, 18]], [[1, 6]], [[1, 5], [1, 13]], [[2, 1], [-1, 9]], [[1, 3], [-2, 11]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[-2, 1], [1, 9]], [[-1, 5], [-1, 13]], [[-2, 7], [1, 15]], [[-1, 5], [-1, 13]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[-1, 3], [2, 11]], [[1, 5], [1, 13]], [[-1, 3], [2, 11]], [[1, 3], [-2, 11]], [[2, 7], [-1, 15]]]}
id: 319109
{'center': '12.a1.a1', 'center_index': 12, 'center_order': 16, 'counter': 72, 'cyclotomic_n': 48, 'dim': 2, 'faithful': False, 'field': [81, 0, 0, 0, 0, 0, 0, 0, 1], 'group': '192.61', 'group_counter': 61, 'group_order': 192, 'image': None, 'image_isoclass': '96.5', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.b1', 'kernel_order': 2, 'label': '192.61.2l8', 'nt': [48, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 12]], [[-2, 12]], [[-2, 12]], [[2, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 18]], [[2, 6]], [[-2, 6]], [[-2, 18]], [[2, 18]], [[2, 18]], [[2, 6]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 12]], [[-1, 12]], [[-1, 12]], [[1, 12]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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, 18]], [[-1, 6]], [[1, 6]], [[1, 18]], [[1, 18]], [[1, 6]], [[-1, 6]], [[-1, 18]], [[1, 3], [-2, 11]], [[2, 7], [-1, 15]], [[1, 5], [1, 13]], [[-2, 7], [1, 15]], [[2, 1], [-1, 9]], [[-2, 7], [1, 15]], [[-1, 3], [2, 11]], [[-2, 1], [1, 9]], [[-1, 3], [2, 11]], [[-2, 1], [1, 9]], [[2, 7], [-1, 15]], [[-1, 5], [-1, 13]], [[1, 3], [-2, 11]], [[-1, 5], [-1, 13]], [[1, 5], [1, 13]], [[2, 1], [-1, 9]]]}

Column	Type
Agroup	boolean
Zgroup	boolean
abelian	boolean
ambient	text
ambient_counter	integer
ambient_order	numeric
ambient_tex	text
central	boolean
central_factor	boolean
centralizer_order	numeric
characteristic	boolean
core_order	numeric
counter	integer
cyclic	boolean
direct	boolean
hall	numeric
label	text
maximal	boolean
maximal_normal	boolean
metabelian	boolean
metacyclic	boolean
minimal	boolean
minimal_normal	boolean
nilpotent	boolean
normal	boolean
old_label	text
outer_equivalence	boolean
perfect	boolean
proper	boolean
quotient	text
quotient_Agroup	boolean
quotient_abelian	boolean
quotient_cyclic	boolean
quotient_hash	bigint
quotient_metabelian	boolean
quotient_nilpotent	boolean
quotient_order	numeric
quotient_simple	boolean
quotient_solvable	boolean
quotient_supersolvable	boolean
quotient_tex	text
simple	boolean
solvable	boolean
special_labels	text[]
split	boolean
standard_generators	boolean
stem	boolean
subgroup	text
subgroup_hash	bigint
subgroup_order	numeric
subgroup_tex	text
supersolvable	boolean
sylow	smallint

gps_subgroup_search • Show schema

id: 20353650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 192, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '192.61.1.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': '192.61', 'subgroup_hash': 61, 'subgroup_order': 192, 'subgroup_tex': 'C_{48}:C_4', 'supersolvable': True, 'sylow': 0}
id: 20353661
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 96, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.20', 'subgroup_hash': 20, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 20353672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 96, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.59', 'subgroup_hash': 59, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times C_{48}', 'supersolvable': True, 'sylow': 0}
id: 20353683
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 96, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.18', 'subgroup_hash': 18, 'subgroup_order': 96, 'subgroup_tex': 'C_6:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353694
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '192.61.3.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': '64.27', 'subgroup_hash': 27, 'subgroup_order': 64, 'subgroup_tex': 'C_{16}:C_4', 'supersolvable': True, 'sylow': 2}
id: 20353700
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 20353701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 48, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.4.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': '4.2', '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': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
id: 20353702
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 20353703
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.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': '48.1', 'subgroup_hash': 1, 'subgroup_order': 48, 'subgroup_tex': 'C_3:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353651
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.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': '48.1', 'subgroup_hash': 1, 'subgroup_order': 48, 'subgroup_tex': 'C_3:C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353652
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 11, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.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': '48.2', 'subgroup_hash': 2, 'subgroup_order': 48, 'subgroup_tex': 'C_{48}', 'supersolvable': True, 'sylow': 0}
id: 20353653
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 48, 'counter': 12, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.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': '48.2', 'subgroup_hash': 2, 'subgroup_order': 48, 'subgroup_tex': 'C_{48}', 'supersolvable': True, 'sylow': 0}
id: 20353654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.6.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': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353655
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.6.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': '32.3', 'subgroup_hash': 3, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 20353656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.16', 'subgroup_hash': 16, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.8.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 20353658
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20353659
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 20353660
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 20353662
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.8.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 20353663
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 21, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 20353664
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 24, 'counter': 22, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
id: 20353665
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.12.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': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 20353666
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.12.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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353667
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 16, 'counter': 25, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.12.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': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353668
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 20353669
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 20353670
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353671
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 29, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.1', 'subgroup_hash': 1, 'subgroup_order': 16, 'subgroup_tex': 'C_{16}', 'supersolvable': True, 'sylow': 0}
id: 20353673
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 20353674
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 31, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 20353675
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 12, 'counter': 32, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 20353676
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 20353677
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 20353678
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20353679
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 36, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 20353680
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 8, 'counter': 37, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.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': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 20353681
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20353682
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '192.61.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 20353684
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 20353685
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 20353686
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{32}', '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: 20353687
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 43, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.32.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{32}', '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: 20353688
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 6, 'counter': 44, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.3', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C5'], '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: 20353689
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.61.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_8', '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: 20353690
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 20353691
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 4, 'counter': 47, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 20353692
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.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': 48, '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: 20353693
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '192.61.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.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': 48, '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: 20353695
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 3, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '192.61.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}:C_4', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], '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: 20353696
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{48}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], '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: 20353697
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.96.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{48}:C_2', 'simple': True, 'solvable': True, 'special_labels': [], '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: 20353698
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 2, 'counter': 53, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '192.61.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.20', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 20, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}:C_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 20353699
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '192.61', 'ambient_counter': 61, 'ambient_order': 192, 'ambient_tex': 'C_{48}:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '192.61.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '192.61', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 61, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{48}:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], '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: 20353693
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.d1.b1'], 'contains': ['96.a1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [880, -1, 7274, -1, 1189, -1, 1378, -1], 'generators': [17], 'label': '192.61.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.d1.b1', 'projective_image': '96.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353650
{'ambient': '192.61', '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': '12.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7271, 5865, 2364, 5831, 6685, 5406, 6649, 5456], 'generators': [1, 96, 48, 12, 64, 2, 24], 'label': '192.61.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '12.4', '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': '12.4'}
id: 20353651
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': ['48.d1.a1', '48.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.d1.a1', '12.e1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8767, 7065, 1223, 4801, 6339, 4523, 9704, 4479], 'generators': [13, 64, 122, 48, 96], 'label': '192.61.4.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353652
{'ambient': '192.61', 'aut_centralizer_order': 24, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '12.b1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6631, 8241, 4321, 8905, 9724, 7664, 6485, 7648], 'generators': [12, 96, 64, 24, 48], 'label': '192.61.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.e1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '24.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353653
{'ambient': '192.61', 'aut_centralizer_order': 24, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.10', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': ['48.d1.a1', '48.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.e1.a1', '12.b1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6631, 8241, 2799, 8144, 9724, 7664, 5969, 8370], 'generators': [14, 96, 64, 24, 48], 'label': '192.61.4.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.e1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': '24.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353654
{'ambient': '192.61', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.48', 'aut_weyl_index': 24, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8088, 9157, 1658, 9346, 8732, 9147, 7223, 9405], 'generators': [2, 12], 'label': '192.61.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353655
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.46', 'aut_weyl_index': 24, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5672, -1, 4858, -1, 4047, -1, 4351, -1], 'generators': [1, 24], 'label': '192.61.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.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': '2.1'}
id: 20353656
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.48', 'aut_weyl_index': 24, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.e1.a1', '12.e1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9704, -1, 438, -1, 7449, -1, 8179, -1], 'generators': [5, 24], 'label': '192.61.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353657
{'ambient': '192.61', 'aut_centralizer_order': 96, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 96, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3072, 2709, 6066, 5122, 3346, 3912, 4298, 4856], 'generators': [2, 48, 64, 96], 'label': '192.61.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353658
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '24.d1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [944, 843, 9109, 645, 669, 876, 1771, 1983], 'generators': [1, 96, 2, 64], 'label': '192.61.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353659
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '8.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '16.d1.b1', '24.d1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [944, 843, 8077, 2091, 669, 876, 792, 612], 'generators': [17, 96, 98, 64], 'label': '192.61.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353660
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.b1.a1', '24.e1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2048, 4157, 6839, 3217, 1693, 2406, 3008, 3805], 'generators': [9, 146, 96, 64], 'label': '192.61.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353661
{'ambient': '192.61', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1514', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4816, 3682, 4930, 3918, 4047, 3135, 4351, 3641], 'generators': [1, 64, 96, 24, 2, 48], 'label': '192.61.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353662
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 32, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.b1.a1', '24.e1.b1'], 'core': '8.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2048, 4157, 5294, 4013, 1693, 2406, 3547, 3050], 'generators': [25, 50, 96, 64], 'label': '192.61.8.c1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': ['4.c1.a1'], 'normal_contains': ['16.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.b1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353663
{'ambient': '192.61', 'aut_centralizer_order': 96, 'aut_label': '8.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 96, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.d1.a1', '4.d1.b1'], 'contains': ['16.c1.a1', '24.b1.a1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6847, 5176, 2498, 6212, 5409, 5394, 8695, 5891], 'generators': [26, 64, 48, 96], 'label': '192.61.8.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.b1.a1', '4.d1.b1', '4.d1.a1'], 'normal_contains': ['16.c1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353664
{'ambient': '192.61', 'aut_centralizer_order': 96, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 96, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.a1', '4.e1.b1'], 'contains': ['16.c1.a1', '24.c1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4992, 6171, 4025, 7598, 7866, 6429, 5834, 6613], 'generators': [24, 64, 48, 96], 'label': '192.61.8.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.b1.a1', '4.e1.a1', '4.e1.b1'], 'normal_contains': ['16.c1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.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.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353665
{'ambient': '192.61', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 96, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6983, 7020, 1869, 7295, 6291, 7747, 6491, 7533], 'generators': [2, 24], 'label': '192.61.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.b1.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: 20353666
{'ambient': '192.61', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '2.b1.a1', 'complements': ['16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1'], 'contains': ['24.c1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8184, 8286, 3076, 9355, 8732, 9064, 7663, 8452], 'generators': [12], 'label': '192.61.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '24.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353667
{'ambient': '192.61', 'aut_centralizer_order': 48, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '2.b1.a1', 'complements': ['16.d1.a1', '16.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.a1.a1'], 'contains': ['24.c1.a1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8184, 8286, 2545, 8594, 8732, 9064, 7148, 9175], 'generators': [14], 'label': '192.61.12.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.e1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '24.7', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353668
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.d1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4112, -1, 6935, -1, 2378, -1, 2498, -1], 'generators': [1, 48], 'label': '192.61.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353669
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 48, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.e1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5592, -1, 4901, -1, 4528, -1, 5177, -1], 'generators': [9, 48], 'label': '192.61.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353670
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1'], 'contains': ['24.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8896, -1, 963, -1, 7173, -1, 8179, -1], 'generators': [5], 'label': '192.61.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353671
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 96, 'centralizer': '6.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.c1.a1'], 'contains': ['24.b1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8896, -1, 359, -1, 7173, -1, 9211, -1], 'generators': [13], 'label': '192.61.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353672
{'ambient': '192.61', 'aut_centralizer_order': 12, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.263', 'aut_weyl_index': 12, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.e1.b1', '6.a1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6784, 7959, 2902, 8144, 8764, 7582, 6150, 7648], 'generators': [2, 96, 48, 12, 64, 24], 'label': '192.61.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.e1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353673
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'contains': ['32.a1.a1', '32.a1.b1', '32.b1.a1', '48.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1816, 1454, 8360, 2480, 2260, 2300, 2222, 3370], 'generators': [2, 96, 64], 'label': '192.61.16.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normal_contains': ['32.b1.a1', '32.a1.b1', '32.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '48.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353674
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.c1.a1', '8.c1.b1'], 'contains': ['32.b1.a1', '48.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2712, 2721, 6265, 4013, 3142, 3617, 3676, 4290], 'generators': [50, 64, 96], 'label': '192.61.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.b1', '8.c1.a1'], 'normal_contains': ['32.b1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '48.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353675
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.d1.a1', '8.e1.a1'], 'contains': ['32.b1.a1', '48.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3719, 4146, 4146, 5528, 5472, 4653, 5834, 5012], 'generators': [48, 64, 96], 'label': '192.61.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1', '8.e1.a1', '8.d1.a1'], 'normal_contains': ['32.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '48.11', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353676
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 64, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.a1.a1', '48.d1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [296, -1, 9641, -1, 291, -1, 756, -1], 'generators': [1, 2, 64], 'label': '192.61.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '96.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20353677
{'ambient': '192.61', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 64, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1'], 'contains': ['32.a1.b1', '48.d1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [296, -1, 7672, -1, 291, -1, 217, -1], 'generators': [17, 98, 64], 'label': '192.61.16.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.d1.b1', 'projective_image': '96.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 20353678
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5056, 5062, 4539, 5268, 4591, 5970, 5177, 5932], 'generators': [2, 48], 'label': '192.61.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '24.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353679
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.a1', '12.e1.a1', '12.e1.b1'], 'contains': ['48.c1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7479, 6238, 1343, 6498, 6228, 7194, 8179, 6785], 'generators': [26], 'label': '192.61.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.d1.a1', '12.a1.a1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '24.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353680
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '24.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1'], 'contains': ['48.c1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6648, 7189, 2998, 8048, 7299, 8041, 6491, 7533], 'generators': [24], 'label': '192.61.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.e1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1'], 'normal_contains': ['48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.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.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353681
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '48.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1104, -1, 9115, -1, 1189, -1, 3020, -1], 'generators': [1, 96], 'label': '192.61.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353682
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1'], 'contains': ['48.a1.a1', '48.d1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1104, -1, 6917, -1, 1189, -1, 1425, -1], 'generators': [17, 96], 'label': '192.61.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.b1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353683
{'ambient': '192.61', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1520', 'aut_weyl_index': 4, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.d1.b1', '6.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8896, 5865, 1821, 5831, 5953, 5406, 8244, 5456], 'generators': [5, 64, 96, 24, 170, 144], 'label': '192.61.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.b1', '4.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353684
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3920, -1, 5831, -1, 3772, -1, 4145, -1], 'generators': [9], 'label': '192.61.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353685
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 192, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.b1', '12.d1.a1'], 'contains': ['48.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3920, -1, 5396, -1, 3772, -1, 4567, -1], 'generators': [25], 'label': '192.61.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '48.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353686
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1'], 'contains': ['64.a1.a1', '96.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1344, 1306, 8898, 2480, 1929, 2618, 2222, 3699], 'generators': [2, 64], 'label': '192.61.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '96.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.1', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353687
{'ambient': '192.61', 'aut_centralizer_order': 192, 'aut_label': '32.a1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.b1'], 'contains': ['64.a1.a1', '96.a1.b1'], 'core': '32.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1344, 1306, 8463, 1857, 1929, 2618, 1800, 3107], 'generators': [98, 64], 'label': '192.61.32.a1.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.b1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.b1', 'projective_image': '96.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.1', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353688
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '32.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'contains': ['64.a1.a1', '96.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2568, 2596, 6604, 3434, 3142, 3465, 3612, 4290], 'generators': [96, 64], 'label': '192.61.32.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '96.20', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353689
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.d1.b1'], 'contains': ['96.a1.a1', '96.a1.b1', '96.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2104, 3275, 7739, 3866, 2535, 4370, 3096, 4922], 'generators': [2, 96], 'label': '192.61.48.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1', '96.a1.b1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '48.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.4', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353690
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.e1.a1', '24.e1.b1'], 'contains': ['96.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3616, 4146, 5854, 4862, 3740, 5276, 4145, 5554], 'generators': [50], 'label': '192.61.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '48.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.4', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353691
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '48.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['96.b1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5056, 5367, 4013, 6022, 5472, 6123, 5834, 6145], 'generators': [48], 'label': '192.61.48.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.c1.a1', '24.a1.a1', '24.c1.a1', '24.b1.a1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '48.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.11', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353692
{'ambient': '192.61', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '6.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.d1.a1'], 'contains': ['96.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [880, -1, 9230, -1, 1189, -1, 2644, -1], 'generators': [1], 'label': '192.61.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '96.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353694
{'ambient': '192.61', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.2167', 'aut_weyl_index': 6, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8104, -1, 957, -1, 7417, -1, 7153, -1], 'generators': [1, 12], 'label': '192.61.3.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': '12.4', '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': '4.2'}
id: 20353695
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '64.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 384, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.a1.b1', '32.b1.a1'], 'contains': ['192.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2120, 1974, 8524, 2299, 2559, 3065, 2222, 3699], 'generators': [64], 'label': '192.61.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.b1.a1', '32.a1.b1', '32.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '192.61', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.16', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353696
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.d1.a1'], 'contains': ['192.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1472, 2630, 8789, 3398, 1953, 3912, 2644, 4881], 'generators': [2], 'label': '192.61.96.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '96.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.5', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353697
{'ambient': '192.61', 'aut_centralizer_order': 384, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.b1', '48.a1.a1', '48.d1.b1'], 'contains': ['192.a1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1472, 2630, 7829, 2775, 1953, 3912, 1800, 4290], 'generators': [98], 'label': '192.61.96.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1.b1', 'normal_contained_in': ['32.a1.b1', '48.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.b1', 'projective_image': '96.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.5', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353698
{'ambient': '192.61', 'aut_centralizer_order': 768, 'aut_label': '96.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'contains': ['192.a1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2888, 3457, 6604, 4386, 3142, 4759, 3612, 5472], 'generators': [96], 'label': '192.61.96.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': '96.20', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.20', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353699
{'ambient': '192.61', 'aut_centralizer_order': None, 'aut_label': '192.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': ['64.a1.a1', '96.a1.a1', '96.a1.b1', '96.b1.a1'], 'contains': [], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2120, 2630, 7932, 3086, 2559, 3912, 2433, 4585], 'generators': [], 'label': '192.61.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.b1.a1', '96.a1.b1', '96.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.61', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 20353700
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.c1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2664, 1714, 7461, 2108, 1535, 876, 2480, 1933], 'generators': [1, 64, 48, 2, 96], 'label': '192.61.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.b1', '8.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353701
{'ambient': '192.61', 'aut_centralizer_order': 48, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 48, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.e1.a1', '12.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5624, 5469, 3560, 7052, 5228, 6182, 5230, 6613], 'generators': [2, 96, 24, 64, 48], 'label': '192.61.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.a1', '8.d1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.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.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 20353702
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '96.209', 'aut_weyl_index': 8, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.c1.b1', '12.d1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4000, 3603, 5613, 3563, 2850, 2841, 3459, 3305], 'generators': [9, 64, 48, 146, 96], 'label': '192.61.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.b1', '8.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 20353703
{'ambient': '192.61', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.35', 'aut_weyl_index': 16, 'centralizer': '12.a1.a1', 'complements': ['48.d1.a1', '48.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.d1.a1', '12.e1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8767, 7065, 1941, 5831, 6339, 4523, 9006, 5456], 'generators': [5, 64, 170, 144, 96], 'label': '192.61.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}

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.