LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-23T03:10:12.696874

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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 12, 8], 'aut_gens': [[1, 2, 12, 144, 432], [1201, 318, 352, 864, 144], [449, 54, 1096, 288, 432], [1065, 410, 876, 864, 144], [161, 1102, 1288, 1152, 720]], 'aut_group': None, 'aut_hash': 6992198563583357107, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 174, 'aut_perms': [2097351505924504136760990941322516135939717530329546538878876730562486745413256074377652530304077965778707215607426087021287874157473487520652790289759863671406257779930338748855510856683285978478843769450075583480935232803333087305978981345599612558448212772993893011134897145361437353352326316468422570891438420716, 4377818128753290910673662205742376219791113840547399679874643403485408377248340156834492041590134516224669149871171415299507595317818090596260553131428631690821036417824148955145810823037389088981460243772960332700937935785323821383120492035422032760731543146052186378956972358486399592884652936746112636820222354780, 2265087000917404902333791108010817967942091109139465669754432866435573249193635848903844699099065358842276913314257762949652743446440535000635527300667410628808614338890506306879388635834311254588125203299764182893586647356796276196692686786717826054299992603780490844287471265638107088741059846448515889223188649526, 5109193311157278586100749290439704554575478952118145860983068069275993030911360444417555053975838201418081460650696084714338975322925394327105252311607203126321676450072000698057814556630619795839938983129873683705090193587813456745505735747426691904450344450522686195047448406881329572856380567720948406921221569344], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 12, 1, 1], [3, 2, 4, 1], [3, 8, 1, 1], [3, 8, 8, 1], [4, 18, 1, 1], [4, 324, 1, 1], [6, 12, 8, 1], [6, 18, 4, 1], [6, 24, 1, 1], [6, 24, 8, 1], [8, 162, 1, 2], [12, 36, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_6^2.C_{12}.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 6992198563583357107, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3:S_3.C_6^2.C_{12}.C_2^3', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 12, 1], [3, 2, 4], [3, 8, 9], [4, 18, 1], [4, 324, 1], [6, 12, 8], [6, 18, 4], [6, 24, 9], [8, 162, 2], [12, 36, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1296.3514', 'commutator_count': 1, 'commutator_label': '324.161', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3514, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 12, 1, 1], [3, 2, 1, 4], [3, 8, 1, 1], [3, 8, 2, 4], [4, 18, 1, 1], [4, 324, 1, 1], [6, 12, 2, 4], [6, 18, 1, 4], [6, 24, 1, 1], [6, 24, 2, 4], [8, 162, 2, 1], [12, 36, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 13440, 'exponent': 24, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1296.3514', 'hash': 3514, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 6, 12, 3, 3], 'inner_gens': [[1, 46, 60, 576, 720], [113, 2, 84, 144, 864], [97, 74, 12, 864, 144], [865, 2, 588, 144, 432], [145, 866, 732, 144, 432]], 'inner_hash': 3514, 'inner_nilpotent': False, 'inner_order': 1296, 'inner_split': True, 'inner_tex': 'C_3^4:\\SD_{16}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 19], [4, 4], [8, 18]], 'label': '1296.3514', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^4:SD16', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 45, 'number_divisions': 32, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 84, 'number_subgroup_classes': 185, 'number_subgroups': 2204, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 21], [3, 80], [4, 342], [6, 384], [8, 324], [12, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [72, 36], 'outer_gens': [[109, 118, 92, 1008, 1152], [1, 130, 112, 864, 144]], 'outer_group': '48.29', 'outer_hash': 29, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 8, 'outer_perms': [10911, 37136], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 9], [4, 9], [8, 2], [16, 8]], 'representations': {'PC': {'code': 558438406397054838478453318473795775067749487414401835183610663, 'gens': [1, 2, 4, 7, 8], 'pres': [8, -2, -2, -3, -2, -2, -3, -3, 3, 864, 737, 41, 194, 1923, 1355, 91, 4804, 116, 4613, 32262, 4062, 710, 46087, 27663, 799, 2343]}, 'Perm': {'d': 15, 'gens': [7316754505, 12936712320, 21083695920, 27909186480, 114053189040, 208569317040, 147, 4]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:\\SD_{16}', 'transitive_degree': 72, '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: 114811389
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3514, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 114811400
{'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 3514, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 72, 'size': 9}
id: 114811411
{'aut_label': '2B', 'centralizer': '12.b1', 'counter': 3, 'group_counter': 3514, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 6, 'size': 12}
id: 114811422
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 4, 'group_counter': 3514, 'group_order': 1296, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 4, 'size': 2}
id: 114811429
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 3514, 'group_order': 1296, 'label': '3B', 'order': 3, 'powers': [5, 1], 'representative': 100, 'size': 2}
id: 114811430
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 3514, 'group_order': 1296, 'label': '3C', 'order': 3, 'powers': [6, 1], 'representative': 52, 'size': 2}
id: 114811431
{'aut_label': '3A', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 3514, 'group_order': 1296, 'label': '3D', 'order': 3, 'powers': [7, 1], 'representative': 96, 'size': 2}
id: 114811432
{'aut_label': '3E', 'centralizer': '8.b1', 'counter': 8, 'group_counter': 3514, 'group_order': 1296, 'label': '3E', 'order': 3, 'powers': [8, 1], 'representative': 288, 'size': 8}
id: 114811433
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 9, 'group_counter': 3514, 'group_order': 1296, 'label': '3F1', 'order': 3, 'powers': [10, 1], 'representative': 292, 'size': 8}
id: 114811390
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 10, 'group_counter': 3514, 'group_order': 1296, 'label': '3F-1', 'order': 3, 'powers': [9, 1], 'representative': 152, 'size': 8}
id: 114811391
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 11, 'group_counter': 3514, 'group_order': 1296, 'label': '3G1', 'order': 3, 'powers': [12, 1], 'representative': 388, 'size': 8}
id: 114811392
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 12, 'group_counter': 3514, 'group_order': 1296, 'label': '3G-1', 'order': 3, 'powers': [11, 1], 'representative': 200, 'size': 8}
id: 114811393
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 13, 'group_counter': 3514, 'group_order': 1296, 'label': '3H1', 'order': 3, 'powers': [14, 1], 'representative': 916, 'size': 8}
id: 114811394
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 14, 'group_counter': 3514, 'group_order': 1296, 'label': '3H-1', 'order': 3, 'powers': [13, 1], 'representative': 536, 'size': 8}
id: 114811395
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 15, 'group_counter': 3514, 'group_order': 1296, 'label': '3I1', 'order': 3, 'powers': [16, 1], 'representative': 384, 'size': 8}
id: 114811396
{'aut_label': '3F1', 'centralizer': '8.b1', 'counter': 16, 'group_counter': 3514, 'group_order': 1296, 'label': '3I-1', 'order': 3, 'powers': [15, 1], 'representative': 192, 'size': 8}
id: 114811397
{'aut_label': '4A', 'centralizer': '18.d1', 'counter': 17, 'group_counter': 3514, 'group_order': 1296, 'label': '4A', 'order': 4, 'powers': [2, 17], 'representative': 36, 'size': 18}
id: 114811398
{'aut_label': '4B', 'centralizer': '324.c1', 'counter': 18, 'group_counter': 3514, 'group_order': 1296, 'label': '4B', 'order': 4, 'powers': [2, 18], 'representative': 55, 'size': 324}
id: 114811399
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 19, 'group_counter': 3514, 'group_order': 1296, 'label': '6A1', 'order': 6, 'powers': [4, 3], 'representative': 2, 'size': 12}
id: 114811401
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 20, 'group_counter': 3514, 'group_order': 1296, 'label': '6A-1', 'order': 6, 'powers': [4, 3], 'representative': 10, 'size': 12}
id: 114811402
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 21, 'group_counter': 3514, 'group_order': 1296, 'label': '6B1', 'order': 6, 'powers': [5, 3], 'representative': 50, 'size': 12}
id: 114811403
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 22, 'group_counter': 3514, 'group_order': 1296, 'label': '6B-1', 'order': 6, 'powers': [5, 3], 'representative': 14, 'size': 12}
id: 114811404
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 23, 'group_counter': 3514, 'group_order': 1296, 'label': '6C1', 'order': 6, 'powers': [6, 3], 'representative': 26, 'size': 12}
id: 114811405
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 24, 'group_counter': 3514, 'group_order': 1296, 'label': '6C-1', 'order': 6, 'powers': [6, 3], 'representative': 62, 'size': 12}
id: 114811406
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 25, 'group_counter': 3514, 'group_order': 1296, 'label': '6D1', 'order': 6, 'powers': [7, 3], 'representative': 54, 'size': 12}
id: 114811407
{'aut_label': '6A1', 'centralizer': '12.b1', 'counter': 26, 'group_counter': 3514, 'group_order': 1296, 'label': '6D-1', 'order': 6, 'powers': [7, 3], 'representative': 30, 'size': 12}
id: 114811408
{'aut_label': '6E', 'centralizer': '18.b1', 'counter': 27, 'group_counter': 3514, 'group_order': 1296, 'label': '6E', 'order': 6, 'powers': [7, 2], 'representative': 24, 'size': 18}
id: 114811409
{'aut_label': '6E', 'centralizer': '18.b1', 'counter': 28, 'group_counter': 3514, 'group_order': 1296, 'label': '6F', 'order': 6, 'powers': [6, 2], 'representative': 32, 'size': 18}
id: 114811410
{'aut_label': '6E', 'centralizer': '18.b1', 'counter': 29, 'group_counter': 3514, 'group_order': 1296, 'label': '6G', 'order': 6, 'powers': [5, 2], 'representative': 28, 'size': 18}
id: 114811412
{'aut_label': '6E', 'centralizer': '18.b1', 'counter': 30, 'group_counter': 3514, 'group_order': 1296, 'label': '6H', 'order': 6, 'powers': [4, 2], 'representative': 80, 'size': 18}
id: 114811413
{'aut_label': '6I', 'centralizer': '24.c1', 'counter': 31, 'group_counter': 3514, 'group_order': 1296, 'label': '6I', 'order': 6, 'powers': [8, 3], 'representative': 150, 'size': 24}
id: 114811414
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 32, 'group_counter': 3514, 'group_order': 1296, 'label': '6J1', 'order': 6, 'powers': [9, 3], 'representative': 146, 'size': 24}
id: 114811415
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 33, 'group_counter': 3514, 'group_order': 1296, 'label': '6J-1', 'order': 6, 'powers': [10, 3], 'representative': 154, 'size': 24}
id: 114811416
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 34, 'group_counter': 3514, 'group_order': 1296, 'label': '6K1', 'order': 6, 'powers': [11, 3], 'representative': 194, 'size': 24}
id: 114811417
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 35, 'group_counter': 3514, 'group_order': 1296, 'label': '6K-1', 'order': 6, 'powers': [12, 3], 'representative': 446, 'size': 24}
id: 114811418
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 36, 'group_counter': 3514, 'group_order': 1296, 'label': '6L1', 'order': 6, 'powers': [13, 3], 'representative': 458, 'size': 24}
id: 114811419
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 37, 'group_counter': 3514, 'group_order': 1296, 'label': '6L-1', 'order': 6, 'powers': [14, 3], 'representative': 494, 'size': 24}
id: 114811420
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 38, 'group_counter': 3514, 'group_order': 1296, 'label': '6M1', 'order': 6, 'powers': [15, 3], 'representative': 198, 'size': 24}
id: 114811421
{'aut_label': '6J1', 'centralizer': '24.c1', 'counter': 39, 'group_counter': 3514, 'group_order': 1296, 'label': '6M-1', 'order': 6, 'powers': [16, 3], 'representative': 462, 'size': 24}
id: 114811423
{'aut_label': '8A1', 'centralizer': '162.c1', 'counter': 40, 'group_counter': 3514, 'group_order': 1296, 'label': '8A1', 'order': 8, 'powers': [17, 40], 'representative': 121, 'size': 162}
id: 114811424
{'aut_label': '8A-1', 'centralizer': '162.c1', 'counter': 41, 'group_counter': 3514, 'group_order': 1296, 'label': '8A-1', 'order': 8, 'powers': [17, 41], 'representative': 13, 'size': 162}
id: 114811425
{'aut_label': '12A', 'centralizer': '36.c1', 'counter': 42, 'group_counter': 3514, 'group_order': 1296, 'label': '12A', 'order': 12, 'powers': [27, 17], 'representative': 12, 'size': 36}
id: 114811426
{'aut_label': '12A', 'centralizer': '36.c1', 'counter': 43, 'group_counter': 3514, 'group_order': 1296, 'label': '12B', 'order': 12, 'powers': [28, 17], 'representative': 16, 'size': 36}
id: 114811427
{'aut_label': '12A', 'centralizer': '36.c1', 'counter': 44, 'group_counter': 3514, 'group_order': 1296, 'label': '12C', 'order': 12, 'powers': [29, 17], 'representative': 20, 'size': 36}
id: 114811428
{'aut_label': '12A', 'centralizer': '36.c1', 'counter': 45, 'group_counter': 3514, 'group_order': 1296, 'label': '12D', 'order': 12, 'powers': [30, 17], 'representative': 40, 'size': 36}

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: 5491878
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.1a', '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], 'schur_index': 1}
id: 5491889
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.1b', '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], 'schur_index': 1}
id: 5491900
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.1c', '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], 'schur_index': 1}
id: 5491904
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.1d', '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], 'schur_index': 1}
id: 5491905
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 0, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, -1, 2, -1, -1], 'schur_index': 1}
id: 5491906
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, 0, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, -1, -1, -1, 2], 'schur_index': 1}
id: 5491907
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 0, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, -1, -1, 2, -1], 'schur_index': 1}
id: 5491908
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 0, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 2, -1, -1, -1], 'schur_index': 1}
id: 5491909
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2], 'schur_index': 1}
id: 5491879
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 0, 1, 1, 1, 1, 1, 1, -2, -2, -1, -1, 2, -1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, -1, 2, -1, -1], 'schur_index': 1}
id: 5491880
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, 2, 0, 1, 1, 1, 1, -2, -2, 1, 1, -1, 2, -1, -1, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, -1, -1, -1, 2], 'schur_index': 1}
id: 5491881
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 0, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, 2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, -1, -1, 2, -1], 'schur_index': 1}
id: 5491882
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 0, 1, 1, -2, -2, 1, 1, 1, 1, 2, -1, -1, -1, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 2, -1, -1, -1], 'schur_index': 1}
id: 5491883
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2j', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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], 'schur_index': 1}
id: 5491884
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2k', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, -2, 4, -2, 4, 4, -2, -2, -2, 4, -2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2], 'schur_index': 1}
id: 5491885
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2l', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, -2, 4, 4, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4], 'schur_index': 1}
id: 5491886
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2m', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, -2, 4, -2, -2, -2, -2, -2, 4, -2, -2, 4, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2], 'schur_index': 1}
id: 5491887
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.2n', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, 4, 0, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, 4, -2, -2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2], 'schur_index': 1}
id: 5491888
{'cdim': 4, 'counter': 19, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.4a', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 0, -2, -2, -2, 4, -2, 4, 4, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5491890
{'cdim': 4, 'counter': 20, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.4b', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 0, -2, -2, 4, -2, -2, -2, -2, -2, 4, -2, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5491891
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.4c', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 0, -2, 4, -2, -2, -2, -2, -2, 4, -2, -2, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5491892
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.4d', 'multiplicity': 1, 'nt': [24, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 5491893
{'cdim': 8, 'counter': 23, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8a', 'multiplicity': 1, 'nt': [9, 19], 'qdim': 8, 'qvalues': [8, 0, 2, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491894
{'cdim': 8, 'counter': 24, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8b', 'multiplicity': 1, 'nt': [18, 68], 'qdim': 8, 'qvalues': [8, 0, -2, 8, 8, 8, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491895
{'cdim': 8, 'counter': 25, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8c', 'multiplicity': 2, 'nt': [24, 1331], 'qdim': 16, 'qvalues': [16, 0, 4, -8, -8, -8, 16, 1, -2, -2, 1, 1, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491896
{'cdim': 8, 'counter': 26, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8d', 'multiplicity': 2, 'nt': [24, 1331], 'qdim': 16, 'qvalues': [16, 0, 4, -8, -8, 16, -8, 1, 1, 1, 1, -2, 1, -2, -2, 1, 0, 0, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491897
{'cdim': 8, 'counter': 27, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8e', 'multiplicity': 2, 'nt': [24, 1331], 'qdim': 16, 'qvalues': [16, 0, 4, -8, 16, -8, -8, 1, 1, 1, -2, 1, 1, -2, 1, -2, 0, 0, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, 1, 1, 1, 1, 1, 1, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491898
{'cdim': 8, 'counter': 28, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8f', 'multiplicity': 2, 'nt': [24, 1331], 'qdim': 16, 'qvalues': [16, 0, 4, 16, -8, -8, -8, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, -2, 1, 1, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491899
{'cdim': 8, 'counter': 29, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8g', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -4, -8, -8, -8, 16, 1, -2, -2, 1, 1, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491901
{'cdim': 8, 'counter': 30, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8h', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -4, -8, -8, 16, -8, 1, 1, 1, 1, -2, 1, -2, -2, 1, 0, 0, 2, 2, 2, 2, -4, -4, 2, 2, 0, 0, 0, 0, 2, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491902
{'cdim': 8, 'counter': 31, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8i', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -4, -8, 16, -8, -8, 1, 1, 1, -2, 1, 1, -2, 1, -2, 0, 0, -4, -4, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 5491903
{'cdim': 8, 'counter': 32, 'faithful': False, 'group': '1296.3514', 'group_order': 1296, 'image': None, 'label': '1296.3514.8j', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -4, 16, -8, -8, -8, -2, 1, 1, 1, 1, -2, -2, 1, 1, 0, 0, 2, 2, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 2, -1, -1, 2, 2, -1, -1, -1, -1, 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: 10698054
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1296, 'label': '1296.3514.1a', '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]]]}
id: 10698065
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 648, 'label': '1296.3514.1b', '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]]]}
id: 10698076
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 648, 'label': '1296.3514.1c', '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]]]}
id: 10698087
{'center': '1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 648, 'label': '1296.3514.1d', '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]]]}
id: 10698094
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.3514.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10698095
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.3514.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
id: 10698096
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 7, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.3514.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
id: 10698097
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 8, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 216, 'label': '1296.3514.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10698098
{'center': '4.a1', 'center_index': 4, 'center_order': 324, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 162, 'label': '1296.3514.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]]]}
id: 10698055
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.3514.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10698056
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.3514.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]]]}
id: 10698057
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.3514.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
id: 10698058
{'center': '6.a1', 'center_index': 6, 'center_order': 216, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 108, 'label': '1296.3514.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 10698059
{'center': '8.a1', 'center_index': 8, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1', 'kernel_order': 81, 'label': '1296.3514.2j1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698060
{'center': '8.a1', 'center_index': 8, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.a1', 'kernel_order': 81, 'label': '1296.3514.2j2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698061
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2k1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
id: 10698062
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2k2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]]]}
id: 10698063
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2l1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
id: 10698064
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 19, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2l2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]]]}
id: 10698066
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 20, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2m1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
id: 10698067
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2m2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
id: 10698068
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2n1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10698069
{'center': '12.a1', 'center_index': 12, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 54, 'label': '1296.3514.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 10698070
{'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.a1', 'kernel_order': 27, 'label': '1296.3514.4a', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[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]]]}
id: 10698071
{'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.a1', 'kernel_order': 27, 'label': '1296.3514.4b', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[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]]]}
id: 10698072
{'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.a1', 'kernel_order': 27, 'label': '1296.3514.4c', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-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]]]}
id: 10698073
{'center': '24.a1', 'center_index': 24, 'center_order': 54, 'counter': 27, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '48.16', 'image_order': 48, 'indicator': -1, 'kernel': '48.a1', 'kernel_order': 27, 'label': '1296.3514.4d', 'nt': [24, 42], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[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]]]}
id: 10698074
{'center': '144.a1', 'center_index': 144, 'center_order': 9, 'counter': 28, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 9, 'label': '1296.3514.8a', 'nt': [9, 19], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698075
{'center': '144.a1', 'center_index': 144, 'center_order': 9, 'counter': 29, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1', 'kernel_order': 9, 'label': '1296.3514.8b', 'nt': [18, 68], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698077
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 30, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8c1', 'nt': [24, 1331], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698078
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 31, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698079
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 32, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8d1', 'nt': [24, 1331], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698080
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 33, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8d2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698081
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 34, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8e1', 'nt': [24, 1331], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698082
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 35, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8e2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698083
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 36, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8f1', 'nt': [24, 1331], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698084
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 37, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8f2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[2, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698085
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 38, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8g1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698086
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 39, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8g2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698088
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 40, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8h1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698089
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 41, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8h2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698090
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 42, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8i1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698091
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 43, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8i2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0], [-3, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698092
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 44, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8j1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 10698093
{'center': '432.a1', 'center_index': 432, 'center_order': 3, 'counter': 45, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3514', 'group_counter': 3514, 'group_order': 1296, 'image': None, 'image_isoclass': '432.738', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1', 'kernel_order': 3, 'label': '1296.3514.8j2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-1, 0]], [[2, 0], [3, 1]], [[-1, 0], [-3, 1]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-3, 1]], [[2, 0], [3, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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: 71128254
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.3514.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, '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': '1296.3514', 'subgroup_hash': 3514, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 71128265
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, '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': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
id: 71128276
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.728', 'subgroup_hash': 728, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
id: 71128287
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.709', 'subgroup_hash': 709, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
id: 71128298
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 216, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, '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': '432.738', 'subgroup_hash': 738, 'subgroup_order': 432, 'subgroup_tex': 'C_3^3:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
id: 71128309
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, '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': ['D', 'L1', 'D1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 71128320
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 162, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128331
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
id: 71128337
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 216, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
id: 71128255
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, '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': '216.161', 'subgroup_hash': 161, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': False, 'sylow': 0}
id: 71128256
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 108, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, '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': '216.155', 'subgroup_hash': 155, 'subgroup_order': 216, 'subgroup_tex': 'C_3:F_9', 'supersolvable': False, 'sylow': 0}
id: 71128257
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
id: 71128258
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1', 'outer_equivalence': True, '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': 8, '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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
id: 71128259
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, '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': 9, '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': '144.97', 'subgroup_hash': 97, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
id: 71128260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, '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': 9, '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': '144.182', 'subgroup_hash': 182, 'subgroup_order': 144, 'subgroup_tex': 'F_9:C_2', 'supersolvable': False, 'sylow': 0}
id: 71128261
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, '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': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
id: 71128262
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 71128263
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, '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': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128264
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, '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': '108.37', 'subgroup_hash': 37, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
id: 71128266
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1296.3514.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S', 'L3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
id: 71128267
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 72, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
id: 71128268
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, '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': 18, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, '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': 18, '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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 71128270
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 9, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, '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': 18, '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': '72.13', 'subgroup_hash': 13, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:C_8', 'supersolvable': True, 'sylow': 0}
id: 71128271
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, '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': 18, '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': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
id: 71128272
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, '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': 18, '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': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
id: 71128273
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 71128274
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128275
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128277
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128278
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128279
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128280
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, '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': 27, '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': '48.16', 'subgroup_hash': 16, 'subgroup_order': 48, 'subgroup_tex': 'C_3:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 71128281
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 36, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 71128282
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, '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': 36, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
id: 71128283
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, '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': 36, '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': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 71128284
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, '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': 36, '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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 71128285
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, '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': 36, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 71128286
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, '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': 36, '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': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128288
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, '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': 36, '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': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
id: 71128289
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 71128290
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1', 'outer_equivalence': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 71128291
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
id: 71128292
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, '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': 54, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 71128293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, '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': 54, '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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 71128294
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, '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': 54, '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': '24.1', 'subgroup_hash': 1, 'subgroup_order': 24, 'subgroup_tex': 'C_3:C_8', 'supersolvable': True, 'sylow': 0}
id: 71128295
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 18, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.35', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
id: 71128296
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, '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': 72, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128297
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, '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': 72, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 71128299
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, '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': 72, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, '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': 72, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128301
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, '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': 72, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128302
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, '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': 72, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 71128303
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, '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': 72, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 71128304
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, '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': 72, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
id: 71128305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.3514.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, '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': 81, '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': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 2}
id: 71128306
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, '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': 108, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 71128307
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, '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': 108, '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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
id: 71128308
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, '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': 108, '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: 71128310
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, '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': 108, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 71128311
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 9, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.144.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 182, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128312
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3514.144.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '144.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '144.97', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 97, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128313
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.144.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1', 'outer_equivalence': True, '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': 144, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128314
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.144.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1', 'outer_equivalence': True, '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': 144, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128315
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.144.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1', 'outer_equivalence': True, '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': 144, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128316
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.144.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1', 'outer_equivalence': True, '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': 144, '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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
id: 71128317
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, '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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 71128318
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, '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': 162, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 71128319
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, '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': 162, '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: 71128321
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1', 'outer_equivalence': True, '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': 216, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 71128322
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1', 'outer_equivalence': True, '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': 216, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 71128323
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, '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': 216, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 71128324
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, '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': 216, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 71128325
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, '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': 216, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 71128326
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, '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': 216, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 71128327
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3514.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, '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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 71128328
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, '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': 324, '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: 71128329
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, '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': 324, '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: 71128330
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3514.432.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '432.738', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 738, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:\\SD_{16}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 71128332
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.432.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1', 'outer_equivalence': True, '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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 71128333
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.432.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1', 'outer_equivalence': True, '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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
id: 71128334
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.a1', 'outer_equivalence': True, '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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 71128335
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3514.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1', 'outer_equivalence': True, '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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 71128336
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3514', 'ambient_counter': 3514, 'ambient_order': 1296, 'ambient_tex': 'C_3^4:\\SD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1296.3514.1296.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1296.3514', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3514, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'PC', 'U0', 'D3', '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: 71128254
{'ambient': '1296.3514', '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': '1296.a1', 'complements': ['1296.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8297, 4126, 7353, 3423], 'generators': [1, 4, 48, 6, 72, 432, 1008, 108], 'label': '1296.3514.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.3514'}
id: 71128255
{'ambient': '1296.3514', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '12.d1', '18.e1', '54.b1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8691, -1, 8129, -1], 'generators': [47, 432, 1008, 108, 72, 48], 'label': '1296.3514.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '432.738'}
id: 71128256
{'ambient': '1296.3514', 'aut_centralizer_order': 6, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '18.f1', '54.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9435, -1, 8953, -1], 'generators': [1, 432, 1008, 108, 72, 48], 'label': '1296.3514.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '432.738'}
id: 71128257
{'ambient': '1296.3514', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '24.a1', '24.b1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5079, 2480, 3439, 1630], 'generators': [72, 432, 4, 48, 576], 'label': '1296.3514.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.a1', '24.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128258
{'ambient': '1296.3514', 'aut_centralizer_order': 27, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 108, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1'], 'contains': ['16.a1', '24.c1', '24.d1', '24.e1', '24.f1'], 'core': '16.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2320, -1, 1631, -1], 'generators': [6, 432, 4, 48, 576], 'label': '1296.3514.8.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '8.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 71128259
{'ambient': '1296.3514', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '3456.in', 'aut_weyl_index': 18, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.b1', '18.c1', '18.d1', '27.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8500, -1, 7353, -1], 'generators': [1, 48, 4, 6, 108, 72], 'label': '1296.3514.9.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '72.35'}
id: 71128260
{'ambient': '1296.3514', 'aut_centralizer_order': 48, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.e1', '18.f1', '81.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9883, -1, 9408, -1], 'generators': [1, 432, 1008, 6, 108, 72], 'label': '1296.3514.9.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128261
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.a1', '6.b1', '6.c1'], 'contains': ['24.a1', '36.a1', '108.b1'], 'core': '12.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7698, 5720, 6941, 5333], 'generators': [108, 432, 48, 72, 576], 'label': '1296.3514.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128262
{'ambient': '1296.3514', 'aut_centralizer_order': 18, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.851', 'aut_weyl_index': 216, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1'], 'contains': ['24.b1', '24.c1', '24.f1', '36.b1', '36.e1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3983, -1, 2659, -1], 'generators': [6, 432, 72, 4, 48], 'label': '1296.3514.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '12.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128263
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '144.186', 'aut_weyl_index': 432, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.a1', '24.e1', '36.e1', '36.f1'], 'core': '24.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5072, -1, 4114, -1], 'generators': [6, 432, 72, 48, 576], 'label': '1296.3514.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 71128264
{'ambient': '1296.3514', 'aut_centralizer_order': 6, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '432.742', 'aut_weyl_index': 144, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.b1'], 'contains': ['24.a1', '36.g1', '108.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [6771, -1, 5639, -1], 'generators': [47, 432, 72, 48, 1008], 'label': '1296.3514.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '12.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '216.161'}
id: 71128265
{'ambient': '1296.3514', 'aut_centralizer_order': 9, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1', '18.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6257, 8779, 5353, 6914], 'generators': [6, 576, 72, 108, 432, 4, 48], 'label': '1296.3514.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128266
{'ambient': '1296.3514', 'aut_centralizer_order': 81, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '768.1086791', 'aut_weyl_index': 81, 'centralizer': '16.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1'], 'contains': ['48.a1', '48.b1', '48.c1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2468, 1118, 855, 1630], 'generators': [4, 48, 576, 432], 'label': '1296.3514.16.a1', 'mobius_quo': -3, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['48.a1', '144.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '1296.3514', 'quotient_action_image': '16.8', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
id: 71128267
{'ambient': '1296.3514', 'aut_centralizer_order': 432, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.b1'], 'contains': ['36.a1', '36.f1', '162.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8183, 8779, 7776, 8708], 'generators': [6, 432, 108, 72, 576], 'label': '1296.3514.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['36.a1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128268
{'ambient': '1296.3514', 'aut_centralizer_order': 18, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '384.17972', 'aut_weyl_index': 162, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.b1', '36.c1', '54.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6620, -1, 5028, -1], 'generators': [6, 72, 108, 4, 48], 'label': '1296.3514.18.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 71128269
{'ambient': '1296.3514', 'aut_centralizer_order': 2, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '3456.in', 'aut_weyl_index': 18, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '9.a1'], 'contains': ['36.c1', '36.d1', '54.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7128, -1, 6172, -1], 'generators': [47, 48, 108, 72, 4], 'label': '1296.3514.18.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '72.35'}
id: 71128270
{'ambient': '1296.3514', 'aut_centralizer_order': 8, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '9.a1'], 'contains': ['36.c1', '54.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8673, -1, 8298, -1], 'generators': [1, 48, 108, 72, 4], 'label': '1296.3514.18.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
id: 71128271
{'ambient': '1296.3514', 'aut_centralizer_order': 48, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.b1'], 'contains': ['36.a1', '36.g1', '162.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9346, -1, 9408, -1], 'generators': [47, 432, 108, 72, 1008], 'label': '1296.3514.18.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128272
{'ambient': '1296.3514', 'aut_centralizer_order': 48, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.b1'], 'contains': ['36.a1', '162.c1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9824, -1, 9894, -1], 'generators': [1, 432, 108, 72, 1008], 'label': '1296.3514.18.f1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128273
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.a1', '12.c1', '12.d1'], 'contains': ['48.a1', '72.a1', '72.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5466, 3714, 4651, 4021], 'generators': [72, 48, 576, 432], 'label': '1296.3514.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['48.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128274
{'ambient': '1296.3514', 'aut_centralizer_order': 18, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.851', 'aut_weyl_index': 216, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1'], 'contains': ['48.c1', '72.b1', '72.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4035, -1, 3165, -1], 'generators': [72, 4, 48, 432], 'label': '1296.3514.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128275
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.b1'], 'contains': ['48.c1', '72.d1', '72.e1', '72.f1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1747, -1, 1325, -1], 'generators': [6, 4, 48, 144], 'label': '1296.3514.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '24.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128276
{'ambient': '1296.3514', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '1296.a1', 'complements': ['648.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.b1', '18.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7293, 4126, 6063, 3423], 'generators': [47, 1008, 48, 108, 432, 72, 4], 'label': '1296.3514.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '1296.3514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '1296.3514'}
id: 71128277
{'ambient': '1296.3514', 'aut_centralizer_order': 27, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1'], 'contains': ['48.b1', '72.e1', '72.g1', '72.h1'], 'core': '432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1170, -1, 388, -1], 'generators': [438, 1156, 48, 432], 'label': '1296.3514.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '24.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128278
{'ambient': '1296.3514', 'aut_centralizer_order': 162, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '12.c1'], 'contains': ['48.a1', '72.d1', '72.g1', '72.h1', '72.i1'], 'core': '48.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [3299, -1, 2553, -1], 'generators': [6, 48, 576, 432], 'label': '1296.3514.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '24.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 71128279
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '288.851', 'aut_weyl_index': 216, 'centralizer': '24.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '12.b1'], 'contains': ['48.c1', '72.f1', '72.g1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2465, -1, 1941, -1], 'generators': [6, 4, 48, 432], 'label': '1296.3514.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '24.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128280
{'ambient': '1296.3514', 'aut_centralizer_order': 12, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1296, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '9.a1'], 'contains': ['54.a1', '54.b1', '54.c1', '81.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9518, -1, 8867, -1], 'generators': [1, 48, 6, 108, 72], 'label': '1296.3514.27.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 71128281
{'ambient': '1296.3514', 'aut_centralizer_order': 432, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.a1', '18.e1', '18.f1'], 'contains': ['72.a1', '324.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8559, 6337, 8447, 6798], 'generators': [108, 72, 576, 432], 'label': '1296.3514.36.a1', 'mobius_quo': 0, 'mobius_sub': 54, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '18.a1'], 'normal_contains': ['72.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128282
{'ambient': '1296.3514', 'aut_centralizer_order': 36, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.b1'], 'contains': ['72.b1', '72.f1', '108.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5175, -1, 4165, -1], 'generators': [6, 72, 4, 48], 'label': '1296.3514.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '36.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128283
{'ambient': '1296.3514', 'aut_centralizer_order': 72, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '18.b1', '18.c1', '18.d1'], 'contains': ['72.b1', '108.b1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6628, -1, 6059, -1], 'generators': [108, 4, 48, 72], 'label': '1296.3514.36.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 71128284
{'ambient': '1296.3514', 'aut_centralizer_order': 4, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '18.c1'], 'contains': ['72.b1', '108.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5977, -1, 5518, -1], 'generators': [47, 72, 4, 48], 'label': '1296.3514.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
id: 71128285
{'ambient': '1296.3514', 'aut_centralizer_order': 108, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.b1', '12.c1'], 'contains': ['72.c1', '72.d1', '72.g1', '108.a1', '108.d1'], 'core': '432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4494, -1, 3737, -1], 'generators': [6, 72, 48, 432], 'label': '1296.3514.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128286
{'ambient': '1296.3514', 'aut_centralizer_order': 432, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.40', 'aut_weyl_index': 864, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.a1'], 'contains': ['72.a1', '72.i1', '108.d1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5476, -1, 5137, -1], 'generators': [6, 72, 576, 432], 'label': '1296.3514.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 71128287
{'ambient': '1296.3514', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '1296.a1', 'complements': ['648.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.c1', '18.d1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8845, 1221, 7882, 1244], 'generators': [1, 1008, 48, 108, 432, 72, 4], 'label': '1296.3514.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '1296.3514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '1296.3514'}
id: 71128288
{'ambient': '1296.3514', 'aut_centralizer_order': 48, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.41', 'aut_weyl_index': 864, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.a1', '324.c1'], 'core': '72.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7293, -1, 7459, -1], 'generators': [47, 72, 1008, 432], 'label': '1296.3514.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1', 'old_label': '36.g1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
id: 71128289
{'ambient': '1296.3514', 'aut_centralizer_order': 486, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '32.40', 'aut_weyl_index': 1944, 'centralizer': '16.a1', 'complements': ['27.a1'], 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '24.a1', '24.e1'], 'contains': ['144.b1', '144.c1', '144.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3299, 2403, 3435, 3173], 'generators': [48, 576, 432], 'label': '1296.3514.48.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1'], 'normal_contains': ['144.b1', '432.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '1296.3514', 'quotient_action_image': '16.8', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
id: 71128290
{'ambient': '1296.3514', 'aut_centralizer_order': 81, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.a1', '24.d1'], 'contains': ['144.c1', '144.d1', '144.e1', '144.f1'], 'core': '432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [842, -1, 125, -1], 'generators': [4, 624, 432], 'label': '1296.3514.48.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '48.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128291
{'ambient': '1296.3514', 'aut_centralizer_order': 162, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.b1', '24.c1', '24.f1'], 'contains': ['144.a1', '144.c1', '144.d1'], 'core': '144.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2108, -1, 1514, -1], 'generators': [4, 48, 432], 'label': '1296.3514.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '48.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128292
{'ambient': '1296.3514', 'aut_centralizer_order': 108, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '16.11', 'aut_weyl_index': 3888, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '18.b1', '27.a1'], 'contains': ['108.a1', '108.b1', '162.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7404, -1, 6800, -1], 'generators': [6, 108, 48, 72], 'label': '1296.3514.54.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 71128293
{'ambient': '1296.3514', 'aut_centralizer_order': 12, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1296, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.b1', '18.c1', '27.a1'], 'contains': ['108.b1', '108.c1', '162.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8286, -1, 7878, -1], 'generators': [47, 108, 72, 48], 'label': '1296.3514.54.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '24.8'}
id: 71128294
{'ambient': '1296.3514', 'aut_centralizer_order': 48, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '324.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.c1', '18.d1', '27.a1'], 'contains': ['108.b1', '162.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8993, -1, 8867, -1], 'generators': [1, 108, 72, 48], 'label': '1296.3514.54.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 71128295
{'ambient': '1296.3514', 'aut_centralizer_order': 432, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.a1', '36.f1', '36.g1'], 'contains': ['144.b1', '216.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6128, 4074, 6188, 4851], 'generators': [72, 576, 432], 'label': '1296.3514.72.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '36.a1'], 'normal_contains': ['144.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128296
{'ambient': '1296.3514', 'aut_centralizer_order': 144, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1296, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1', '36.b1', '36.c1', '36.d1'], 'contains': ['144.a1', '216.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5709, -1, 4925, -1], 'generators': [72, 4, 48], 'label': '1296.3514.72.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '72.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128297
{'ambient': '1296.3514', 'aut_centralizer_order': 108, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.a1', '24.b1', '36.e1'], 'contains': ['144.c1', '216.a1', '216.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [4788, -1, 4392, -1], 'generators': [72, 48, 432], 'label': '1296.3514.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128298
{'ambient': '1296.3514', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '9.b1', '27.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9655, -1, 8580, -1], 'generators': [1, 1008, 48, 6, 432, 108, 72], 'label': '1296.3514.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '432.738'}
id: 71128299
{'ambient': '1296.3514', 'aut_centralizer_order': 324, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.e1', '36.e1'], 'contains': ['144.c1', '216.c1', '216.d1', '216.e1'], 'core': '432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [3509, -1, 3008, -1], 'generators': [6, 48, 144], 'label': '1296.3514.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128300
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '24.d1'], 'contains': ['144.d1', '216.c1', '216.e1'], 'core': '432.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [530, -1, 553, -1], 'generators': [438, 292, 48], 'label': '1296.3514.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '72.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128301
{'ambient': '1296.3514', 'aut_centralizer_order': 108, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1296, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '24.f1', '36.b1'], 'contains': ['144.a1', '216.c1'], 'core': '144.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2229, -1, 1941, -1], 'generators': [6, 4, 48], 'label': '1296.3514.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '72.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128302
{'ambient': '1296.3514', 'aut_centralizer_order': 324, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '24.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.e1', '24.f1', '36.e1'], 'contains': ['144.c1', '216.c1', '216.f1'], 'core': '432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2868, -1, 2474, -1], 'generators': [6, 48, 432], 'label': '1296.3514.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '72.g1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128303
{'ambient': '1296.3514', 'aut_centralizer_order': 162, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '24.e1'], 'contains': ['144.e1', '216.e1', '216.f1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1309, -1, 1086, -1], 'generators': [6, 624, 432], 'label': '1296.3514.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '72.h1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128304
{'ambient': '1296.3514', 'aut_centralizer_order': 1296, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '48.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1', '36.f1'], 'contains': ['144.b1', '216.d1', '216.f1'], 'core': '144.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4149, -1, 3863, -1], 'generators': [6, 576, 432], 'label': '1296.3514.72.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '72.i1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 71128305
{'ambient': '1296.3514', 'aut_centralizer_order': 96, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 7776, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '27.a1'], 'contains': ['162.a1', '162.b1', '162.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9750, -1, 9239, -1], 'generators': [1, 6], 'label': '1296.3514.81.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 71128306
{'ambient': '1296.3514', 'aut_centralizer_order': 216, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.b1', '36.e1', '54.a1'], 'contains': ['216.a1', '216.c1', '324.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5606, -1, 5741, -1], 'generators': [6, 72, 48], 'label': '1296.3514.108.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128307
{'ambient': '1296.3514', 'aut_centralizer_order': 432, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '36.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.a1', '36.c1', '54.a1', '54.b1', '54.c1'], 'contains': ['216.a1', '324.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7635, -1, 7145, -1], 'generators': [108, 48, 72], 'label': '1296.3514.108.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '108.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 71128308
{'ambient': '1296.3514', 'aut_centralizer_order': 24, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['12.d1', '36.d1', '54.b1'], 'contains': ['216.a1', '324.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [6506, -1, 6549, -1], 'generators': [47, 72, 48], 'label': '1296.3514.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1', 'old_label': '108.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 71128309
{'ambient': '1296.3514', 'aut_centralizer_order': 9, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '36.c1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6257, 4126, 5455, 3018], 'generators': [108, 432, 576, 4, 48, 72], 'label': '1296.3514.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
id: 71128310
{'ambient': '1296.3514', 'aut_centralizer_order': 864, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1', '36.f1'], 'contains': ['216.b1', '216.d1', '216.f1', '324.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4848, -1, 5333, -1], 'generators': [6, 72, 432], 'label': '1296.3514.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128311
{'ambient': '1296.3514', 'aut_centralizer_order': 1296, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1296, 'centralizer': '2.a1', 'complements': ['9.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.c1', '72.b1', '72.f1'], 'contains': ['432.a1'], 'core': '144.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1931, 8882, 2702, 5583], 'generators': [4, 48], 'label': '1296.3514.144.a1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '144.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['432.a1'], 'normalizer': '1.a1', 'old_label': '144.a1', 'projective_image': '1296.3514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.40', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128312
{'ambient': '1296.3514', 'aut_centralizer_order': 3888, 'aut_label': '144.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 3888, 'centralizer': '16.a1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '72.a1', '72.i1'], 'contains': ['432.b1'], 'core': '144.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4306, 3252, 3870, 4002], 'generators': [576, 432], 'label': '1296.3514.144.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': ['48.a1', '72.a1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '144.b1', 'projective_image': '1296.3514', 'quotient_action_image': '16.8', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '144.b1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
id: 71128313
{'ambient': '1296.3514', 'aut_centralizer_order': 972, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.a1', '48.b1', '48.c1', '72.c1', '72.d1', '72.g1'], 'contains': ['432.a1', '432.b1', '432.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2828, -1, 2380, -1], 'generators': [48, 432], 'label': '1296.3514.144.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '144.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128314
{'ambient': '1296.3514', 'aut_centralizer_order': 162, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.b1', '48.c1', '72.e1'], 'contains': ['432.a1', '432.c1'], 'core': '432.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [460, -1, 1455, -1], 'generators': [4, 480], 'label': '1296.3514.144.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '144.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128315
{'ambient': '1296.3514', 'aut_centralizer_order': 486, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['48.a1', '48.b1', '72.h1'], 'contains': ['432.b1', '432.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1309, -1, 2059, -1], 'generators': [624, 432], 'label': '1296.3514.144.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '144.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128316
{'ambient': '1296.3514', 'aut_centralizer_order': 81, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.8', 'aut_weyl_index': 3888, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['48.b1'], 'contains': ['432.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [117, -1, 627, -1], 'generators': [436, 624], 'label': '1296.3514.144.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1', 'old_label': '144.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128317
{'ambient': '1296.3514', 'aut_centralizer_order': 864, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.3', 'aut_weyl_index': 7776, 'centralizer': '72.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '54.a1', '81.a1'], 'contains': ['324.a1', '324.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7867, -1, 7792, -1], 'generators': [6, 108], 'label': '1296.3514.162.a1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 71128318
{'ambient': '1296.3514', 'aut_centralizer_order': 96, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 7776, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1', '54.b1', '81.a1'], 'contains': ['324.b1', '324.c1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8845, -1, 8074, -1], 'generators': [47, 108], 'label': '1296.3514.162.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 71128319
{'ambient': '1296.3514', 'aut_centralizer_order': 384, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '54.c1', '81.a1'], 'contains': ['324.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9710, -1, 9051, -1], 'generators': [1], 'label': '1296.3514.162.c1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128320
{'ambient': '1296.3514', 'aut_centralizer_order': 9, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3456.kh', 'aut_weyl_index': 18, 'centralizer': '144.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.b1', '12.b1', '12.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4300, -1, 3439, -1], 'generators': [6, 432, 576, 72, 4, 48], 'label': '1296.3514.4.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
id: 71128321
{'ambient': '1296.3514', 'aut_centralizer_order': 864, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '18.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.b1', '72.c1', '108.a1', '108.b1', '108.c1'], 'contains': ['432.a1', '648.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5786, -1, 5439, -1], 'generators': [72, 48], 'label': '1296.3514.216.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '216.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128322
{'ambient': '1296.3514', 'aut_centralizer_order': 864, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '72.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.c1', '108.d1'], 'contains': ['432.b1', '648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4884, -1, 5157, -1], 'generators': [72, 432], 'label': '1296.3514.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128323
{'ambient': '1296.3514', 'aut_centralizer_order': 648, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.e1', '72.f1', '72.g1', '108.a1'], 'contains': ['432.a1', '648.b1'], 'core': '432.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2420, -1, 3004, -1], 'generators': [6, 48], 'label': '1296.3514.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128324
{'ambient': '1296.3514', 'aut_centralizer_order': 2592, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.i1', '108.d1'], 'contains': ['432.b1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3946, -1, 3569, -1], 'generators': [6, 144], 'label': '1296.3514.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.d1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128325
{'ambient': '1296.3514', 'aut_centralizer_order': 324, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.d1', '72.e1', '72.h1'], 'contains': ['432.c1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1099, -1, 1757, -1], 'generators': [6, 336], 'label': '1296.3514.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '216.e1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128326
{'ambient': '1296.3514', 'aut_centralizer_order': 2592, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '24.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1', '72.h1', '72.i1', '108.d1'], 'contains': ['432.b1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3527, -1, 3286, -1], 'generators': [6, 432], 'label': '1296.3514.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '216.f1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 71128327
{'ambient': '1296.3514', 'aut_centralizer_order': 1728, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '36.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.d1', '162.a1'], 'contains': ['648.a1', '648.b1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5506, -1, 5741, -1], 'generators': [6, 72], 'label': '1296.3514.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '324.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128328
{'ambient': '1296.3514', 'aut_centralizer_order': 3456, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '18.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '108.b1', '162.a1', '162.b1', '162.c1'], 'contains': ['648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8357, -1, 7933, -1], 'generators': [108], 'label': '1296.3514.324.b1', 'mobius_quo': None, 'mobius_sub': -54, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128329
{'ambient': '1296.3514', 'aut_centralizer_order': 192, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '324.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1', '108.c1', '162.b1'], 'contains': ['648.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6716, -1, 6984, -1], 'generators': [47], 'label': '1296.3514.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1', 'old_label': '324.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128330
{'ambient': '1296.3514', 'aut_centralizer_order': 7776, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '2.a1', 'complements': ['3.a1'], 'conjugacy_class_count': 4, 'contained_in': ['144.a1', '144.c1', '144.d1', '216.a1', '216.c1'], 'contains': ['1296.a1'], 'core': '432.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2206, 8882, 2780, 5583], 'generators': [48], 'label': '1296.3514.432.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1', 'normal_contained_in': ['48.a1', '144.a1'], 'normal_contains': ['1296.a1'], 'normalizer': '1.a1', 'old_label': '432.a1', 'projective_image': '1296.3514', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.157', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128331
{'ambient': '1296.3514', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '1296.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.a1', '12.d1', '36.d1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6941, -1, 4725, -1], 'generators': [47, 432, 1008, 72, 4, 48], 'label': '1296.3514.4.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '648.728'}
id: 71128332
{'ambient': '1296.3514', 'aut_centralizer_order': 7776, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1', '144.c1', '144.e1', '216.b1', '216.d1', '216.f1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3530, -1, 3427, -1], 'generators': [432], 'label': '1296.3514.432.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1', 'old_label': '432.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 71128333
{'ambient': '1296.3514', 'aut_centralizer_order': 972, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '8.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['144.c1', '144.d1', '144.e1', '144.f1', '216.e1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1203, -1, 1910, -1], 'generators': [480], 'label': '1296.3514.432.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1', 'old_label': '432.c1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128334
{'ambient': '1296.3514', 'aut_centralizer_order': 6912, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '324.a1', '324.b1', '324.c1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5664, -1, 5588, -1], 'generators': [72], 'label': '1296.3514.648.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '648.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128335
{'ambient': '1296.3514', 'aut_centralizer_order': 5184, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1', '216.d1', '216.e1', '216.f1', '324.a1'], 'contains': ['1296.a1'], 'core': '1296.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2972, -1, 3145, -1], 'generators': [6], 'label': '1296.3514.648.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '648.b1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128336
{'ambient': '1296.3514', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1', '432.b1', '432.c1', '648.a1', '648.b1'], 'contains': [], 'core': '1296.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2972, 8882, 3145, 5583], 'generators': [], 'label': '1296.3514.1296.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1', 'normal_contained_in': ['144.b1', '432.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1296.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 71128337
{'ambient': '1296.3514', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.c1', '18.a1', '54.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7526, 8779, 6478, 7319], 'generators': [6, 432, 576, 108, 48, 72], 'label': '1296.3514.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '1296.3514', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
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.