LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 4, 4, 2, 2, 4, 2, 2, 6, 6], 'aut_gens': [[1, 2, 4, 16], [297, 130, 140, 304], [105, 322, 332, 16], [105, 66, 68, 88], [97, 202, 12, 16], [1, 330, 324, 272], [105, 138, 132, 376], [297, 10, 12, 88], [9, 194, 204, 112], [193, 138, 324, 368], [9, 330, 332, 216], [1, 322, 324, 216]], 'aut_group': None, 'aut_hash': 2404398907887337476, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 32, 'aut_perms': [179865383647363967378230281623271101, 90834815655618413916672747101064962, 78173031907512503922565526909365707, 214260625270653934358231306199346380, 107209143676323410940671072125736882, 182013476455464508090782151393754339, 28771362334843724057297703912503667, 207629565121270213468921416130759475, 182960134059313424393513136273049415, 111029629594188326180622279149504547, 94593098532876093728201220107265747], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 2, 1], [2, 6, 2, 1], [2, 8, 1, 1], [2, 12, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 6, 2, 2], [4, 8, 1, 1], [4, 12, 1, 1], [4, 12, 2, 1], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 2, 1], [6, 16, 1, 1], [8, 8, 1, 2], [8, 24, 1, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 1], [12, 16, 1, 1], [24, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^4.C_2^6.C_2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 2], [2, 6, 2], [2, 8, 1], [2, 12, 2], [3, 2, 1], [4, 2, 4], [4, 4, 3], [4, 6, 4], [4, 8, 1], [4, 12, 3], [4, 24, 2], [6, 2, 3], [6, 8, 2], [6, 16, 1], [8, 8, 2], [8, 24, 2], [12, 4, 4], [12, 8, 3], [12, 16, 1], [24, 8, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.209', 'commutator_count': 1, 'commutator_label': '24.9', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 13083, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 2], [2, 6, 1, 2], [2, 8, 1, 1], [2, 12, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 1], [4, 4, 2, 1], [4, 6, 2, 2], [4, 8, 1, 1], [4, 12, 1, 1], [4, 12, 2, 1], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 1, 2], [6, 16, 1, 1], [8, 8, 1, 2], [8, 24, 1, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 1], [12, 16, 1, 1], [24, 8, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1048320, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '48.51', 'hash': 13083, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 12], 'inner_gens': [[1, 2, 4, 304], [1, 2, 4, 280], [1, 2, 4, 80], [97, 138, 324, 16]], 'inner_hash': 209, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': None, 'inner_tex': 'D_4\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 14], [8, 1]], 'label': '384.13083', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 64, 'linR_count': 64, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2*D8).D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 109, 'number_conjugacy_classes': 51, 'number_divisions': 42, 'number_normal_subgroups': 117, 'number_subgroup_autclasses': 370, 'number_subgroup_classes': 450, 'number_subgroups': 1590, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 55], [3, 2], [4, 136], [6, 38], [8, 64], [12, 56], [24, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [128, 32, 288, 288, 0, 0], 'outer_gens': [[297, 130, 140, 304], [105, 322, 332, 16], [105, 66, 68, 88], [97, 202, 12, 16], [1, 330, 324, 272], [9, 194, 204, 112]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1987252695887726299102628950722389104143655625911614374195677175161137525260444049408023, 4280060190210255720966682203741286370421100029724695868241751943349027324834480013092280, 6303134199575853538205911758367735940782282497153361624731204400309332312213220258924201, 8317908376181754035069272075764922701084313581680350594218247717267979049582297588573975, 10325398078985016270450017865627035466369500247024770587564995616301325311781904359706664, 16375274327112018113528881407954813017423511995697955917723634276790183330559209875621568], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 10], [8, 3], [16, 1]], 'representations': {'PC': {'code': 34902357572210874186333058649215581436609590273, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, 2, -2, -2, -3, 66, 12164, 5612, 820, 116, 10757, 3853, 1941, 141, 8974, 4502, 166, 8207, 4119]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [1232225, 2764825, 1231525, 111745, 111361, 112207, 2612909, 2157163]}, 'Perm': {'d': 19, 'gens': [6446835113246929, 1089305681962421, 13875745172892715, 20716451327152751, 13875745172889600, 19389, 12341, 3991680]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times D_8).D_6', 'transitive_degree': 96, '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: 104120243
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 13083, 'group_order': 384, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 104120254
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 13083, 'group_order': 384, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 8, 'size': 1}
id: 104120265
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 13083, 'group_order': 384, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 200, 'size': 1}
id: 104120276
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 13083, 'group_order': 384, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 192, 'size': 1}
id: 104120287
{'aut_label': '2D', 'centralizer': '4.bj1.a1', 'counter': 5, 'group_counter': 13083, 'group_order': 384, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 4}
id: 104120290
{'aut_label': '2D', 'centralizer': '4.bj1.a1', 'counter': 6, 'group_counter': 13083, 'group_order': 384, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 9, 'size': 4}
id: 104120291
{'aut_label': '2F', 'centralizer': '6.c1.a1', 'counter': 7, 'group_counter': 13083, 'group_order': 384, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 2, 'size': 6}
id: 104120292
{'aut_label': '2F', 'centralizer': '6.c1.a1', 'counter': 8, 'group_counter': 13083, 'group_order': 384, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 66, 'size': 6}
id: 104120293
{'aut_label': '2H', 'centralizer': '8.bf1.a1', 'counter': 9, 'group_counter': 13083, 'group_order': 384, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 151, 'size': 8}
id: 104120244
{'aut_label': '2I', 'centralizer': '12.h1.a1', 'counter': 10, 'group_counter': 13083, 'group_order': 384, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 3, 'size': 12}
id: 104120245
{'aut_label': '2I', 'centralizer': '12.h1.a1', 'counter': 11, 'group_counter': 13083, 'group_order': 384, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 35, 'size': 12}
id: 104120246
{'aut_label': '3A', 'centralizer': '2.d1.a1', 'counter': 12, 'group_counter': 13083, 'group_order': 384, 'label': '3A', 'order': 3, 'powers': [12, 1], 'representative': 256, 'size': 2}
id: 104120247
{'aut_label': '4A', 'centralizer': '2.j1.a1', 'counter': 13, 'group_counter': 13083, 'group_order': 384, 'label': '4A', 'order': 4, 'powers': [4, 13], 'representative': 104, 'size': 2}
id: 104120248
{'aut_label': '4B', 'centralizer': '2.j1.a1', 'counter': 14, 'group_counter': 13083, 'group_order': 384, 'label': '4B', 'order': 4, 'powers': [4, 14], 'representative': 96, 'size': 2}
id: 104120249
{'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 15, 'group_counter': 13083, 'group_order': 384, 'label': '4C1', 'order': 4, 'powers': [2, 16], 'representative': 14, 'size': 2}
id: 104120250
{'aut_label': '4C1', 'centralizer': '2.b1.a1', 'counter': 16, 'group_counter': 13083, 'group_order': 384, 'label': '4C-1', 'order': 4, 'powers': [2, 15], 'representative': 6, 'size': 2}
id: 104120251
{'aut_label': '4D', 'centralizer': '4.i1.a1', 'counter': 17, 'group_counter': 13083, 'group_order': 384, 'label': '4D', 'order': 4, 'powers': [3, 17], 'representative': 110, 'size': 4}
id: 104120252
{'aut_label': '4E1', 'centralizer': '4.bj1.a1', 'counter': 18, 'group_counter': 13083, 'group_order': 384, 'label': '4E1', 'order': 4, 'powers': [2, 19], 'representative': 15, 'size': 4}
id: 104120253
{'aut_label': '4E1', 'centralizer': '4.bj1.a1', 'counter': 19, 'group_counter': 13083, 'group_order': 384, 'label': '4E-1', 'order': 4, 'powers': [2, 18], 'representative': 7, 'size': 4}
id: 104120255
{'aut_label': '4F1', 'centralizer': '6.c1.a1', 'counter': 20, 'group_counter': 13083, 'group_order': 384, 'label': '4F1', 'order': 4, 'powers': [2, 21], 'representative': 4, 'size': 6}
id: 104120256
{'aut_label': '4F1', 'centralizer': '6.c1.a1', 'counter': 21, 'group_counter': 13083, 'group_order': 384, 'label': '4F-1', 'order': 4, 'powers': [2, 20], 'representative': 12, 'size': 6}
id: 104120257
{'aut_label': '4G1', 'centralizer': '6.h1.a1', 'counter': 22, 'group_counter': 13083, 'group_order': 384, 'label': '4G1', 'order': 4, 'powers': [3, 23], 'representative': 36, 'size': 6}
id: 104120258
{'aut_label': '4G1', 'centralizer': '6.h1.a1', 'counter': 23, 'group_counter': 13083, 'group_order': 384, 'label': '4G-1', 'order': 4, 'powers': [3, 22], 'representative': 44, 'size': 6}
id: 104120259
{'aut_label': '4H', 'centralizer': '8.bp1.a1', 'counter': 24, 'group_counter': 13083, 'group_order': 384, 'label': '4H', 'order': 4, 'powers': [4, 24], 'representative': 337, 'size': 8}
id: 104120260
{'aut_label': '4I', 'centralizer': '12.s1.a1', 'counter': 25, 'group_counter': 13083, 'group_order': 384, 'label': '4I', 'order': 4, 'powers': [4, 25], 'representative': 34, 'size': 12}
id: 104120261
{'aut_label': '4J1', 'centralizer': '12.h1.a1', 'counter': 26, 'group_counter': 13083, 'group_order': 384, 'label': '4J1', 'order': 4, 'powers': [2, 27], 'representative': 5, 'size': 12}
id: 104120262
{'aut_label': '4J1', 'centralizer': '12.h1.a1', 'counter': 27, 'group_counter': 13083, 'group_order': 384, 'label': '4J-1', 'order': 4, 'powers': [2, 26], 'representative': 13, 'size': 12}
id: 104120263
{'aut_label': '4K', 'centralizer': '24.bp1.a1', 'counter': 28, 'group_counter': 13083, 'group_order': 384, 'label': '4K', 'order': 4, 'powers': [2, 28], 'representative': 189, 'size': 24}
id: 104120264
{'aut_label': '4L', 'centralizer': '24.w1.a1', 'counter': 29, 'group_counter': 13083, 'group_order': 384, 'label': '4L', 'order': 4, 'powers': [3, 29], 'representative': 219, 'size': 24}
id: 104120266
{'aut_label': '6A', 'centralizer': '2.d1.a1', 'counter': 30, 'group_counter': 13083, 'group_order': 384, 'label': '6A', 'order': 6, 'powers': [12, 4], 'representative': 64, 'size': 2}
id: 104120267
{'aut_label': '6B', 'centralizer': '2.d1.a1', 'counter': 31, 'group_counter': 13083, 'group_order': 384, 'label': '6B', 'order': 6, 'powers': [12, 2], 'representative': 264, 'size': 2}
id: 104120268
{'aut_label': '6C', 'centralizer': '2.d1.a1', 'counter': 32, 'group_counter': 13083, 'group_order': 384, 'label': '6C', 'order': 6, 'powers': [12, 3], 'representative': 72, 'size': 2}
id: 104120269
{'aut_label': '6D', 'centralizer': '8.v1.a1', 'counter': 33, 'group_counter': 13083, 'group_order': 384, 'label': '6D', 'order': 6, 'powers': [12, 5], 'representative': 129, 'size': 8}
id: 104120270
{'aut_label': '6D', 'centralizer': '8.v1.a1', 'counter': 34, 'group_counter': 13083, 'group_order': 384, 'label': '6E', 'order': 6, 'powers': [12, 6], 'representative': 137, 'size': 8}
id: 104120271
{'aut_label': '6F', 'centralizer': '16.k1.a1', 'counter': 35, 'group_counter': 13083, 'group_order': 384, 'label': '6F', 'order': 6, 'powers': [12, 9], 'representative': 23, 'size': 16}
id: 104120272
{'aut_label': '8A', 'centralizer': '8.n1.a1', 'counter': 36, 'group_counter': 13083, 'group_order': 384, 'label': '8A', 'order': 8, 'powers': [14, 36], 'representative': 48, 'size': 8}
id: 104120273
{'aut_label': '8B', 'centralizer': '8.o1.a1', 'counter': 37, 'group_counter': 13083, 'group_order': 384, 'label': '8B', 'order': 8, 'powers': [14, 37], 'representative': 246, 'size': 8}
id: 104120274
{'aut_label': '8C', 'centralizer': '24.bh1.a1', 'counter': 38, 'group_counter': 13083, 'group_order': 384, 'label': '8C', 'order': 8, 'powers': [13, 38], 'representative': 28, 'size': 24}
id: 104120275
{'aut_label': '8D', 'centralizer': '24.bi1.a1', 'counter': 39, 'group_counter': 13083, 'group_order': 384, 'label': '8D', 'order': 8, 'powers': [13, 39], 'representative': 18, 'size': 24}
id: 104120277
{'aut_label': '12A', 'centralizer': '4.y1.a1', 'counter': 40, 'group_counter': 13083, 'group_order': 384, 'label': '12A', 'order': 12, 'powers': [30, 13], 'representative': 40, 'size': 4}
id: 104120278
{'aut_label': '12B', 'centralizer': '4.y1.a1', 'counter': 41, 'group_counter': 13083, 'group_order': 384, 'label': '12B', 'order': 12, 'powers': [30, 14], 'representative': 32, 'size': 4}
id: 104120279
{'aut_label': '12C1', 'centralizer': '4.c1.a1', 'counter': 42, 'group_counter': 13083, 'group_order': 384, 'label': '12C1', 'order': 12, 'powers': [31, 15], 'representative': 134, 'size': 4}
id: 104120280
{'aut_label': '12C1', 'centralizer': '4.c1.a1', 'counter': 43, 'group_counter': 13083, 'group_order': 384, 'label': '12C-1', 'order': 12, 'powers': [31, 16], 'representative': 70, 'size': 4}
id: 104120281
{'aut_label': '12D', 'centralizer': '8.g1.a1', 'counter': 44, 'group_counter': 13083, 'group_order': 384, 'label': '12D', 'order': 12, 'powers': [32, 17], 'representative': 38, 'size': 8}
id: 104120282
{'aut_label': '12E1', 'centralizer': '8.v1.a1', 'counter': 45, 'group_counter': 13083, 'group_order': 384, 'label': '12E1', 'order': 12, 'powers': [31, 18], 'representative': 135, 'size': 8}
id: 104120283
{'aut_label': '12E1', 'centralizer': '8.v1.a1', 'counter': 46, 'group_counter': 13083, 'group_order': 384, 'label': '12E-1', 'order': 12, 'powers': [31, 19], 'representative': 39, 'size': 8}
id: 104120284
{'aut_label': '12F', 'centralizer': '16.n1.a1', 'counter': 47, 'group_counter': 13083, 'group_order': 384, 'label': '12F', 'order': 12, 'powers': [30, 24], 'representative': 17, 'size': 16}
id: 104120285
{'aut_label': '24A1', 'centralizer': '8.n1.a1', 'counter': 48, 'group_counter': 13083, 'group_order': 384, 'label': '24A1', 'order': 24, 'powers': [41, 36], 'representative': 16, 'size': 8}
id: 104120286
{'aut_label': '24A1', 'centralizer': '8.n1.a1', 'counter': 49, 'group_counter': 13083, 'group_order': 384, 'label': '24A7', 'order': 24, 'powers': [41, 36], 'representative': 24, 'size': 8}
id: 104120288
{'aut_label': '24B1', 'centralizer': '8.o1.a1', 'counter': 50, 'group_counter': 13083, 'group_order': 384, 'label': '24B1', 'order': 24, 'powers': [41, 37], 'representative': 22, 'size': 8}
id: 104120289
{'aut_label': '24B1', 'centralizer': '8.o1.a1', 'counter': 51, 'group_counter': 13083, 'group_order': 384, 'label': '24B-1', 'order': 24, 'powers': [41, 37], 'representative': 30, 'size': 8}

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: 2664713
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664724
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664735
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664746
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664750
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664751
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664752
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664753
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664754
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664714
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664715
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664716
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664717
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664718
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664719
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664720
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664721
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664722
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 2, -2, -2, -2, -2, 0, 2, 0, 2, -2, -2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664723
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 2, -2, -2, 2, 2, 0, -2, 0, -2, 2, 2, -2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664725
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, -2, -2, -2, -2, 0, 2, 0, -2, 2, 2, -2, 0, 0, 0, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664726
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, -2, -2, 2, 2, 0, -2, 0, 2, -2, -2, 2, 0, 0, 0, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664727
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 0, 0, -1, 2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -2, 2, 0, 0, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664728
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -2, 0, 0, -1, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 2, 2, 0, 0, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1], 'schur_index': 1}
id: 2664729
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -1, 2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, 2, -2, 0, 0, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664730
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 0, 0, -1, 2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, -2, -2, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664731
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, -1, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 2, -2, 0, 0, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1], 'schur_index': 1}
id: 2664732
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -2, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, -2, -2, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 2664733
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, -1, 2, 2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -2, 2, 0, 0, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1], 'schur_index': 1}
id: 2664734
{'cdim': 2, 'counter': 29, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2m', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664736
{'cdim': 2, 'counter': 30, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2n', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, -4, 4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664737
{'cdim': 2, 'counter': 31, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2o', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 4, -4, 4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664738
{'cdim': 2, 'counter': 32, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.2p', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664739
{'cdim': 4, 'counter': 33, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4a', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664740
{'cdim': 4, 'counter': 34, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4b', 'multiplicity': 1, 'nt': [8, 15], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664741
{'cdim': 4, 'counter': 35, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4c', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -4, -4, -4, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664742
{'cdim': 4, 'counter': 36, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4d', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, -2, -4, -4, 4, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664743
{'cdim': 4, 'counter': 37, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4e', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -4, 4, 0, 0, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2664744
{'cdim': 4, 'counter': 38, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4f', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 0, 0, 0, 0, 0, -2, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 2, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2664745
{'cdim': 4, 'counter': 39, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4g', 'multiplicity': 2, 'nt': [16, 100], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664747
{'cdim': 4, 'counter': 40, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4h', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -4, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664749
{'cdim': 8, 'counter': 42, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.8a', 'multiplicity': 1, 'nt': [24, 362], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2664748
{'cdim': 4, 'counter': 41, 'faithful': False, 'group': '384.13083', 'group_order': 384, 'image': None, 'label': '384.13083.4i', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], '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: 3526341
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 384, 'label': '384.13083.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3526352
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.o1.a1', 'kernel_order': 192, 'label': '384.13083.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 3526363
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.n1.a1', 'kernel_order': 192, 'label': '384.13083.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3526374
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.m1.a1', 'kernel_order': 192, 'label': '384.13083.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 3526385
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.l1.a1', 'kernel_order': 192, 'label': '384.13083.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3526388
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 192, 'label': '384.13083.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 3526389
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 192, 'label': '384.13083.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3526390
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 192, 'label': '384.13083.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 3526391
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 192, 'label': '384.13083.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3526342
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 192, 'label': '384.13083.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 3526343
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 192, 'label': '384.13083.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3526344
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 192, 'label': '384.13083.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 3526345
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 192, 'label': '384.13083.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3526346
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id: 3526347
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id: 3526348
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id: 3526349
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id: 3526350
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id: 3526351
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id: 3526353
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id: 3526354
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id: 3526355
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id: 3526356
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id: 3526357
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id: 3526358
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id: 3526359
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id: 3526360
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id: 3526361
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id: 3526362
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id: 3526364
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id: 3526365
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id: 3526366
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id: 3526367
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id: 3526368
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id: 3526369
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id: 3526370
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id: 3526371
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id: 3526372
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id: 3526373
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id: 3526375
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id: 3526376
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id: 3526377
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id: 3526378
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id: 3526379
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id: 3526380
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id: 3526381
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id: 3526382
{'center': '48.b1.a1', 'center_index': 48, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '192.1327', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.13083.4i1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 6]], [[4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[0, 0]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
id: 3526383
{'center': '48.b1.a1', 'center_index': 48, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '192.1327', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.13083.4i2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 6]], [[-4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[0, 0]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
id: 3526384
{'center': '48.b1.a1', 'center_index': 48, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '192.1327', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.13083.4i3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-4, 6]], [[4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 6]], [[0, 0]], [[-2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
id: 3526386
{'center': '48.b1.a1', 'center_index': 48, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [9, 0, 0, 0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '192.1327', 'image_order': 192, 'indicator': 0, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.13083.4i4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 6]], [[-4, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 6]], [[0, 0]], [[2, 6]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3], [1, 5], [-2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[-1, 1], [-1, 3], [-1, 5], [2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
id: 3526387
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '384.13083', 'group_counter': 13083, 'group_order': 384, 'image': None, 'image_isoclass': '192.1331', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 2, 'label': '384.13083.8a', 'nt': [24, 362], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[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
Showing the first 100 of 450 matching records in this table.

id: 53090432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 384, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '384.13083.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.13083', 'subgroup_hash': 13083, 'subgroup_order': 384, 'subgroup_tex': '(C_2\\times D_8).D_6', 'supersolvable': True, 'sylow': 0}
id: 53090543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '192.715', 'subgroup_hash': 715, 'subgroup_order': 192, 'subgroup_tex': 'D_6:D_8', 'supersolvable': True, 'sylow': 0}
id: 53090654
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1103', 'subgroup_hash': 1103, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': True, 'sylow': 0}
id: 53090765
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.728', 'subgroup_hash': 728, 'subgroup_order': 192, 'subgroup_tex': 'D_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53090827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 192, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.896', 'subgroup_hash': 896, 'subgroup_order': 192, 'subgroup_tex': '(C_4\\times D_4):C_6', 'supersolvable': True, 'sylow': 0}
id: 53090838
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.711', 'subgroup_hash': 711, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
id: 53090849
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.568', 'subgroup_hash': 568, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090860
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.723', 'subgroup_hash': 723, 'subgroup_order': 192, 'subgroup_tex': 'C_{24}:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
id: 53090871
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1239', 'subgroup_hash': 1239, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090433
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.333', 'subgroup_hash': 333, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090444
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 192, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.394', 'subgroup_hash': 394, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.364', 'subgroup_hash': 364, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53090466
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.l1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.616', 'subgroup_hash': 616, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090477
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.m1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.344', 'subgroup_hash': 344, 'subgroup_order': 192, 'subgroup_tex': 'D_4:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 53090488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.n1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.406', 'subgroup_hash': 406, 'subgroup_order': 192, 'subgroup_tex': 'D_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090499
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 192, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.2.o1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.376', 'subgroup_hash': 376, 'subgroup_order': 192, 'subgroup_tex': 'Q_8:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
id: 53090510
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '384.13083.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1846', 'subgroup_hash': 1846, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.D_4', 'supersolvable': True, 'sylow': 2}
id: 53090521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.209', 'subgroup_hash': 209, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 53090532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.179', 'subgroup_hash': 179, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 53090544
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.180', 'subgroup_hash': 180, 'subgroup_order': 96, 'subgroup_tex': 'C_6\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53090577
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090599
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53090610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 96, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.78', 'subgroup_hash': 78, 'subgroup_order': 96, 'subgroup_tex': 'S_3\\times C_4^2', 'supersolvable': True, 'sylow': 0}
id: 53090621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090632
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090643
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53090655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53090666
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.138', 'subgroup_hash': 138, 'subgroup_order': 96, 'subgroup_tex': 'C_6:D_8', 'supersolvable': True, 'sylow': 0}
id: 53090677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.171', 'subgroup_hash': 171, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': True, 'sylow': 0}
id: 53090688
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090699
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090710
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090721
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.80', 'subgroup_hash': 80, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090732
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.100', 'subgroup_hash': 100, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090743
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.148', 'subgroup_hash': 148, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:D_6', 'supersolvable': True, 'sylow': 0}
id: 53090754
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090766
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.28', 'subgroup_hash': 28, 'subgroup_order': 96, 'subgroup_tex': 'D_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090777
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.77', 'subgroup_hash': 77, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 96, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.55', 'subgroup_hash': 55, 'subgroup_order': 96, 'subgroup_tex': 'C_4:C_{24}', 'supersolvable': True, 'sylow': 0}
id: 53090799
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.11', 'subgroup_hash': 11, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_8', 'supersolvable': True, 'sylow': 0}
id: 53090810
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 96, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.53', 'subgroup_hash': 53, 'subgroup_order': 96, 'subgroup_tex': 'Q_8:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.14', 'subgroup_hash': 14, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090823
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.15', 'subgroup_hash': 15, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.152', 'subgroup_hash': 152, 'subgroup_order': 96, 'subgroup_tex': 'C_3:C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.22', 'subgroup_hash': 22, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090826
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 96, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.22', 'subgroup_hash': 22, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.42', 'subgroup_hash': 42, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 53090829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.25', 'subgroup_hash': 25, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.4.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.24', 'subgroup_hash': 24, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090831
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 48, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
id: 53090832
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.87', 'subgroup_hash': 87, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090833
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53090834
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090835
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.90', 'subgroup_hash': 90, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090836
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.84', 'subgroup_hash': 84, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.4.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.86', 'subgroup_hash': 86, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53090840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 64, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.144', 'subgroup_hash': 144, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090841
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.128', 'subgroup_hash': 128, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
id: 53090842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 32, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.196', 'subgroup_hash': 196, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
id: 53090843
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.131', 'subgroup_hash': 131, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53090844
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '64.123', 'subgroup_hash': 123, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090845
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.159', 'subgroup_hash': 159, 'subgroup_order': 64, 'subgroup_tex': 'D_4.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090846
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.121', 'subgroup_hash': 121, 'subgroup_order': 64, 'subgroup_tex': '\\SD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.210', 'subgroup_hash': 210, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 53090848
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.161', 'subgroup_hash': 161, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
id: 53090850
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.113', 'subgroup_hash': 113, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_4', 'supersolvable': True, 'sylow': 0}
id: 53090851
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.164', 'subgroup_hash': 164, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090852
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.144', 'subgroup_hash': 144, 'subgroup_order': 64, 'subgroup_tex': 'D_4.D_4', 'supersolvable': True, 'sylow': 0}
id: 53090853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.123', 'subgroup_hash': 123, 'subgroup_order': 64, 'subgroup_tex': 'D_8:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090854
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.159', 'subgroup_hash': 159, 'subgroup_order': 64, 'subgroup_tex': 'D_4.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.121', 'subgroup_hash': 121, 'subgroup_order': 64, 'subgroup_tex': '\\SD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090856
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 53090857
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 53090858
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 48, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 53090859
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 53090861
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 48, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 53090862
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090863
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090864
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 48, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090865
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090866
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 48, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 53090867
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090868
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 48, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 48, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090870
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
id: 53090872
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 48, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
id: 53090873
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53090874
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 48, 'counter': 92, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.9', 'subgroup_hash': 9, 'subgroup_order': 48, 'subgroup_tex': 'C_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53090875
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.r1.a1', 'outer_equivalence': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090876
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 48, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13083.8.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.s1.a1', 'outer_equivalence': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53090877
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 53090878
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 53090879
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53090881
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
id: 53090434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13083', 'ambient_counter': 13083, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.13083.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}

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
Showing the first 100 of 450 matching records in this table.

id: 53090432
{'ambient': '384.13083', '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': '96.a1.a1', 'complements': ['384.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '2.l1.a1', '2.m1.a1', '2.n1.a1', '2.o1.a1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6802, 4419, 2758, 4562, 6922, 4853, 2936, 4633], 'generators': [1, 8, 96, 2, 48, 128, 192, 4], 'label': '384.13083.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '2.l1.a1', '2.m1.a1', '2.n1.a1', '2.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090433
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.d1.a1', '192.d1.b1', '192.g1.a1', '192.g1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.r1.a1', '4.bb1.a1', '4.bh1.a1', '6.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7585, 2399, 2718, 3711, 6228, 6616, 3434, 4313], 'generators': [5, 192, 288, 2, 128, 48, 8], 'label': '384.13083.2.i1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.j1.a1', '4.l1.a1', '4.p1.a1', '4.r1.a1', '4.bb1.a1', '4.bh1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090434
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.f1.a1', '16.j1.a1', '16.o1.a1', '24.m1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1424, -1, 7248, -1, 2104, -1, 7041, -1], 'generators': [1, 128, 292, 200, 192], 'label': '384.13083.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.y1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090435
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.p1.a1', '16.u1.a1', '16.u1.b1', '24.n1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2462, -1, 6933, -1, 3054, -1, 7211, -1], 'generators': [21, 128, 2, 192, 8], 'label': '384.13083.8.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.z1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.z1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090436
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.ba1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '16.o1.a1', '16.w1.a1', '16.w1.b1', '24.r1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [713, -1, 8284, -1, 697, -1, 8067, -1], 'generators': [5, 128, 2, 192, 8], 'label': '384.13083.8.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.ba1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090437
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '16.q1.a1', '24.s1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2656, -1, 6449, -1, 3437, -1, 5665, -1], 'generators': [337, 128, 2, 8, 192], 'label': '384.13083.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bb1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090438
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.n1.a1', '24.t1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2808, -1, 6375, -1, 3799, -1, 5748, -1], 'generators': [337, 192, 6, 128, 200], 'label': '384.13083.8.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bc1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090439
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '8.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '4.bo1.a1', '4.bq1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.n1.a1', '24.u1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3655, -1, 6523, -1, 3936, -1, 5464, -1], 'generators': [337, 192, 294, 128, 8], 'label': '384.13083.8.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bd1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090440
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bn1.a1', '4.bq1.a1'], 'contains': ['16.e1.a1', '16.k1.a1', '16.q1.a1', '24.v1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3399, -1, 7000, -1, 3370, -1, 6112, -1], 'generators': [19, 128, 4, 200, 192], 'label': '384.13083.8.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.be1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.be1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090441
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '4.bo1.a1', '4.bp1.a1'], 'contains': ['16.f1.a1', '16.k1.a1', '16.q1.a1', '16.bb1.a1', '16.bb1.a2', '24.w1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2955, -1, 6229, -1, 3662, -1, 5253, -1], 'generators': [19, 128, 292, 192, 200], 'label': '384.13083.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bf1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090442
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.g1.a1', '16.k1.a1', '16.p1.a1', '24.x1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3339, -1, 6302, -1, 4038, -1, 5986, -1], 'generators': [21, 128, 290, 8, 192], 'label': '384.13083.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bg1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090443
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.c1.a1', '16.l1.a1', '16.o1.a1', '16.x1.a1', '16.x1.a2', '24.y1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1011, -1, 8077, -1, 850, -1, 7942, -1], 'generators': [5, 128, 6, 192, 8], 'label': '384.13083.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bh1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090444
{'ambient': '384.13083', 'aut_centralizer_order': 8, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1083472', 'aut_weyl_index': 8, 'centralizer': '48.a1.a1', 'complements': ['192.d1.a1', '192.d1.b1', '192.g1.a1', '192.g1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.l1.a1', '4.m1.a1', '4.y1.a1', '4.z1.a1', '4.be1.a1', '4.bf1.a1', '6.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7746, 3207, 1938, 1990, 7743, 5230, 2002, 2866], 'generators': [2, 192, 96, 4, 128, 48, 8], 'label': '384.13083.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.l1.a1', '4.m1.a1', '4.y1.a1', '4.z1.a1', '4.be1.a1', '4.bf1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090445
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '16.o1.a1', '24.z1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1947, -1, 7444, -1, 1766, -1, 6986, -1], 'generators': [5, 128, 294, 8, 192], 'label': '384.13083.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bi1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090446
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.e1.a1', '16.l1.a1', '16.m1.a1', '16.y1.a1', '16.y1.a2', '24.ba1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1523, -1, 8493, -1, 1137, -1, 7472, -1], 'generators': [3, 128, 4, 192, 8], 'label': '384.13083.8.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bj1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090447
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bk1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.f1.a1', '16.l1.a1', '16.m1.a1', '24.bb1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1622, -1, 7199, -1, 2037, -1, 6820, -1], 'generators': [3, 128, 292, 200, 192], 'label': '384.13083.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bk1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090448
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bl1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.c1.a1', '16.p1.a1', '16.q1.a1', '24.bk1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2716, -1, 6684, -1, 3149, -1, 6166, -1], 'generators': [21, 128, 6, 8, 192], 'label': '384.13083.8.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bl1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090449
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bm1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '4.bo1.a1', '4.bq1.a1'], 'contains': ['16.d1.a1', '16.p1.a1', '16.q1.a1', '24.bm1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3460, -1, 6733, -1, 3216, -1, 5931, -1], 'generators': [21, 128, 294, 8, 192], 'label': '384.13083.8.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bm1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090450
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bn1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.g1.a1', '16.m1.a1', '16.o1.a1', '24.bn1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2268, -1, 7395, -1, 1833, -1, 7288, -1], 'generators': [5, 128, 290, 8, 192], 'label': '384.13083.8.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bn1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090451
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.bn1.a1', '4.bq1.a1'], 'contains': ['16.e1.a1', '16.n1.a1', '16.p1.a1', '24.bo1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3529, -1, 7056, -1, 3293, -1, 6049, -1], 'generators': [337, 128, 4, 8, 192], 'label': '384.13083.8.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bo1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090452
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '4.bo1.a1', '4.bp1.a1'], 'contains': ['16.f1.a1', '16.n1.a1', '16.p1.a1', '24.bp1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3254, -1, 5967, -1, 3532, -1, 5358, -1], 'generators': [337, 128, 292, 200, 192], 'label': '384.13083.8.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bp1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090453
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '8.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.g1.a1', '16.n1.a1', '16.q1.a1', '24.bq1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3805, -1, 5899, -1, 4105, -1, 5169, -1], 'generators': [337, 128, 290, 200, 192], 'label': '384.13083.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.bq1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '48.51'}
id: 53090454
{'ambient': '384.13083', 'aut_centralizer_order': 8, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.51', 'aut_weyl_index': 128, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.r1.a1', '16.s1.a1', '16.t1.a1', '16.v1.a1', '16.w1.a1', '16.x1.a1', '16.y1.a1', '24.br1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 9410, -1, 473, -1, 9505, -1], 'generators': [1, 128, 2, 196, 8], 'label': '384.13083.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.br1.a1', 'projective_image': '192.1331', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 53090455
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.k1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.d1.a1', '192.d1.b1', '192.g1.a1', '192.g1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.a1', '4.k1.a1', '4.m1.a1', '4.ba1.a1', '4.bc1.a1', '4.bg1.a1', '4.bi1.a1', '6.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7366, 5191, 2568, 4014, 7388, 2968, 2337, 5861], 'generators': [337, 192, 96, 2, 128, 20, 8], 'label': '384.13083.2.k1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.j1.a1', '4.k1.a1', '4.m1.a1', '4.ba1.a1', '4.bc1.a1', '4.bg1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090456
{'ambient': '384.13083', 'aut_centralizer_order': 8, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.51', 'aut_weyl_index': 128, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.r1.a1', '16.s1.a2', '16.t1.a2', '16.v1.a1', '16.w1.a1', '16.x1.a2', '16.y1.a2', '24.br1.a2'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 9252, -1, 473, -1, 9380, -1], 'generators': [1, 128, 2, 4, 8], 'label': '384.13083.8.br1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.br1.a2', 'projective_image': '192.1331', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 53090457
{'ambient': '384.13083', 'aut_centralizer_order': 8, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.51', 'aut_weyl_index': 128, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.r1.b1', '16.s1.a1', '16.t1.a2', '16.v1.b1', '16.w1.b1', '16.x1.a1', '16.y1.a2', '24.br1.b1'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 9052, -1, 473, -1, 9194, -1], 'generators': [1, 128, 194, 4, 8], 'label': '384.13083.8.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.br1.b1', 'projective_image': '192.1331', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 53090458
{'ambient': '384.13083', 'aut_centralizer_order': 8, 'aut_label': '8.br1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.51', 'aut_weyl_index': 128, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1'], 'contains': ['16.r1.b1', '16.s1.a2', '16.t1.a1', '16.v1.b1', '16.w1.b1', '16.x1.a2', '16.y1.a1', '24.br1.b2'], 'core': '32.b1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [351, -1, 8698, -1, 473, -1, 9069, -1], 'generators': [1, 128, 194, 196, 8], 'label': '384.13083.8.br1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.bj1.a1', 'old_label': '8.br1.b2', 'projective_image': '192.1331', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.br1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 53090459
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.i1.a1', '16.bc1.a1', '16.bc1.c1', '16.bd1.a1', '16.bd1.c1', '16.be1.a1', '16.bf1.a1', '24.bs1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3968, -1, 4865, -1, 6236, -1, 4767, -1], 'generators': [1, 128, 2, 296, 192], 'label': '384.13083.8.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bs1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090460
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bs1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.i1.b1', '16.bc1.b1', '16.bc1.d1', '16.bd1.b1', '16.bd1.d1', '16.be1.a1', '16.bf1.a1', '24.bs1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3968, -1, 5009, -1, 6236, -1, 4605, -1], 'generators': [289, 128, 2, 296, 192], 'label': '384.13083.8.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bs1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090461
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.a1', '16.bc1.a1', '16.bc1.b1', '16.bd1.a1', '16.bd1.b1', '16.bg1.a1', '16.bj1.a1', '24.bt1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4082, -1, 4794, -1, 5882, -1, 4686, -1], 'generators': [1, 128, 2, 288, 192], 'label': '384.13083.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bt1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090462
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bt1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.h1.b1', '16.bc1.c1', '16.bc1.d1', '16.bd1.c1', '16.bd1.d1', '16.bg1.a1', '16.bj1.a1', '24.bt1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4082, -1, 4937, -1, 5882, -1, 4848, -1], 'generators': [9, 128, 2, 288, 192], 'label': '384.13083.8.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.bt1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090463
{'ambient': '384.13083', 'aut_centralizer_order': 48, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.h1.a1', '16.bi1.a1', '16.bp1.a1', '24.bu1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4852, -1, 1506, -1, 7757, -1, 2447, -1], 'generators': [1, 192, 246, 128, 96], 'label': '384.13083.8.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bu1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090464
{'ambient': '384.13083', 'aut_centralizer_order': 48, 'aut_label': '8.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.h1.b1', '16.bi1.a1', '16.bp1.a1', '24.bu1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4852, -1, 1434, -1, 7757, -1, 2529, -1], 'generators': [9, 192, 246, 128, 96], 'label': '384.13083.8.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '8.bu1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090465
{'ambient': '384.13083', 'aut_centralizer_order': 48, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.h1.a1', '16.bn1.a1', '16.bo1.a1', '24.bv1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7186, -1, 3557, -1, 7321, -1, 2210, -1], 'generators': [1, 192, 48, 128, 96], 'label': '384.13083.8.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.bv1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090466
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.l1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.e1.a1', '192.e1.b1', '192.d1.a1', '192.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.o1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '4.z1.a1', '4.bg1.a1', '6.l1.a1'], 'core': '2.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5907, 3721, 3636, 6369, 7949, 5955, 2211, 5036], 'generators': [337, 192, 96, 18, 128, 20, 296], 'label': '384.13083.2.l1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.l1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.o1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '4.z1.a1', '4.bg1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.l1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.l1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090467
{'ambient': '384.13083', 'aut_centralizer_order': 48, 'aut_label': '8.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '32.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['16.h1.b1', '16.bn1.a1', '16.bo1.a1', '24.bv1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7186, -1, 3673, -1, 7321, -1, 2341, -1], 'generators': [9, 192, 48, 128, 96], 'label': '384.13083.8.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '8.bv1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090468
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.i1.a1', '16.bh1.a1', '16.bl1.a1', '24.bw1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4206, -1, 4734, -1, 9973, -1, 1560, -1], 'generators': [3, 128, 20, 104, 192], 'label': '384.13083.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '8.bw1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090469
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1'], 'contains': ['16.i1.b1', '16.bh1.a1', '16.bl1.a1', '24.bw1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4206, -1, 4685, -1, 9973, -1, 1724, -1], 'generators': [291, 128, 20, 104, 192], 'label': '384.13083.8.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.m1.a1', 'old_label': '8.bw1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090470
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1'], 'contains': ['16.i1.a1', '16.bk1.a1', '16.bm1.a1', '24.bx1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5338, -1, 4551, -1, 8297, -1, 1451, -1], 'generators': [337, 128, 18, 296, 192], 'label': '384.13083.8.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '8.bx1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090471
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '8.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.209', 'aut_weyl_index': 64, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1'], 'contains': ['16.i1.b1', '16.bk1.a1', '16.bm1.a1', '24.bx1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5338, -1, 4503, -1, 8297, -1, 1506, -1], 'generators': [241, 128, 18, 296, 192], 'label': '384.13083.8.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.o1.a1', 'old_label': '8.bx1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090472
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.g1.a1', '24.bu1.a1', '24.bu1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8048, 8926, 229, 7368, 9068, 8862, 1000, 7588], 'generators': [1, 246, 8], 'label': '384.13083.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090473
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '8.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1', '24.j1.a1', '24.k1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6312, 7635, 2917, 6695, 5583, 7761, 3427, 8146], 'generators': [1, 6, 288], 'label': '384.13083.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090474
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.a1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.f1.a1', '24.bv1.a1', '24.bv1.b1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9133, 8600, 1267, 8306, 8803, 8552, 839, 8457], 'generators': [1, 8, 48], 'label': '384.13083.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.e1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.e1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090475
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '16.f1.a1', 'complements': ['32.z1.a1', '32.z1.c1', '32.z1.b1', '32.z1.d1', '32.z1.f1', '32.z1.h1', '32.z1.e1', '32.z1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.a1.a1', '6.h1.a1', '6.l1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.e1.a1', '24.t1.a1', '24.u1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7380, 6982, 2305, 8021, 7124, 8279, 2664, 7389], 'generators': [337, 6, 288], 'label': '384.13083.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.o1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.a1', '24.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090476
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '32.a1.a1', 'complements': ['32.z1.a1', '32.z1.c1', '32.z1.b1', '32.z1.d1', '32.z1.e1', '32.z1.g1', '32.z1.f1', '32.z1.h1'], 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.a1.a1', '6.i1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.f1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9707, 7844, 1022, 8661, 8230, 7960, 1287, 7787], 'generators': [7, 48], 'label': '384.13083.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.p1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.d1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090477
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.m1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.e1.a1', '192.e1.b1', '192.d1.a1', '192.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.p1.a1', '4.q1.a1', '4.t1.a1', '4.w1.a1', '4.bc1.a1', '4.be1.a1', '6.m1.a1'], 'core': '2.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7003, 5786, 3408, 5561, 6994, 3353, 2557, 5526], 'generators': [3, 192, 96, 4, 128, 48, 8], 'label': '384.13083.2.m1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.m1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.n1.a1', '4.p1.a1', '4.q1.a1', '4.t1.a1', '4.w1.a1', '4.bc1.a1', '4.be1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.m1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.m1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090478
{'ambient': '384.13083', 'aut_centralizer_order': 192, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '16.b1.a1', 'complements': ['32.z1.a1', '32.z1.c1', '32.z1.b1', '32.z1.d1', '32.z1.f1', '32.z1.h1', '32.z1.e1', '32.z1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '6.a1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.g1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9962, 8247, 19, 7853, 8917, 7561, 636, 7229], 'generators': [6, 48], 'label': '384.13083.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.y1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.f1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090479
{'ambient': '384.13083', 'aut_centralizer_order': 96, 'aut_label': '12.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '32.a1.a1', 'complements': ['32.z1.a1', '32.z1.c1', '32.z1.b1', '32.z1.d1', '32.z1.f1', '32.z1.h1', '32.z1.e1', '32.z1.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '6.a1.a1', '6.k1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.g1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9856, 8079, 169, 7577, 8688, 8120, 745, 7947], 'generators': [337, 246], 'label': '384.13083.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.ba1.a1', '6.a1.a1'], 'normal_contains': ['24.d1.a1', '24.e1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090480
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1', '6.c1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.l1.a1', '24.p1.a1', '24.r1.a1', '24.y1.a1', '24.ba1.a1', '24.br1.a1', '24.br1.a2', '24.br1.b1', '24.br1.b2'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3621, -1, 5851, -1, 1408, -1, 7362, -1], 'generators': [1, 2, 4, 192], 'label': '384.13083.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.h1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 53090481
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '6.c1.a1'], 'contains': ['24.h1.a1', '24.k1.a1', '24.m1.a1', '24.q1.a1', '24.r1.a1', '24.z1.a1', '24.bb1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3759, -1, 5687, -1, 2359, -1, 6737, -1], 'generators': [1, 2, 292], 'label': '384.13083.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.i1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090482
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '6.c1.a1'], 'contains': ['24.i1.a1', '24.j1.a1', '24.m1.a1', '24.y1.a1', '24.bb1.a1', '24.bj1.a1', '24.bn1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3891, -1, 5601, -1, 2578, -1, 6640, -1], 'generators': [1, 290, 292], 'label': '384.13083.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.j1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090483
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bm1.a1', '6.c1.a1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.l1.a1', '24.z1.a1', '24.ba1.a1', '24.bl1.a1', '24.bn1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4055, -1, 5773, -1, 2478, -1, 6559, -1], 'generators': [1, 290, 4], 'label': '384.13083.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090484
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.i1.a1', '24.o1.a1', '24.bc1.a1', '24.bs1.a1', '24.bs1.b1', '24.bt1.a1', '24.bt1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6114, -1, 2487, -1, 6650, -1, 3339, -1], 'generators': [1, 2, 8, 288], 'label': '384.13083.12.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090485
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.l1.a1', '24.m1.a1', '24.bd1.a1', '24.be1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7480, -1, 2768, -1, 5782, -1, 3683, -1], 'generators': [1, 4, 288], 'label': '384.13083.12.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090486
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.b1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.bf1.a1', '24.bh1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7884, -1, 1655, -1, 8984, -1, 1396, -1], 'generators': [1, 20], 'label': '384.13083.12.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090487
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.bg1.a1', '24.bi1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8333, -1, 1558, -1, 8487, -1, 1068, -1], 'generators': [1, 18], 'label': '384.13083.12.o1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090488
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.n1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.e1.a1', '192.e1.b1', '192.d1.a1', '192.d1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.s1.a1', '4.v1.a1', '4.w1.a1', '4.x1.a1', '4.y1.a1', '4.bh1.a1', '4.bi1.a1', '6.n1.a1'], 'core': '2.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7465, 4764, 2421, 5947, 6094, 4097, 3324, 4633], 'generators': [5, 192, 288, 6, 128, 48, 8], 'label': '384.13083.2.n1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.n1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.s1.a1', '4.v1.a1', '4.w1.a1', '4.x1.a1', '4.y1.a1', '4.bh1.a1', '4.bi1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.n1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.n1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090489
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bn1.a1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.p1.a1', '24.s1.a1', '24.t1.a1', '24.v1.a1', '24.bk1.a1', '24.bo1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4240, -1, 4375, -1, 4210, -1, 5579, -1], 'generators': [337, 2, 4], 'label': '384.13083.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.p1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53090490
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bo1.a1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.q1.a1', '24.s1.a1', '24.u1.a1', '24.w1.a1', '24.bm1.a1', '24.bp1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4599, -1, 3872, -1, 4333, -1, 5101, -1], 'generators': [337, 2, 292], 'label': '384.13083.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.q1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53090491
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.b1.a1', '24.n1.a1', '24.o1.a1', '24.x1.a1', '24.bf1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7263, -1, 2086, -1, 6949, -1, 2970, -1], 'generators': [149, 2, 288], 'label': '384.13083.12.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090492
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.c1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.c1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.bd1.a1', '24.bj1.a1', '24.bl1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5938, -1, 3115, -1, 4681, -1, 3514, -1], 'generators': [2, 4, 288], 'label': '384.13083.12.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090493
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.c1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.d1.a1', '24.o1.a1', '24.r1.a1', '24.be1.a1', '24.bn1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8744, -1, 728, -1, 5372, -1, 4024, -1], 'generators': [5, 2, 288], 'label': '384.13083.12.t1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090494
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.e1.a1', '24.o1.a1', '24.s1.a1', '24.bg1.a1', '24.bq1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7766, -1, 2027, -1, 7199, -1, 2603, -1], 'generators': [337, 2, 288], 'label': '384.13083.12.u1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090495
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.d1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.f1.a1', '24.o1.a1', '24.bi1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9632, -1, 548, -1, 9289, -1, 575, -1], 'generators': [2, 48], 'label': '384.13083.12.v1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090496
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.b1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.g1.a1', '24.o1.a1', '24.bh1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9774, -1, 420, -1, 9730, -1, 241, -1], 'generators': [258, 20], 'label': '384.13083.12.w1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090497
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1', '6.h1.a1'], 'contains': ['24.t1.a1', '24.w1.a1', '24.x1.a1', '24.bj1.a1', '24.bk1.a1', '24.bp1.a1', '24.bq1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5027, -1, 3772, -1, 4885, -1, 4941, -1], 'generators': [337, 290, 292], 'label': '384.13083.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.x1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53090498
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1', '6.h1.a1'], 'contains': ['24.u1.a1', '24.v1.a1', '24.x1.a1', '24.bl1.a1', '24.bm1.a1', '24.bo1.a1', '24.bq1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5597, -1, 3993, -1, 4779, -1, 5027, -1], 'generators': [337, 290, 4], 'label': '384.13083.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '12.y1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53090499
{'ambient': '384.13083', 'aut_centralizer_order': 4, 'aut_label': '2.o1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408526564', 'aut_weyl_index': 4, 'centralizer': '96.a1.a1', 'complements': ['192.e1.a1', '192.e1.b1', '192.d1.a1', '192.d1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.t1.a1', '4.u1.a1', '4.v1.a1', '4.ba1.a1', '4.bb1.a1', '4.bd1.a1', '4.bf1.a1', '6.o1.a1'], 'core': '2.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6619, 4419, 2321, 4954, 6475, 6987, 2700, 3941], 'generators': [337, 192, 96, 18, 128, 4, 296], 'label': '384.13083.2.o1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.o1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.t1.a1', '4.u1.a1', '4.v1.a1', '4.ba1.a1', '4.bb1.a1', '4.bd1.a1', '4.bf1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.o1.a1', 'projective_image': '96.209', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.o1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
id: 53090500
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.b1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.bc1.a1', '24.bh1.a1', '24.bw1.a1', '24.bw1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7959, -1, 1961, -1, 9889, -1, 167, -1], 'generators': [259, 20, 288], 'label': '384.13083.12.z1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090501
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.e1.a1', '6.h1.a1', '6.m1.a1'], 'contains': ['24.b1.a1', '24.v1.a1', '24.w1.a1', '24.bd1.a1', '24.bg1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7569, -1, 2173, -1, 6758, -1, 2733, -1], 'generators': [147, 4, 288], 'label': '384.13083.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.ba1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090502
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.e1.a1', '6.i1.a1', '6.l1.a1'], 'contains': ['24.b1.a1', '24.be1.a1', '24.bi1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8828, -1, 1071, -1, 8554, -1, 1123, -1], 'generators': [261, 18], 'label': '384.13083.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bb1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090503
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.c1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.c1.a1', '24.y1.a1', '24.z1.a1', '24.bc1.a1', '24.be1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6451, -1, 2636, -1, 5483, -1, 3602, -1], 'generators': [5, 6, 288], 'label': '384.13083.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090504
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.c1.a1', '6.m1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7049, -1, 2564, -1, 5683, -1, 3251, -1], 'generators': [3, 4, 288], 'label': '384.13083.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 53090505
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.d1.a1', '6.l1.a1', '6.o1.a1'], 'contains': ['24.e1.a1', '24.bc1.a1', '24.bi1.a1', '24.bx1.a1', '24.bx1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8495, -1, 1758, -1, 9411, -1, 60, -1], 'generators': [337, 18, 288], 'label': '384.13083.12.be1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090506
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.b1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.bc1.a1', '24.bf1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8393, -1, 474, -1, 8029, -1, 1342, -1], 'generators': [21, 246], 'label': '384.13083.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bf1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090507
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.d1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.f1.a1', '24.bc1.a1', '24.bg1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9321, -1, 1348, -1, 8096, -1, 1232, -1], 'generators': [3, 48], 'label': '384.13083.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090508
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.x1.a1', '6.f1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.c1.a1', '24.bf1.a1', '24.bg1.a1', '24.bk1.a1', '24.bm1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6601, -1, 2353, -1, 6053, -1, 3031, -1], 'generators': [21, 6, 288], 'label': '384.13083.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.x1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bh1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090509
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.z1.a1', '6.f1.a1', '6.j1.a1', '6.l1.a1'], 'contains': ['24.c1.a1', '24.bh1.a1', '24.bi1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8223, -1, 1840, -1, 9805, -1, 302, -1], 'generators': [18, 20], 'label': '384.13083.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.z1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090510
{'ambient': '384.13083', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.n1.a1', '6.o1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8674, -1, 1336, -1, 8606, -1, 1232, -1], 'generators': [1, 2, 4, 48], 'label': '384.13083.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090511
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bb1.a1', '6.f1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.bf1.a1', '24.bi1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8659, -1, 1146, -1, 7962, -1, 1615, -1], 'generators': [21, 18], 'label': '384.13083.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bb1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bj1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090512
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '6.f1.a1', '6.k1.a1', '6.m1.a1'], 'contains': ['24.d1.a1', '24.bg1.a1', '24.bh1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8599, -1, 1607, -1, 8621, -1, 932, -1], 'generators': [19, 20], 'label': '384.13083.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bc1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bk1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090513
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '6.g1.a1', '6.h1.a1', '6.o1.a1'], 'contains': ['24.e1.a1', '24.bd1.a1', '24.bf1.a1', '24.bo1.a1', '24.bp1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7660, -1, 2244, -1, 6137, -1, 2814, -1], 'generators': [337, 4, 288], 'label': '384.13083.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bd1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bl1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090514
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.be1.a1', '6.g1.a1', '6.j1.a1', '6.m1.a1'], 'contains': ['24.f1.a1', '24.bd1.a1', '24.bh1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9409, -1, 1420, -1, 9557, -1, 488, -1], 'generators': [4, 48], 'label': '384.13083.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.be1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bm1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090515
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bf1.a1', '6.e1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.bd1.a1', '24.bi1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9002, -1, 91, -1, 9183, -1, 382, -1], 'generators': [146, 4], 'label': '384.13083.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bf1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bn1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53090516
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '6.g1.a1', '6.k1.a1', '6.l1.a1'], 'contains': ['24.e1.a1', '24.be1.a1', '24.bh1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8889, -1, 1491, -1, 9655, -1, 691, -1], 'generators': [337, 20], 'label': '384.13083.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bg1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bo1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090517
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '6.g1.a1', '6.i1.a1', '6.n1.a1'], 'contains': ['24.f1.a1', '24.be1.a1', '24.bf1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9496, -1, 602, -1, 7673, -1, 1670, -1], 'generators': [5, 48], 'label': '384.13083.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bh1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bp1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090518
{'ambient': '384.13083', 'aut_centralizer_order': 32, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bi1.a1', '6.e1.a1', '6.k1.a1', '6.n1.a1'], 'contains': ['24.g1.a1', '24.be1.a1', '24.bg1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9236, -1, 366, -1, 8164, -1, 1178, -1], 'generators': [5, 246], 'label': '384.13083.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.bi1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bq1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53090519
{'ambient': '384.13083', 'aut_centralizer_order': 256, 'aut_label': '16.a1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '8.t1.a1', '8.z1.a1', '8.ba1.a1', '8.bb1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.n1.a1', '32.u1.a1', '48.f1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1425, 1722, 7744, 1708, 2590, 2597, 7306, 2096], 'generators': [2, 8, 192, 128], 'label': '384.13083.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1', '8.c1.a1', '8.d1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090520
{'ambient': '384.13083', 'aut_centralizer_order': 1536, 'aut_label': '16.b1', 'aut_quo_index': 20160, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '4.y1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1', '8.p1.a1', '8.q1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.d1.a1', '48.a1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6708, 4873, 3243, 5265, 5975, 5362, 3078, 4999], 'generators': [8, 288, 128, 192], 'label': '384.13083.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.j1.a1', '8.k1.a1', '8.l1.a1', '8.m1.a1', '8.n1.a1', '8.o1.a1', '8.p1.a1', '8.q1.a1'], 'normal_contains': ['32.a1.a1', '32.d1.a1', '32.c1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090521
{'ambient': '384.13083', 'aut_centralizer_order': 16, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 16, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.f1.a1', '8.t1.a1', '8.u1.a1', '8.bs1.a1', '8.bs1.b1', '8.bt1.a1', '8.bt1.b1', '12.l1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4300, 5770, 4564, 6620, 5183, 1081, 4548, 600], 'generators': [1, 128, 192, 2, 8, 288], 'label': '384.13083.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090522
{'ambient': '384.13083', 'aut_centralizer_order': 768, 'aut_label': '16.c1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '4.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.g1.a1', '8.r1.a1', '8.v1.a1', '8.bc1.a1', '8.bh1.a1', '8.bl1.a1'], 'contains': ['32.a1.a1', '32.h1.a1', '48.b1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1693, 3239, 7422, 3257, 1681, 4026, 7780, 2953], 'generators': [6, 192, 128, 8], 'label': '384.13083.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.c1.a1', '8.g1.a1', '8.r1.a1'], 'normal_contains': ['32.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '96.209', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53090523
{'ambient': '384.13083', 'aut_centralizer_order': 768, 'aut_label': '16.d1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '8.g1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.g1.a1', '8.s1.a1', '8.w1.a1', '8.bd1.a1', '8.bi1.a1', '8.bm1.a1'], 'contains': ['32.a1.a1', '32.q1.a1', '48.c1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2227, 2943, 7619, 2960, 2916, 3454, 5740, 3525], 'generators': [294, 192, 128, 200], 'label': '384.13083.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.d1.a1', '8.g1.a1', '8.s1.a1'], 'normal_contains': ['32.a1.a1', '48.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '96.209', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53090524
{'ambient': '384.13083', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '12.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.i1.a1', '8.s1.a1', '8.x1.a1', '8.be1.a1', '8.bj1.a1', '8.bo1.a1'], 'contains': ['32.a1.a1', '32.j1.a1', '48.j1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1935, 1053, 7946, 2610, 2357, 3740, 7496, 3239], 'generators': [4, 192, 8, 128], 'label': '384.13083.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.c1.a1', '8.i1.a1', '8.s1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090525
{'ambient': '384.13083', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.i1.a1', '8.r1.a1', '8.y1.a1', '8.bf1.a1', '8.bk1.a1', '8.bp1.a1'], 'contains': ['32.a1.a1', '32.r1.a1', '48.k1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1825, 2319, 6979, 2003, 3201, 2878, 5642, 2377], 'generators': [292, 192, 200, 128], 'label': '384.13083.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.d1.a1', '8.i1.a1', '8.r1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.f1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 53090526
{'ambient': '384.13083', 'aut_centralizer_order': 256, 'aut_label': '16.g1', 'aut_quo_index': 16, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '24.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.r1.a1', '8.s1.a1', '8.u1.a1', '8.bg1.a1', '8.bn1.a1', '8.bq1.a1'], 'contains': ['32.a1.a1', '32.y1.a1', '48.m1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2592, 2016, 6725, 2306, 4044, 3167, 5450, 2667], 'generators': [290, 8, 192, 128], 'label': '384.13083.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.b1.a1', '8.r1.a1', '8.s1.a1'], 'normal_contains': ['32.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
id: 53090527
{'ambient': '384.13083', 'aut_centralizer_order': 192, 'aut_label': '16.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bt1.a1', '8.bu1.a1', '8.bv1.a1'], 'contains': ['32.d1.a1', '32.t1.a1', '48.d1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4895, 7112, 3535, 5787, 6633, 6807, 3167, 6718], 'generators': [1, 288, 128, 192], 'label': '384.13083.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.d1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090528
{'ambient': '384.13083', 'aut_centralizer_order': 192, 'aut_label': '16.h1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.bt1.b1', '8.bu1.b1', '8.bv1.b1'], 'contains': ['32.d1.a1', '32.t1.b1', '48.d1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4895, 7112, 3607, 5537, 6633, 6807, 3248, 6480], 'generators': [9, 288, 128, 192], 'label': '384.13083.16.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.d1.a1', '48.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.h1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53090529
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.38', 'aut_weyl_index': 128, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.bs1.a1', '8.bw1.a1', '8.bx1.a1'], 'contains': ['32.c1.a1', '32.w1.a1', '48.bi1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5143, 5218, 4753, 6069, 7051, 4397, 2950, 3903], 'generators': [3, 296, 192, 128], 'label': '384.13083.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.f1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.a1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090530
{'ambient': '384.13083', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '48.38', 'aut_weyl_index': 128, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.bs1.b1', '8.bw1.b1', '8.bx1.b1'], 'contains': ['32.c1.a1', '32.w1.b1', '48.bi1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5143, 5218, 4991, 6449, 7051, 4397, 3003, 3745], 'generators': [291, 296, 192, 128], 'label': '384.13083.16.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': ['8.f1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.i1.b1', 'projective_image': '192.1165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.b1', 'subgroup_fusion': None, 'weyl_group': '48.38'}
id: 53090531
{'ambient': '384.13083', 'aut_centralizer_order': 384, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '8.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.t1.a1', '8.u1.a1', '8.v1.a1', '8.w1.a1', '8.x1.a1', '8.y1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.m1.a1', '32.t1.a1', '32.t1.b1', '48.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1053, -1, 8113, -1, 2026, -1, 7026, -1], 'generators': [1, 8, 192, 128], 'label': '384.13083.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '16.j1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}

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.