LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-07-25T16:44:51.281662

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': [2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 32], [193, 82, 28, 352], [1, 18, 28, 176], [1, 2, 220, 240], [9, 274, 204, 160], [17, 18, 204, 160], [201, 18, 204, 240], [9, 82, 4, 160], [201, 18, 204, 352], [25, 210, 204, 352], [217, 18, 12, 48], [25, 18, 204, 224]], 'aut_group': None, 'aut_hash': 2404398907887337476, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 32, 'aut_perms': [24146162499927622268292169665732440, 93345001259616101935595681734685275, 7709124535354148814406568062891856, 220690204843380296548463966589772439, 98399441012640580962632191724415206, 58066387871427267560019588521140915, 18833155559167212507062492924996797, 90958019504698268623839830384667115, 188248791229367251262292596684659588, 64968471994905301874548633254390889, 64968471963877262239164988867050649], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 2, 1], [2, 8, 1, 2], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 6, 2, 2], [4, 12, 1, 1], [4, 12, 2, 2], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 2, 1], [6, 16, 1, 2], [8, 4, 2, 1], [8, 8, 1, 1], [8, 12, 2, 1], [8, 24, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 1], [24, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^6.C_2^5)', '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, 8, 2], [2, 12, 1], [3, 2, 1], [4, 2, 2], [4, 4, 4], [4, 6, 4], [4, 12, 5], [4, 24, 2], [6, 2, 3], [6, 8, 2], [6, 16, 2], [8, 4, 2], [8, 8, 1], [8, 12, 2], [8, 24, 1], [12, 4, 4], [12, 8, 3], [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': 12892, '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, 8, 1, 2], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 6, 2, 2], [4, 12, 1, 3], [4, 12, 2, 1], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 1, 2], [6, 16, 1, 2], [8, 4, 2, 1], [8, 8, 1, 1], [8, 12, 2, 1], [8, 24, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 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': 12892, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 4, 6], 'inner_gens': [[1, 2, 28, 32], [1, 2, 4, 176], [9, 2, 4, 224], [1, 274, 196, 32]], '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': '384.12892', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 10, 'linQ_dim': 14, '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': 41, 'number_normal_subgroups': 115, 'number_subgroup_autclasses': 362, 'number_subgroup_classes': 396, 'number_subgroups': 1302, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 39], [3, 2], [4, 152], [6, 54], [8, 64], [12, 40], [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': [0, 0, 0, 0, 0, 0], 'outer_gens': [[193, 82, 28, 352], [1, 18, 28, 176], [1, 2, 220, 240], [9, 274, 204, 160], [17, 18, 204, 160], [201, 18, 204, 240]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1987252695887726299102628950722389833714523966310308548100225432486780947673155387432193, 4280060218467498459157957136335147776342177567433001507415165479798416968493171695770880, 6303134340285190835306089164506674997533308316264178041357172415930561341164842038246404, 8317916730683905238570523375705049843604187221901473143969831940463952284013968720463204, 10332514603342474881345067021754704576537059818180182550633497265403385601646390217632605, 12347017433414028037398929999645308439212828899801945653585482568744780362280160221257390], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 27, '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, 8], [8, 4], [16, 1]], 'representations': {'PC': {'code': 2454404830450046093289098432576825290241, 'gens': [1, 2, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 1545, 674, 66, 771, 91, 4237, 2709, 141, 8974, 166, 8207]}, 'Perm': {'d': 27, 'gens': [405234858872999126641028400, 870677086695415830487132801, 78385920768906056730547200, 4370528679143168242317625, 3719544, 1307991117668345899491225600, 1726294691134515892270003200, 3]}}, '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': 192, 'wreath_data': None, 'wreath_product': False}

Column	Type
aut_label	text
centralizer	text
counter	integer
group_counter	integer
group_order	numeric
label	text
order	integer
powers	integer[]
representative	numeric
size	numeric

gps_conj_classes • Show schema

id: 104110100
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 12892, 'group_order': 384, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 104110111
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 12892, 'group_order': 384, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 192, 'size': 1}
id: 104110122
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 12892, 'group_order': 384, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 208, 'size': 1}
id: 104110133
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 12892, 'group_order': 384, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 16, 'size': 1}
id: 104110144
{'aut_label': '2D', 'centralizer': '4.bl1.a1', 'counter': 5, 'group_counter': 12892, 'group_order': 384, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 1, 'size': 4}
id: 104110147
{'aut_label': '2D', 'centralizer': '4.bl1.a1', 'counter': 6, 'group_counter': 12892, 'group_order': 384, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 193, 'size': 4}
id: 104110148
{'aut_label': '2F', 'centralizer': '8.bc1.a1', 'counter': 7, 'group_counter': 12892, 'group_order': 384, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 5, 'size': 8}
id: 104110149
{'aut_label': '2G', 'centralizer': '8.bh1.a1', 'counter': 8, 'group_counter': 12892, 'group_order': 384, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 293, 'size': 8}
id: 104110150
{'aut_label': '2H', 'centralizer': '12.bc1.a1', 'counter': 9, 'group_counter': 12892, 'group_order': 384, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 42, 'size': 12}
id: 104110101
{'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 12892, 'group_order': 384, 'label': '3A', 'order': 3, 'powers': [10, 1], 'representative': 256, 'size': 2}
id: 104110102
{'aut_label': '4A', 'centralizer': '2.n1.a1', 'counter': 11, 'group_counter': 12892, 'group_order': 384, 'label': '4A', 'order': 4, 'powers': [4, 11], 'representative': 200, 'size': 2}
id: 104110103
{'aut_label': '4B', 'centralizer': '2.n1.a1', 'counter': 12, 'group_counter': 12892, 'group_order': 384, 'label': '4B', 'order': 4, 'powers': [4, 12], 'representative': 24, 'size': 2}
id: 104110104
{'aut_label': '4C', 'centralizer': '4.d1.a1', 'counter': 13, 'group_counter': 12892, 'group_order': 384, 'label': '4C', 'order': 4, 'powers': [2, 13], 'representative': 96, 'size': 4}
id: 104110105
{'aut_label': '4D', 'centralizer': '4.w1.a1', 'counter': 14, 'group_counter': 12892, 'group_order': 384, 'label': '4D', 'order': 4, 'powers': [3, 14], 'representative': 120, 'size': 4}
id: 104110106
{'aut_label': '4E1', 'centralizer': '4.bj1.a1', 'counter': 15, 'group_counter': 12892, 'group_order': 384, 'label': '4E1', 'order': 4, 'powers': [2, 16], 'representative': 97, 'size': 4}
id: 104110107
{'aut_label': '4E1', 'centralizer': '4.bj1.a1', 'counter': 16, 'group_counter': 12892, 'group_order': 384, 'label': '4E-1', 'order': 4, 'powers': [2, 15], 'representative': 289, 'size': 4}
id: 104110108
{'aut_label': '4F1', 'centralizer': '6.c1.a1', 'counter': 17, 'group_counter': 12892, 'group_order': 384, 'label': '4F1', 'order': 4, 'powers': [2, 18], 'representative': 2, 'size': 6}
id: 104110109
{'aut_label': '4F1', 'centralizer': '6.c1.a1', 'counter': 18, 'group_counter': 12892, 'group_order': 384, 'label': '4F-1', 'order': 4, 'powers': [2, 17], 'representative': 66, 'size': 6}
id: 104110110
{'aut_label': '4G1', 'centralizer': '6.m1.a1', 'counter': 19, 'group_counter': 12892, 'group_order': 384, 'label': '4G1', 'order': 4, 'powers': [3, 20], 'representative': 10, 'size': 6}
id: 104110112
{'aut_label': '4G1', 'centralizer': '6.m1.a1', 'counter': 20, 'group_counter': 12892, 'group_order': 384, 'label': '4G-1', 'order': 4, 'powers': [3, 19], 'representative': 74, 'size': 6}
id: 104110113
{'aut_label': '4H', 'centralizer': '12.l1.a1', 'counter': 21, 'group_counter': 12892, 'group_order': 384, 'label': '4H', 'order': 4, 'powers': [4, 21], 'representative': 34, 'size': 12}
id: 104110114
{'aut_label': '4I', 'centralizer': '12.k1.a1', 'counter': 22, 'group_counter': 12892, 'group_order': 384, 'label': '4I', 'order': 4, 'powers': [4, 22], 'representative': 35, 'size': 12}
id: 104110115
{'aut_label': '4I', 'centralizer': '12.k1.a1', 'counter': 23, 'group_counter': 12892, 'group_order': 384, 'label': '4J', 'order': 4, 'powers': [4, 23], 'representative': 99, 'size': 12}
id: 104110116
{'aut_label': '4K1', 'centralizer': '12.i1.a1', 'counter': 24, 'group_counter': 12892, 'group_order': 384, 'label': '4K1', 'order': 4, 'powers': [2, 25], 'representative': 3, 'size': 12}
id: 104110117
{'aut_label': '4K1', 'centralizer': '12.i1.a1', 'counter': 25, 'group_counter': 12892, 'group_order': 384, 'label': '4K-1', 'order': 4, 'powers': [2, 24], 'representative': 67, 'size': 12}
id: 104110118
{'aut_label': '4L', 'centralizer': '24.q1.a1', 'counter': 26, 'group_counter': 12892, 'group_order': 384, 'label': '4L', 'order': 4, 'powers': [2, 26], 'representative': 223, 'size': 24}
id: 104110119
{'aut_label': '4M', 'centralizer': '24.v1.a1', 'counter': 27, 'group_counter': 12892, 'group_order': 384, 'label': '4M', 'order': 4, 'powers': [3, 27], 'representative': 239, 'size': 24}
id: 104110120
{'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 28, 'group_counter': 12892, 'group_order': 384, 'label': '6A', 'order': 6, 'powers': [10, 4], 'representative': 144, 'size': 2}
id: 104110121
{'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 29, 'group_counter': 12892, 'group_order': 384, 'label': '6B', 'order': 6, 'powers': [10, 2], 'representative': 64, 'size': 2}
id: 104110123
{'aut_label': '6C', 'centralizer': '2.a1.a1', 'counter': 30, 'group_counter': 12892, 'group_order': 384, 'label': '6C', 'order': 6, 'powers': [10, 3], 'representative': 80, 'size': 2}
id: 104110124
{'aut_label': '6D', 'centralizer': '8.u1.a1', 'counter': 31, 'group_counter': 12892, 'group_order': 384, 'label': '6D', 'order': 6, 'powers': [10, 5], 'representative': 129, 'size': 8}
id: 104110125
{'aut_label': '6D', 'centralizer': '8.u1.a1', 'counter': 32, 'group_counter': 12892, 'group_order': 384, 'label': '6E', 'order': 6, 'powers': [10, 6], 'representative': 65, 'size': 8}
id: 104110126
{'aut_label': '6F', 'centralizer': '16.k1.a1', 'counter': 33, 'group_counter': 12892, 'group_order': 384, 'label': '6F', 'order': 6, 'powers': [10, 7], 'representative': 133, 'size': 16}
id: 104110127
{'aut_label': '6G', 'centralizer': '16.l1.a1', 'counter': 34, 'group_counter': 12892, 'group_order': 384, 'label': '6G', 'order': 6, 'powers': [10, 8], 'representative': 37, 'size': 16}
id: 104110128
{'aut_label': '8A1', 'centralizer': '4.bd1.a1', 'counter': 35, 'group_counter': 12892, 'group_order': 384, 'label': '8A1', 'order': 8, 'powers': [12, 36], 'representative': 12, 'size': 4}
id: 104110129
{'aut_label': '8A1', 'centralizer': '4.bd1.a1', 'counter': 36, 'group_counter': 12892, 'group_order': 384, 'label': '8A3', 'order': 8, 'powers': [12, 35], 'representative': 4, 'size': 4}
id: 104110130
{'aut_label': '8B', 'centralizer': '8.o1.a1', 'counter': 37, 'group_counter': 12892, 'group_order': 384, 'label': '8B', 'order': 8, 'powers': [12, 37], 'representative': 300, 'size': 8}
id: 104110131
{'aut_label': '8C1', 'centralizer': '12.bl1.a1', 'counter': 38, 'group_counter': 12892, 'group_order': 384, 'label': '8C1', 'order': 8, 'powers': [11, 38], 'representative': 6, 'size': 12}
id: 104110132
{'aut_label': '8C1', 'centralizer': '12.bl1.a1', 'counter': 39, 'group_counter': 12892, 'group_order': 384, 'label': '8C-1', 'order': 8, 'powers': [11, 39], 'representative': 70, 'size': 12}
id: 104110134
{'aut_label': '8D', 'centralizer': '24.bh1.a1', 'counter': 40, 'group_counter': 12892, 'group_order': 384, 'label': '8D', 'order': 8, 'powers': [11, 40], 'representative': 246, 'size': 24}
id: 104110135
{'aut_label': '12A', 'centralizer': '4.y1.a1', 'counter': 41, 'group_counter': 12892, 'group_order': 384, 'label': '12A', 'order': 12, 'powers': [28, 11], 'representative': 72, 'size': 4}
id: 104110136
{'aut_label': '12B', 'centralizer': '4.y1.a1', 'counter': 42, 'group_counter': 12892, 'group_order': 384, 'label': '12B', 'order': 12, 'powers': [28, 12], 'representative': 264, 'size': 4}
id: 104110137
{'aut_label': '12C1', 'centralizer': '4.d1.a1', 'counter': 43, 'group_counter': 12892, 'group_order': 384, 'label': '12C1', 'order': 12, 'powers': [29, 13], 'representative': 32, 'size': 4}
id: 104110138
{'aut_label': '12C1', 'centralizer': '4.d1.a1', 'counter': 44, 'group_counter': 12892, 'group_order': 384, 'label': '12C-1', 'order': 12, 'powers': [29, 13], 'representative': 160, 'size': 4}
id: 104110139
{'aut_label': '12D', 'centralizer': '8.g1.a1', 'counter': 45, 'group_counter': 12892, 'group_order': 384, 'label': '12D', 'order': 12, 'powers': [30, 14], 'representative': 40, 'size': 8}
id: 104110140
{'aut_label': '12E1', 'centralizer': '8.u1.a1', 'counter': 46, 'group_counter': 12892, 'group_order': 384, 'label': '12E1', 'order': 12, 'powers': [29, 15], 'representative': 33, 'size': 8}
id: 104110141
{'aut_label': '12E1', 'centralizer': '8.u1.a1', 'counter': 47, 'group_counter': 12892, 'group_order': 384, 'label': '12E-1', 'order': 12, 'powers': [29, 16], 'representative': 41, 'size': 8}
id: 104110142
{'aut_label': '24A1', 'centralizer': '8.n1.a1', 'counter': 48, 'group_counter': 12892, 'group_order': 384, 'label': '24A1', 'order': 24, 'powers': [42, 35], 'representative': 132, 'size': 8}
id: 104110143
{'aut_label': '24A1', 'centralizer': '8.n1.a1', 'counter': 49, 'group_counter': 12892, 'group_order': 384, 'label': '24A5', 'order': 24, 'powers': [42, 36], 'representative': 148, 'size': 8}
id: 104110145
{'aut_label': '24B1', 'centralizer': '8.o1.a1', 'counter': 50, 'group_counter': 12892, 'group_order': 384, 'label': '24B1', 'order': 24, 'powers': [42, 37], 'representative': 36, 'size': 8}
id: 104110146
{'aut_label': '24B1', 'centralizer': '8.o1.a1', 'counter': 51, 'group_counter': 12892, 'group_order': 384, 'label': '24B-1', 'order': 24, 'powers': [42, 37], 'representative': 164, '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: 2656414
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1a', '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: 2656425
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1b', '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: 2656436
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1c', '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: 2656447
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1d', '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: 2656450
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1e', '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: 2656451
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1f', '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: 2656452
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1g', '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: 2656453
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1h', '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: 2656454
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1i', '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: 2656415
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1j', '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: 2656416
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1k', '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: 2656417
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1l', '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: 2656418
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1m', '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: 2656419
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1n', '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: 2656420
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1o', '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: 2656421
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.1p', '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: 2656422
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2656423
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, -2, 2, -2, -2, -2, 2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656424
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, -2, 2, -2, -2, 2, -2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656426
{'cdim': 2, 'counter': 20, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, -2, 2, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656427
{'cdim': 2, 'counter': 21, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -2, -2, 2, -2, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656428
{'cdim': 2, 'counter': 22, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 0, -1, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2656429
{'cdim': 2, 'counter': 23, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, 2, 0, -1, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, -1, 2, 2, -2, 0, 0, 0, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
id: 2656430
{'cdim': 2, 'counter': 24, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, 0, -1, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, 1, -2, -2, 2, 0, 0, 0, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
id: 2656431
{'cdim': 2, 'counter': 25, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 0, -1, 2, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, -1, -1, -2, -2, -2, 0, 0, 0, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 2656432
{'cdim': 2, 'counter': 26, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 0, -1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, -2, -2, -2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
id: 2656433
{'cdim': 2, 'counter': 27, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, 2, 0, -1, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, -1, -2, -2, 2, 0, 0, 0, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
id: 2656434
{'cdim': 2, 'counter': 28, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -2, 0, -1, 2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 1, 2, 2, -2, 0, 0, 0, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
id: 2656435
{'cdim': 2, 'counter': 29, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2m', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 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, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2656437
{'cdim': 2, 'counter': 30, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2n', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2656438
{'cdim': 2, 'counter': 31, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2o', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2656439
{'cdim': 2, 'counter': 32, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.2p', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 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, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2656440
{'cdim': 4, 'counter': 33, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4a', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, -2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656441
{'cdim': 4, 'counter': 34, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4b', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 0, -2, -4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 0, 0, 2, 0, 0, 0, 0], 'schur_index': 1}
id: 2656442
{'cdim': 4, 'counter': 35, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4c', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 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, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2656443
{'cdim': 4, 'counter': 36, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4d', 'multiplicity': 1, 'nt': [24, 18], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, -4, 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, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2656444
{'cdim': 4, 'counter': 37, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4e', 'multiplicity': 2, 'nt': [16, 80], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 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, 0, 0], 'schur_index': 1}
id: 2656445
{'cdim': 4, 'counter': 38, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4f', 'multiplicity': 2, 'nt': [16, 116], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 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, 0, 0], 'schur_index': 1}
id: 2656446
{'cdim': 4, 'counter': 39, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4g', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 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, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2656449
{'cdim': 8, 'counter': 41, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.8a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 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, 0, 0], 'schur_index': 2}
id: 2656448
{'cdim': 4, 'counter': 40, 'faithful': False, 'group': '384.12892', 'group_order': 384, 'image': None, 'label': '384.12892.4h', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 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, 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: 3516198
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 384, 'label': '384.12892.1a', '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: 3516209
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.o1.a1', 'kernel_order': 192, 'label': '384.12892.1b', '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: 3516220
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.n1.a1', 'kernel_order': 192, 'label': '384.12892.1c', '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: 3516231
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.m1.a1', 'kernel_order': 192, 'label': '384.12892.1d', '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: 3516242
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.l1.a1', 'kernel_order': 192, 'label': '384.12892.1e', '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: 3516245
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 192, 'label': '384.12892.1f', '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: 3516246
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 192, 'label': '384.12892.1g', '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: 3516247
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 192, 'label': '384.12892.1h', '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: 3516248
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 192, 'label': '384.12892.1i', '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: 3516199
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 192, 'label': '384.12892.1j', '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: 3516200
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 192, 'label': '384.12892.1k', '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: 3516201
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 192, 'label': '384.12892.1l', '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: 3516202
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 192, 'label': '384.12892.1m', '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: 3516203
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 192, 'label': '384.12892.1n', '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: 3516204
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 192, 'label': '384.12892.1o', '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: 3516205
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 384, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 192, 'label': '384.12892.1p', '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: 3516206
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 64, 'label': '384.12892.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3516207
{'center': '4.s1.a1', 'center_index': 4, 'center_order': 96, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.s1.a1', 'kernel_order': 48, 'label': '384.12892.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516208
{'center': '4.s1.a1', 'center_index': 4, 'center_order': 96, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.r1.a1', 'kernel_order': 48, 'label': '384.12892.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516210
{'center': '4.s1.a1', 'center_index': 4, 'center_order': 96, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.f1.a1', 'kernel_order': 48, 'label': '384.12892.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516211
{'center': '4.s1.a1', 'center_index': 4, 'center_order': 96, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.e1.a1', 'kernel_order': 48, 'label': '384.12892.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516212
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.g1.a1', 'kernel_order': 32, 'label': '384.12892.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3516213
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 32, 'label': '384.12892.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 3516214
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 32, 'label': '384.12892.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3516215
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 32, 'label': '384.12892.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3516216
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 32, 'label': '384.12892.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3516217
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 32, 'label': '384.12892.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3516218
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 64, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 32, 'label': '384.12892.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 3516219
{'center': '4.e1.a1', 'center_index': 4, 'center_order': 96, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.b1', 'kernel_order': 24, 'label': '384.12892.2m1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516221
{'center': '4.e1.a1', 'center_index': 4, 'center_order': 96, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.b1', 'kernel_order': 24, 'label': '384.12892.2m2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516222
{'center': '4.ba1.a1', 'center_index': 4, 'center_order': 96, 'counter': 31, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.a1', 'kernel_order': 24, 'label': '384.12892.2n1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516223
{'center': '4.ba1.a1', 'center_index': 4, 'center_order': 96, 'counter': 32, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.a1', 'kernel_order': 24, 'label': '384.12892.2n2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516224
{'center': '4.ba1.a1', 'center_index': 4, 'center_order': 96, 'counter': 33, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.b1', 'kernel_order': 24, 'label': '384.12892.2o1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516225
{'center': '4.ba1.a1', 'center_index': 4, 'center_order': 96, 'counter': 34, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.i1.b1', 'kernel_order': 24, 'label': '384.12892.2o2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516226
{'center': '4.e1.a1', 'center_index': 4, 'center_order': 96, 'counter': 35, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.a1', 'kernel_order': 24, 'label': '384.12892.2p1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516227
{'center': '4.e1.a1', 'center_index': 4, 'center_order': 96, 'counter': 36, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.h1.a1', 'kernel_order': 24, 'label': '384.12892.2p2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516228
{'center': '24.d1.a1', 'center_index': 24, 'center_order': 16, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.c1.a1', 'kernel_order': 8, 'label': '384.12892.4a', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516229
{'center': '24.d1.a1', 'center_index': 24, 'center_order': 16, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '48.38', 'image_order': 48, 'indicator': 1, 'kernel': '48.b1.a1', 'kernel_order': 8, 'label': '384.12892.4b', 'nt': [12, 28], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-4, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516230
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 39, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.d1.b1', 'kernel_order': 8, 'label': '384.12892.4c', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516232
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 16, 'counter': 40, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '48.39', 'image_order': 48, 'indicator': -1, 'kernel': '48.d1.a1', 'kernel_order': 8, 'label': '384.12892.4d', 'nt': [24, 18], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516233
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 12, 'counter': 41, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '64.257', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 6, 'label': '384.12892.4e1', 'nt': [16, 80], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 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]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]]]}
id: 3516234
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 12, 'counter': 42, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [-2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '64.257', 'image_order': 64, 'indicator': 1, 'kernel': '64.a1.a1', 'kernel_order': 6, 'label': '384.12892.4e2', 'nt': [16, 80], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 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]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]]]}
id: 3516235
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 12, 'counter': 43, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 6, 'label': '384.12892.4f1', 'nt': [16, 116], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 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]], [[-2, 1], [-2, 3]], [[2, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516236
{'center': '32.a1.a1', 'center_index': 32, 'center_order': 12, 'counter': 44, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '64.258', 'image_order': 64, 'indicator': 0, 'kernel': '64.b1.a1', 'kernel_order': 6, 'label': '384.12892.4f2', 'nt': [16, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 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]], [[2, 1], [2, 3]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516237
{'center': '24.e1.a1', 'center_index': 24, 'center_order': 16, 'counter': 45, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '96.215', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.12892.4g1', 'nt': [24, 101], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516238
{'center': '24.e1.a1', 'center_index': 24, 'center_order': 16, 'counter': 46, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '96.215', 'image_order': 96, 'indicator': 0, 'kernel': '96.b1.a1', 'kernel_order': 4, 'label': '384.12892.4g2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[-4, 1]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3516239
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '192.1316', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 2, 'label': '384.12892.4h1', '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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 4]], [[0, 0]], [[-2, 0], [4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
id: 3516240
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 48, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '192.1316', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 2, 'label': '384.12892.4h2', '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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [-2, -3]], [[2, 3], [2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 4]], [[0, 0]], [[2, 0], [-4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, -3]], [[1, 3], [1, -3]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
id: 3516241
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 49, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '192.1316', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 2, 'label': '384.12892.4h3', '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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-4, 4]], [[0, 0]], [[-2, 0], [4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[1, 1], [-1, 3], [1, 5], [2, 7]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]]]}
id: 3516243
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 50, 'cyclotomic_n': 24, 'dim': 4, 'faithful': False, 'field': [4, 0, 2, 0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '192.1316', 'image_order': 192, 'indicator': 0, 'kernel': '192.a1.a1', 'kernel_order': 2, 'label': '384.12892.4h4', '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]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3], [2, -3]], [[-2, 3], [-2, -3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [4, 4]], [[0, 0]], [[2, 0], [-4, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, -3]], [[-1, 3], [-1, -3]], [[-1, 1], [1, 3], [-1, 5], [-2, 7]], [[1, 1], [-1, 3], [1, 5], [2, 7]]]}
id: 3516244
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 4, 'counter': 51, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '384.12892', 'group_counter': 12892, 'group_order': 384, 'image': None, 'image_isoclass': '192.1334', 'image_order': 192, 'indicator': -1, 'kernel': '192.b1.a1', 'kernel_order': 2, 'label': '384.12892.8a', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 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]], [[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 396 matching records in this table.

id: 53008306
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.1.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': '384.12892', 'subgroup_hash': 12892, 'subgroup_order': 384, 'subgroup_tex': '(C_2\\times D_8).D_6', 'supersolvable': True, 'sylow': 0}
id: 53008417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.892', 'subgroup_hash': 892, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:D_8', 'supersolvable': True, 'sylow': 0}
id: 53008528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.717', 'subgroup_hash': 717, 'subgroup_order': 192, 'subgroup_tex': '(C_6\\times D_8):C_2', 'supersolvable': True, 'sylow': 0}
id: 53008636
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.708', 'subgroup_hash': 708, 'subgroup_order': 192, 'subgroup_tex': 'C_3:C_4\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 53008647
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.717', 'subgroup_hash': 717, 'subgroup_order': 192, 'subgroup_tex': '(C_6\\times D_8):C_2', 'supersolvable': True, 'sylow': 0}
id: 53008658
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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: 53008669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.1105', 'subgroup_hash': 1105, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008680
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.568', 'subgroup_hash': 568, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008691
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.1278', 'subgroup_hash': 1278, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008307
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.634', 'subgroup_hash': 634, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008318
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.2.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': '192.336', 'subgroup_hash': 336, 'subgroup_order': 192, 'subgroup_tex': 'D_6.\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008329
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.316', 'subgroup_hash': 316, 'subgroup_order': 192, 'subgroup_tex': 'C_4.(C_4\\times D_6)', 'supersolvable': True, 'sylow': 0}
id: 53008340
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.333', 'subgroup_hash': 333, 'subgroup_order': 192, 'subgroup_tex': 'D_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53008351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.317', 'subgroup_hash': 317, 'subgroup_order': 192, 'subgroup_tex': 'C_3:(C_4\\times \\SD_{16})', 'supersolvable': True, 'sylow': 0}
id: 53008362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.2.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': '192.399', 'subgroup_hash': 399, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.2.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': '192.388', 'subgroup_hash': 388, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.3.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': '128.1851', 'subgroup_hash': 1851, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2.C_2^3', 'supersolvable': True, 'sylow': 2}
id: 53008395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 53008406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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: 53008418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '96.210', 'subgroup_hash': 210, 'subgroup_order': 96, 'subgroup_tex': 'D_4:D_6', 'supersolvable': True, 'sylow': 0}
id: 53008429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53008440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': ['C2'], '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: 53008451
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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: 53008462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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: 53008473
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.174', 'subgroup_hash': 174, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.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': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '96.52', 'subgroup_hash': 52, 'subgroup_order': 96, 'subgroup_tex': 'D_4:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53008506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.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': '96.39', 'subgroup_hash': 39, 'subgroup_order': 96, 'subgroup_tex': 'C_6.D_8', 'supersolvable': True, 'sylow': 0}
id: 53008540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.145', 'subgroup_hash': 145, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': False, '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: 53008562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': 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: 53008573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.140', 'subgroup_hash': 140, 'subgroup_order': 96, 'subgroup_tex': 'C_6:\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': 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: 53008595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.79', 'subgroup_hash': 79, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': True, 'sylow': 0}
id: 53008606
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53008617
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53008628
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.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': '96.27', 'subgroup_hash': 27, 'subgroup_order': 96, 'subgroup_tex': 'D_6:C_8', 'supersolvable': True, 'sylow': 0}
id: 53008637
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '96.75', 'subgroup_hash': 75, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 53008638
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008639
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008640
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008641
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
id: 53008642
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008643
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008644
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.20', 'subgroup_hash': 20, 'subgroup_order': 96, 'subgroup_tex': 'C_{24}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53008645
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008646
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008648
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.23', 'subgroup_hash': 23, 'subgroup_order': 96, 'subgroup_tex': 'C_6.Q_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008649
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': False, '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: 53008651
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.4.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': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008652
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.4.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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008653
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008654
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.4.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': '96.84', 'subgroup_hash': 84, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008656
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.146', 'subgroup_hash': 146, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008657
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.142', 'subgroup_hash': 142, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.4.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': '96.142', 'subgroup_hash': 142, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
id: 53008660
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.140', 'subgroup_hash': 140, 'subgroup_order': 64, 'subgroup_tex': 'C_4:D_8', 'supersolvable': True, 'sylow': 0}
id: 53008661
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.130', 'subgroup_hash': 130, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008662
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.6.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': '64.118', 'subgroup_hash': 118, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times D_8', 'supersolvable': True, 'sylow': 0}
id: 53008663
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.130', 'subgroup_hash': 130, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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: 53008665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.201', 'subgroup_hash': 201, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 53008666
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.159', 'subgroup_hash': 159, 'subgroup_order': 64, 'subgroup_tex': 'D_4.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53008667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.6.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': '64.221', 'subgroup_hash': 221, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 53008668
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.141', 'subgroup_hash': 141, 'subgroup_order': 64, 'subgroup_tex': 'Q_8:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.6.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': '64.162', 'subgroup_hash': 162, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
id: 53008671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.121', 'subgroup_hash': 121, 'subgroup_order': 64, 'subgroup_tex': '\\SD_{16}:C_4', 'supersolvable': True, 'sylow': 0}
id: 53008672
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.161', 'subgroup_hash': 161, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.D_8', 'supersolvable': True, 'sylow': 0}
id: 53008673
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.6.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': '64.119', 'subgroup_hash': 119, 'subgroup_order': 64, 'subgroup_tex': 'C_4\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 53008674
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.6.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': '64.114', 'subgroup_hash': 114, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2.C_2^2', 'supersolvable': True, 'sylow': 0}
id: 53008675
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.6.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': '64.160', 'subgroup_hash': 160, 'subgroup_order': 64, 'subgroup_tex': 'Q_8.Q_8', 'supersolvable': True, 'sylow': 0}
id: 53008676
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 53008678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.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: 53008679
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.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': '8.5', '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: 53008681
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 53008682
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 53008683
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008685
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
id: 53008687
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008688
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008689
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008693
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.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: 53008694
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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: 53008695
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53008696
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.12892.8.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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53008697
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.8.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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 53008698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.8.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53008699
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.8.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
id: 53008700
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.8.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
id: 53008701
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '384.12892.8.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
id: 53008308
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '384.12892', 'ambient_counter': 12892, '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': '384.12892.8.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', '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 396 matching records in this table.

id: 53008306
{'ambient': '384.12892', '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': [3353, 5452, 5641, 5091, 6449, 5685, 6381, 5090], 'generators': [1, 24, 192, 2, 96, 128, 16, 4], 'label': '384.12892.1.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: 53008307
{'ambient': '384.12892', '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.g1.a1', '192.d1.a1', '192.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.l1.a1', '4.m1.a1', '4.q1.a1', '4.r1.a1', '4.w1.a1', '4.z1.a1', '6.i1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3930, 4170, 5981, 3227, 7218, 4378, 8058, 5488], 'generators': [5, 16, 192, 6, 128, 96, 24], 'label': '384.12892.2.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.m1.a1', '4.l1.a1', '4.r1.a1', '4.q1.a1', '4.w1.a1', '4.z1.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: 53008308
{'ambient': '384.12892', '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.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.g1.a1', '16.j1.a1', '16.n1.a1', '16.bb1.a1', '16.bb1.b1', '16.bb1.c1', '16.bb1.d1', '24.m1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6289, -1, 3550, -1, 3816, -1, 4414, -1], 'generators': [1, 128, 34, 192, 16], 'label': '384.12892.8.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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: 53008309
{'ambient': '384.12892', 'aut_centralizer_order': 96, 'aut_label': '8.z1', '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.h1.a1', '4.bn1.a1', '4.bp1.a1'], 'contains': ['16.c1.a1', '16.k1.a1', '16.l1.a1', '16.t1.a1', '24.n1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9202, -1, 1182, -1, 1121, -1, 656, -1], 'generators': [5, 192, 16, 96, 128], 'label': '384.12892.8.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': '16.14'}
id: 53008310
{'ambient': '384.12892', 'aut_centralizer_order': 96, 'aut_label': '8.ba1', '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.h1.a1', '4.bo1.a1', '4.bq1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.l1.a1', '16.x1.a1', '24.o1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8984, -1, 472, -1, 889, -1, 412, -1], 'generators': [5, 208, 104, 192, 128], 'label': '384.12892.8.ba1.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.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': '16.14'}
id: 53008311
{'ambient': '384.12892', '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.i1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.a1.a1', '16.k1.a1', '16.q1.a1', '16.y1.a1', '24.p1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9324, -1, 1377, -1, 629, -1, 173, -1], 'generators': [21, 128, 58, 192, 208], 'label': '384.12892.8.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.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: 53008312
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '8.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.230', 'aut_weyl_index': 64, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '4.bo1.a1', '4.bp1.a1'], 'contains': ['16.e1.a1', '16.k1.a1', '16.p1.a1', '16.u1.a1', '24.q1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9094, -1, 1059, -1, 1245, -1, 779, -1], 'generators': [21, 128, 2, 16, 192], 'label': '384.12892.8.bc1.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.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': '24.14'}
id: 53008313
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '8.bd1', '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.bq1.a1'], 'contains': ['16.f1.a1', '16.k1.a1', '16.p1.a1', '24.r1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8846, -1, 1457, -1, 1352, -1, 1022, -1], 'generators': [21, 128, 26, 16, 192], 'label': '384.12892.8.bd1.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.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': '48.51'}
id: 53008314
{'ambient': '384.12892', '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.i1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.g1.a1', '16.k1.a1', '16.q1.a1', '24.s1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8057, -1, 917, -1, 1632, -1, 1160, -1], 'generators': [21, 128, 34, 16, 192], 'label': '384.12892.8.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1.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: 53008315
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bn1.a1', '4.bo1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '16.p1.a1', '16.v1.a1', '24.t1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9451, -1, 1276, -1, 1005, -1, 298, -1], 'generators': [309, 128, 58, 16, 192], 'label': '384.12892.8.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.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': '48.51'}
id: 53008316
{'ambient': '384.12892', '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.p1.a1', '4.bo1.a1', '4.bp1.a1'], 'contains': ['16.e1.a1', '16.l1.a1', '16.q1.a1', '24.u1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8652, -1, 746, -1, 1562, -1, 884, -1], 'generators': [309, 128, 2, 16, 192], 'label': '384.12892.8.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.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: 53008317
{'ambient': '384.12892', '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': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '4.bn1.a1', '4.bq1.a1'], 'contains': ['16.f1.a1', '16.l1.a1', '16.q1.a1', '16.z1.a1', '24.v1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8746, -1, 832, -1, 764, -1, 534, -1], 'generators': [309, 128, 26, 192, 208], 'label': '384.12892.8.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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': '24.14'}
id: 53008318
{'ambient': '384.12892', 'aut_centralizer_order': 4, 'aut_label': '2.j1', '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.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.m1.a1', '4.t1.a1', '4.v1.a1', '4.bc1.a1', '4.bi1.a1', '6.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2741, 3829, 5451, 4756, 5744, 6531, 6029, 4362], 'generators': [97, 16, 192, 34, 128, 300, 200], 'label': '384.12892.2.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.j1.a1', '4.m1.a1', '4.t1.a1', '4.v1.a1', '4.bc1.a1', '4.bi1.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': '96.209'}
id: 53008319
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '4.bp1.a1', '4.bq1.a1'], 'contains': ['16.g1.a1', '16.l1.a1', '16.p1.a1', '24.w1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8238, -1, 974, -1, 1702, -1, 1229, -1], 'generators': [309, 128, 34, 208, 192], 'label': '384.12892.8.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.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': '48.51'}
id: 53008320
{'ambient': '384.12892', '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': '48.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bj1.a1', '4.bk1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '16.o1.a1', '16.w1.a1', '24.ba1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7458, -1, 2618, -1, 2573, -1, 1618, -1], 'generators': [97, 128, 58, 16, 192], 'label': '384.12892.8.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '24.14'}
id: 53008321
{'ambient': '384.12892', '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': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.bj1.a1', '4.bl1.a1'], 'contains': ['16.c1.a1', '16.n1.a1', '16.o1.a1', '24.bj1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7558, -1, 3008, -1, 3185, -1, 3077, -1], 'generators': [3, 128, 96, 16, 192], 'label': '384.12892.8.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '12.4'}
id: 53008322
{'ambient': '384.12892', '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': [8908, -1, 1684, -1, 1492, -1, 1091, -1], 'generators': [7, 128, 96, 208, 192], 'label': '384.12892.8.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: 53008323
{'ambient': '384.12892', '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': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '4.bk1.a1', '4.bm1.a1'], 'contains': ['16.d1.a1', '16.n1.a1', '16.o1.a1', '24.bm1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6484, -1, 2309, -1, 3284, -1, 2042, -1], 'generators': [3, 128, 104, 208, 192], 'label': '384.12892.8.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '24.14'}
id: 53008324
{'ambient': '384.12892', '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': '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.bn1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8487, -1, 690, -1, 1422, -1, 953, -1], 'generators': [7, 128, 104, 208, 192], 'label': '384.12892.8.bn1.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.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': '48.51'}
id: 53008325
{'ambient': '384.12892', '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': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.bk1.a1', '4.bl1.a1'], 'contains': ['16.e1.a1', '16.m1.a1', '16.n1.a1', '24.bo1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7230, -1, 3064, -1, 3384, -1, 3008, -1], 'generators': [97, 128, 2, 16, 192], 'label': '384.12892.8.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '24.14'}
id: 53008326
{'ambient': '384.12892', '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.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.ba1.a1', '4.bj1.a1', '4.bm1.a1'], 'contains': ['16.f1.a1', '16.m1.a1', '16.n1.a1', '24.bp1.a1'], 'core': '16.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6758, -1, 2905, -1, 3553, -1, 2911, -1], 'generators': [97, 128, 26, 208, 192], 'label': '384.12892.8.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.ba1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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: 53008327
{'ambient': '384.12892', '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': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '4.bl1.a1', '4.bm1.a1'], 'contains': ['16.g1.a1', '16.m1.a1', '16.o1.a1', '24.bq1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6970, -1, 2826, -1, 3454, -1, 2208, -1], 'generators': [97, 128, 34, 16, 192], 'label': '384.12892.8.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '24.14'}
id: 53008328
{'ambient': '384.12892', 'aut_centralizer_order': 48, 'aut_label': '8.br1', '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.a1.a1'], 'contains': ['16.h1.a1', '16.be1.a1', '16.bm1.a1', '24.br1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2210, -1, 8806, -1, 7136, -1, 8164, -1], 'generators': [1, 16, 4, 128, 24], 'label': '384.12892.8.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.br1.a1', 'projective_image': '192.1165', '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': '16.11'}
id: 53008329
{'ambient': '384.12892', '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.g1.a1', '192.d1.a1', '192.d1.b1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.j1.a1', '4.k1.a1', '4.l1.a1', '4.ba1.a1', '4.bb1.a1', '4.be1.a1', '4.bf1.a1', '6.k1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2858, 6948, 6450, 4081, 6226, 5109, 6909, 5090], 'generators': [97, 16, 192, 2, 128, 300, 200], 'label': '384.12892.2.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.l1.a1', '4.ba1.a1', '4.bb1.a1', '4.be1.a1', '4.bf1.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: 53008330
{'ambient': '384.12892', 'aut_centralizer_order': 48, 'aut_label': '8.br1', '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.a1.a1'], 'contains': ['16.h1.b1', '16.be1.a1', '16.bm1.a1', '24.br1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2210, -1, 8721, -1, 7136, -1, 8061, -1], 'generators': [193, 16, 4, 128, 24], 'label': '384.12892.8.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.br1.b1', 'projective_image': '192.1165', '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': '16.11'}
id: 53008331
{'ambient': '384.12892', 'aut_centralizer_order': 48, 'aut_label': '8.bs1', '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.bg1.a1', '16.bn1.a1', '24.bs1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3079, -1, 8889, -1, 7240, -1, 6737, -1], 'generators': [1, 16, 300, 128, 8], 'label': '384.12892.8.bs1.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.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': '16.11'}
id: 53008332
{'ambient': '384.12892', 'aut_centralizer_order': 48, 'aut_label': '8.bs1', '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.bg1.a1', '16.bn1.a1', '24.bs1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3079, -1, 8973, -1, 7240, -1, 6635, -1], 'generators': [193, 16, 300, 128, 8], 'label': '384.12892.8.bs1.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.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': '16.11'}
id: 53008333
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.i1.a1', '16.ba1.a1', '16.ba1.c1', '16.bb1.a1', '16.bb1.c1', '16.bc1.a1', '16.bh1.a1', '24.bt1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3597, -1, 9077, -1, 5469, -1, 9444, -1], 'generators': [1, 128, 34, 216, 16], 'label': '384.12892.8.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '48.51'}
id: 53008334
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.i1.b1', '16.ba1.b1', '16.ba1.d1', '16.bb1.b1', '16.bb1.d1', '16.bc1.a1', '16.bh1.a1', '24.bt1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3597, -1, 9277, -1, 5469, -1, 9375, -1], 'generators': [193, 128, 34, 216, 16], 'label': '384.12892.8.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '48.51'}
id: 53008335
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '8.bu1', '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.c1.a1'], 'contains': ['16.h1.a1', '16.ba1.a1', '16.ba1.b1', '16.bb1.a1', '16.bb1.b1', '16.bi1.a1', '16.bl1.a1', '24.bu1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3206, -1, 9424, -1, 5399, -1, 9306, -1], 'generators': [1, 128, 34, 24, 16], 'label': '384.12892.8.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '48.51'}
id: 53008336
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '8.bu1', '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.c1.a1'], 'contains': ['16.h1.b1', '16.ba1.c1', '16.ba1.d1', '16.bb1.c1', '16.bb1.d1', '16.bi1.a1', '16.bl1.a1', '24.bu1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3206, -1, 9333, -1, 5399, -1, 9237, -1], 'generators': [193, 128, 34, 24, 16], 'label': '384.12892.8.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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': '48.51'}
id: 53008337
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '8.bv1', '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.l1.a1'], 'contains': ['16.i1.a1', '16.bd1.a1', '16.bk1.a1', '24.bv1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2441, -1, 8479, -1, 7863, -1, 9941, -1], 'generators': [197, 128, 38, 216, 16], 'label': '384.12892.8.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.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': '48.38'}
id: 53008338
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '8.bv1', '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.l1.a1'], 'contains': ['16.i1.b1', '16.bd1.a1', '16.bk1.a1', '24.bv1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2441, -1, 8371, -1, 7863, -1, 9809, -1], 'generators': [5, 128, 38, 216, 16], 'label': '384.12892.8.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.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': '48.38'}
id: 53008339
{'ambient': '384.12892', '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.q1.a1'], 'contains': ['16.i1.a1', '16.bf1.a1', '16.bj1.a1', '24.bw1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5370, -1, 7659, -1, 8067, -1, 9677, -1], 'generators': [293, 128, 6, 200, 16], 'label': '384.12892.8.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.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: 53008340
{'ambient': '384.12892', '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.d1.a1', '192.d1.b1', '192.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.n1.a1', '4.o1.a1', '4.r1.a1', '4.t1.a1', '4.u1.a1', '4.bb1.a1', '4.bh1.a1', '6.l1.a1'], 'core': '2.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4520, 6131, 4985, 5091, 6385, 8378, 5676, 6700], 'generators': [97, 16, 192, 34, 128, 4, 216], 'label': '384.12892.2.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.t1.a1', '4.u1.a1', '4.bb1.a1', '4.bh1.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: 53008341
{'ambient': '384.12892', '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.q1.a1'], 'contains': ['16.i1.b1', '16.bf1.a1', '16.bj1.a1', '24.bw1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5370, -1, 7139, -1, 8067, -1, 9545, -1], 'generators': [101, 128, 6, 200, 16], 'label': '384.12892.8.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.q1.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: 53008342
{'ambient': '384.12892', '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': '16.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.f1.a1', '24.br1.a1', '24.br1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [706, 1189, 7267, 8679, 8537, 1922, 7670, 8870], 'generators': [1, 4, 192], 'label': '384.12892.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.f1.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': '16.11'}
id: 53008343
{'ambient': '384.12892', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.g1.a1', '24.bs1.a1', '24.bs1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [937, 1696, 7828, 9187, 8853, 1666, 6532, 8441], 'generators': [1, 300, 192], 'label': '384.12892.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.g1.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': '32.46'}
id: 53008344
{'ambient': '384.12892', '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': '16.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '24.i1.a1', '24.j1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4051, 2449, 6082, 8417, 6695, 2693, 5568, 9126], 'generators': [1, 24, 96], 'label': '384.12892.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.d1.a1', '24.e1.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': '16.11'}
id: 53008345
{'ambient': '384.12892', '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': '32.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.d1.a1', '24.n1.a1', '24.o1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3832, 1406, 6011, 7531, 5735, 2307, 5379, 7884], 'generators': [5, 24, 96], 'label': '384.12892.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.h1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.c1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53008346
{'ambient': '384.12892', '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': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.a1.a1', '6.j1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.g1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [212, 1913, 6385, 7779, 8239, 2479, 7221, 8227], 'generators': [97, 300], 'label': '384.12892.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.j1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '32.46'}
id: 53008347
{'ambient': '384.12892', 'aut_centralizer_order': 96, 'aut_label': '12.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '16.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.a1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.c1.a1', '24.e1.a1', '24.f1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2304, 2159, 5377, 8896, 8765, 2136, 6239, 8656], 'generators': [97, 4], 'label': '384.12892.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.o1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.e1.a1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 53008348
{'ambient': '384.12892', 'aut_centralizer_order': 192, 'aut_label': '12.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.y1.a1', '6.a1.a1', '6.n1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.f1.a1', '24.g1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [151, 2810, 7688, 8119, 9011, 2908, 7151, 8056], 'generators': [4, 96], 'label': '384.12892.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.y1.a1', '6.a1.a1'], 'normal_contains': ['24.d1.a1', '24.f1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 53008349
{'ambient': '384.12892', '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': '48.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bj1.a1', '6.f1.a1'], 'contains': ['24.h1.a1', '24.i1.a1', '24.l1.a1', '24.y1.a1', '24.ba1.a1', '24.bj1.a1', '24.bp1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5982, -1, 3759, -1, 3940, -1, 3657, -1], 'generators': [1, 26, 96], 'label': '384.12892.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.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': '8.5'}
id: 53008350
{'ambient': '384.12892', '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': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bk1.a1', '6.f1.a1'], 'contains': ['24.h1.a1', '24.j1.a1', '24.k1.a1', '24.z1.a1', '24.ba1.a1', '24.bm1.a1', '24.bo1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5621, -1, 3652, -1, 4431, -1, 3164, -1], 'generators': [1, 2, 104], 'label': '384.12892.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.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': '8.5'}
id: 53008351
{'ambient': '384.12892', '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.g1.a1', '192.d1.a1', '192.d1.b1', '192.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.p1.a1', '4.q1.a1', '4.ba1.a1', '4.bc1.a1', '4.bd1.a1', '4.bg1.a1', '6.m1.a1'], 'core': '2.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4134, 5452, 5575, 5773, 6763, 3597, 6181, 3883], 'generators': [97, 16, 192, 2, 128, 4, 216], 'label': '384.12892.2.m1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.m1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.o1.a1', '4.p1.a1', '4.q1.a1', '4.ba1.a1', '4.bc1.a1', '4.bd1.a1', '4.bg1.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: 53008352
{'ambient': '384.12892', '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': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bl1.a1', '6.f1.a1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.m1.a1', '24.bi1.a1', '24.bj1.a1', '24.bo1.a1', '24.bq1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5855, -1, 3876, -1, 4547, -1, 3771, -1], 'generators': [1, 2, 96], 'label': '384.12892.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.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': '8.5'}
id: 53008353
{'ambient': '384.12892', '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': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bm1.a1', '6.f1.a1'], 'contains': ['24.j1.a1', '24.l1.a1', '24.m1.a1', '24.bl1.a1', '24.bm1.a1', '24.bp1.a1', '24.bq1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5402, -1, 3521, -1, 4678, -1, 3539, -1], 'generators': [1, 34, 104], 'label': '384.12892.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.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': '8.5'}
id: 53008354
{'ambient': '384.12892', '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': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.h1.a1', '24.m1.a1', '24.x1.a1', '24.bc1.a1', '24.bt1.a1', '24.bt1.b1', '24.bu1.a1', '24.bu1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1452, -1, 7945, -1, 7020, -1, 8278, -1], 'generators': [1, 34, 24, 192], 'label': '384.12892.12.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.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': '16.11'}
id: 53008355
{'ambient': '384.12892', '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': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.k1.a1', '24.l1.a1', '24.bb1.a1', '24.bd1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3102, -1, 4299, -1, 6591, -1, 4625, -1], 'generators': [1, 2, 24], 'label': '384.12892.12.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.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': '16.11'}
id: 53008356
{'ambient': '384.12892', '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': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.be1.a1', '24.bg1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1702, -1, 6898, -1, 8625, -1, 7514, -1], 'generators': [1, 6], 'label': '384.12892.12.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': '16.11'}
id: 53008357
{'ambient': '384.12892', '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.b1.a1', '6.e1.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': [1167, -1, 6954, -1, 9081, -1, 6446, -1], 'generators': [1, 38], 'label': '384.12892.12.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: 53008358
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bn1.a1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.p1.a1', '24.r1.a1', '24.t1.a1', '24.v1.a1', '24.y1.a1', '24.bk1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6738, -1, 2056, -1, 1991, -1, 2508, -1], 'generators': [5, 26, 96], 'label': '384.12892.12.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': '16.14'}
id: 53008359
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bo1.a1', '6.h1.a1'], 'contains': ['24.o1.a1', '24.p1.a1', '24.q1.a1', '24.t1.a1', '24.u1.a1', '24.z1.a1', '24.bn1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6382, -1, 1511, -1, 2077, -1, 2423, -1], 'generators': [5, 2, 104], 'label': '384.12892.12.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': '16.14'}
id: 53008360
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bp1.a1', '6.h1.a1'], 'contains': ['24.n1.a1', '24.q1.a1', '24.s1.a1', '24.u1.a1', '24.w1.a1', '24.bi1.a1', '24.bk1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6278, -1, 1606, -1, 2418, -1, 2774, -1], 'generators': [5, 2, 96], 'label': '384.12892.12.r1.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.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': '16.14'}
id: 53008361
{'ambient': '384.12892', 'aut_centralizer_order': 16, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bq1.a1', '6.h1.a1'], 'contains': ['24.o1.a1', '24.r1.a1', '24.s1.a1', '24.v1.a1', '24.w1.a1', '24.bl1.a1', '24.bn1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6146, -1, 1415, -1, 2196, -1, 2625, -1], 'generators': [5, 34, 104], 'label': '384.12892.12.s1.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.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': '16.14'}
id: 53008362
{'ambient': '384.12892', 'aut_centralizer_order': 8, 'aut_label': '2.n1', '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.e1.a1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.s1.a1', '4.u1.a1', '4.v1.a1', '4.y1.a1', '4.z1.a1', '4.bd1.a1', '4.be1.a1', '6.n1.a1'], 'core': '2.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2561, 5816, 7437, 2266, 7383, 7815, 7720, 5807], 'generators': [2, 16, 192, 4, 128, 96, 8], 'label': '384.12892.2.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.u1.a1', '4.v1.a1', '4.y1.a1', '4.z1.a1', '4.bd1.a1', '4.be1.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': '48.51'}
id: 53008363
{'ambient': '384.12892', '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': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.b1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.p1.a1', '24.s1.a1', '24.x1.a1', '24.bf1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1546, -1, 5159, -1, 5320, -1, 4719, -1], 'generators': [5, 34, 24], 'label': '384.12892.12.t1.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.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': '32.46'}
id: 53008364
{'ambient': '384.12892', '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.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.c1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '24.q1.a1', '24.r1.a1', '24.bb1.a1', '24.be1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4484, -1, 5662, -1, 5050, -1, 5465, -1], 'generators': [5, 2, 24], 'label': '384.12892.12.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: 53008365
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.v1', '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.l1.a1', '6.b1.a1', '6.i1.a1', '6.k1.a1'], 'contains': ['24.b1.a1', '24.bc1.a1', '24.bh1.a1', '24.bv1.a1', '24.bv1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [586, -1, 6755, -1, 9597, -1, 9120, -1], 'generators': [5, 38, 192], 'label': '384.12892.12.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': '32.46'}
id: 53008366
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.c1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.bd1.a1', '24.bg1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1015, -1, 5489, -1, 8169, -1, 7583, -1], 'generators': [5, 6], 'label': '384.12892.12.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': '16.11'}
id: 53008367
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.x1', '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.d1.a1', '6.h1.a1', '6.l1.a1'], 'contains': ['24.c1.a1', '24.t1.a1', '24.w1.a1', '24.x1.a1', '24.be1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4567, -1, 4223, -1, 6240, -1, 5302, -1], 'generators': [293, 34, 24], 'label': '384.12892.12.x1.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.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': '32.46'}
id: 53008368
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.y1', '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.p1.a1', '6.e1.a1', '6.h1.a1', '6.m1.a1'], 'contains': ['24.c1.a1', '24.u1.a1', '24.v1.a1', '24.bb1.a1', '24.bf1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3908, -1, 4038, -1, 5225, -1, 3885, -1], 'generators': [293, 2, 24], 'label': '384.12892.12.y1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.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': '16.11'}
id: 53008369
{'ambient': '384.12892', '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': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.d1.a1', '6.i1.a1', '6.m1.a1'], 'contains': ['24.c1.a1', '24.bc1.a1', '24.bg1.a1', '24.bw1.a1', '24.bw1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1323, -1, 6620, -1, 9852, -1, 8954, -1], 'generators': [293, 6, 192], 'label': '384.12892.12.z1.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.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': '16.11'}
id: 53008370
{'ambient': '384.12892', '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': '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.c1.a1', '24.bd1.a1', '24.bh1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2062, -1, 4845, -1, 9151, -1, 6031, -1], 'generators': [293, 38], 'label': '384.12892.12.ba1.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.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': '32.46'}
id: 53008371
{'ambient': '384.12892', 'aut_centralizer_order': 64, 'aut_label': '12.bb1', '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.s1.a1', '6.f1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.d1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1', '24.bb1.a1', '24.bi1.a1', '24.bl1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5107, -1, 4134, -1, 4312, -1, 3407, -1], 'generators': [2, 24, 96], 'label': '384.12892.12.bb1.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.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': '16.14'}
id: 53008372
{'ambient': '384.12892', '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': '48.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.f1.a1', '6.j1.a1', '6.l1.a1'], 'contains': ['24.e1.a1', '24.x1.a1', '24.ba1.a1', '24.bd1.a1', '24.bq1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4153, -1, 4392, -1, 6475, -1, 4824, -1], 'generators': [97, 34, 24], 'label': '384.12892.12.bc1.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.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': '16.11'}
id: 53008373
{'ambient': '384.12892', '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.g1.a1', '192.d1.a1', '192.d1.b1', '192.e1.a1', '192.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.w1.a1', '4.x1.a1', '4.y1.a1', '4.bf1.a1', '4.bg1.a1', '4.bh1.a1', '4.bi1.a1', '6.o1.a1'], 'core': '2.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2969, 7429, 5086, 6478, 5972, 5685, 5929, 2968], 'generators': [3, 16, 192, 4, 128, 96, 24], 'label': '384.12892.2.o1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.o1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.w1.a1', '4.x1.a1', '4.y1.a1', '4.bh1.a1', '4.bi1.a1', '4.bf1.a1', '4.bg1.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: 53008374
{'ambient': '384.12892', 'aut_centralizer_order': 64, 'aut_label': '12.bd1', '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.u1.a1', '6.b1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.f1.a1', '24.x1.a1', '24.bh1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [790, -1, 7625, -1, 9724, -1, 7898, -1], 'generators': [34, 4], 'label': '384.12892.12.bd1.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.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': '16.14'}
id: 53008375
{'ambient': '384.12892', 'aut_centralizer_order': 64, 'aut_label': '12.be1', '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.v1.a1', '6.d1.a1', '6.j1.a1', '6.n1.a1'], 'contains': ['24.g1.a1', '24.x1.a1', '24.bg1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [47, -1, 8030, -1, 9230, -1, 8634, -1], 'generators': [34, 300], 'label': '384.12892.12.be1.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.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': '16.14'}
id: 53008376
{'ambient': '384.12892', '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': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.f1.a1', '6.i1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.bc1.a1', '24.bd1.a1', '24.bj1.a1', '24.bm1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3296, -1, 4565, -1, 6799, -1, 5774, -1], 'generators': [3, 24, 96], 'label': '384.12892.12.bf1.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.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': '16.11'}
id: 53008377
{'ambient': '384.12892', '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.x1.a1', '6.g1.a1', '6.h1.a1', '6.o1.a1'], 'contains': ['24.d1.a1', '24.be1.a1', '24.bf1.a1', '24.bk1.a1', '24.bn1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4763, -1, 4495, -1, 5137, -1, 4183, -1], 'generators': [7, 24, 96], 'label': '384.12892.12.bg1.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.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: 53008378
{'ambient': '384.12892', 'aut_centralizer_order': 64, 'aut_label': '12.bh1', '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.g1.a1', '6.i1.a1', '6.n1.a1'], 'contains': ['24.d1.a1', '24.bg1.a1', '24.bh1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1640, -1, 7057, -1, 9971, -1, 8836, -1], 'generators': [6, 96], 'label': '384.12892.12.bh1.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.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': '16.14'}
id: 53008379
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.bi1', '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.ba1.a1', '6.f1.a1', '6.k1.a1', '6.m1.a1'], 'contains': ['24.e1.a1', '24.bb1.a1', '24.bc1.a1', '24.bo1.a1', '24.bp1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3540, -1, 5260, -1, 6904, -1, 5671, -1], 'generators': [97, 2, 24], 'label': '384.12892.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.ba1.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': '16.11'}
id: 53008380
{'ambient': '384.12892', '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.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': [3668, -1, 5862, -1, 8379, -1, 6308, -1], 'generators': [97, 38], 'label': '384.12892.12.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: 53008381
{'ambient': '384.12892', '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': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bc1.a1', '6.g1.a1', '6.j1.a1', '6.m1.a1'], 'contains': ['24.e1.a1', '24.bf1.a1', '24.bg1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2000, -1, 5546, -1, 8450, -1, 6170, -1], 'generators': [97, 6], 'label': '384.12892.12.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': '16.11'}
id: 53008382
{'ambient': '384.12892', 'aut_centralizer_order': 64, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '12.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bd1.a1', '6.c1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.f1.a1', '24.bb1.a1', '24.bg1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1090, -1, 5792, -1, 9461, -1, 7429, -1], 'generators': [2, 4], 'label': '384.12892.12.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': '4.2'}
id: 53008383
{'ambient': '384.12892', '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.e1.a1', '6.k1.a1', '6.n1.a1'], 'contains': ['24.g1.a1', '24.bb1.a1', '24.bh1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [305, -1, 7535, -1, 9341, -1, 7788, -1], 'generators': [2, 300], 'label': '384.12892.12.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: 53008384
{'ambient': '384.12892', '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': [1933, -1, 5398, -1, 8558, -1, 6674, -1], 'generators': [1, 2, 4, 96], 'label': '384.12892.3.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: 53008385
{'ambient': '384.12892', 'aut_centralizer_order': 32, 'aut_label': '12.bn1', '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.bf1.a1', '6.d1.a1', '6.k1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.bc1.a1', '24.be1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [394, -1, 7407, -1, 8695, -1, 7975, -1], 'generators': [35, 300], 'label': '384.12892.12.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': '32.46'}
id: 53008386
{'ambient': '384.12892', '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': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bg1.a1', '6.b1.a1', '6.m1.a1', '6.o1.a1'], 'contains': ['24.f1.a1', '24.bc1.a1', '24.bf1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [859, -1, 5433, -1, 8940, -1, 6376, -1], 'generators': [35, 4], 'label': '384.12892.12.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': '16.11'}
id: 53008387
{'ambient': '384.12892', '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': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.bh1.a1', '6.c1.a1', '6.l1.a1', '6.o1.a1'], 'contains': ['24.f1.a1', '24.bd1.a1', '24.be1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2523, -1, 5027, -1, 8309, -1, 6101, -1], 'generators': [3, 4], 'label': '384.12892.12.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': '16.11'}
id: 53008388
{'ambient': '384.12892', '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.j1.a1', '6.o1.a1'], 'contains': ['24.g1.a1', '24.bd1.a1', '24.bf1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [456, -1, 4901, -1, 7965, -1, 5963, -1], 'generators': [3, 300], 'label': '384.12892.12.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: 53008389
{'ambient': '384.12892', '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': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.e1.a1', '8.f1.a1', '8.t1.a1', '8.bb1.a1', '8.bf1.a1', '8.bj1.a1'], 'contains': ['32.a1.a1', '32.g1.a1', '32.p1.a1', '32.w1.a1', '48.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8532, 8157, 2281, 2971, 1404, 7199, 1133, 3574], 'generators': [58, 16, 192, 128], 'label': '384.12892.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.d1.a1', '8.e1.a1', '8.f1.a1'], 'normal_contains': ['32.a1.a1'], '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': '24.14'}
id: 53008390
{'ambient': '384.12892', '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.c1.a1', '8.d1.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.b1.a1', '32.c1.a1', '48.a1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4637, 4712, 6442, 5007, 6116, 4839, 5944, 5509], 'generators': [24, 192, 128, 16], 'label': '384.12892.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.g1.a1', '8.h1.a1', '8.i1.a1', '8.k1.a1', '8.j1.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.c1.a1', '32.b1.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: 53008391
{'ambient': '384.12892', '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.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.g1.a1', '8.r1.a1', '8.u1.a1', '8.z1.a1', '8.bk1.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': [8729, 7005, 2379, 3819, 1959, 5609, 1626, 3276], 'generators': [16, 96, 128, 192], 'label': '384.12892.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.e1.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: 53008392
{'ambient': '384.12892', '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.f1.a1', '8.g1.a1', '8.s1.a1', '8.v1.a1', '8.ba1.a1', '8.bm1.a1', '8.bn1.a1'], 'contains': ['32.a1.a1', '32.q1.a1', '48.c1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7938, 6697, 1181, 4129, 1282, 7497, 1253, 3872], 'generators': [104, 192, 128, 208], 'label': '384.12892.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.f1.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: 53008393
{'ambient': '384.12892', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.i1.a1', '8.r1.a1', '8.w1.a1', '8.bc1.a1', '8.bg1.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': [8211, 7818, 1817, 2662, 2085, 8116, 1502, 2953], 'generators': [2, 16, 192, 128], 'label': '384.12892.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.f1.a1', '8.i1.a1', '8.r1.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: 53008394
{'ambient': '384.12892', '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.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.i1.a1', '8.s1.a1', '8.x1.a1', '8.bd1.a1', '8.bh1.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': [8074, 8797, 1941, 2340, 1156, 7804, 1377, 2642], 'generators': [26, 192, 208, 128], 'label': '384.12892.16.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1.a1', 'normal_contained_in': ['8.e1.a1', '8.i1.a1', '8.s1.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: 53008395
{'ambient': '384.12892', 'aut_centralizer_order': 48, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '128.2320', 'aut_weyl_index': 48, 'centralizer': '32.a1.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.n1.a1', '8.br1.a1', '8.br1.b1', '12.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2888, 112, 7723, 9332, 6074, 1318, 7616, 9411], 'generators': [1, 16, 24, 4, 192, 128], 'label': '384.12892.4.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.n1.a1', '12.a1.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': '32.46'}
id: 53008396
{'ambient': '384.12892', '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.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.r1.a1', '8.s1.a1', '8.y1.a1', '8.be1.a1', '8.bi1.a1', '8.bq1.a1'], 'contains': ['32.a1.a1', '32.x1.a1', '48.l1.a1'], 'core': '16.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7727, 8474, 2182, 2011, 3363, 8427, 1976, 2330], 'generators': [34, 192, 16, 128], 'label': '384.12892.16.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1.a1', 'normal_contained_in': ['8.d1.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: 53008397
{'ambient': '384.12892', '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.br1.a1', '8.bs1.a1', '8.bu1.a1'], 'contains': ['32.c1.a1', '32.t1.a1', '48.d1.a1'], 'core': '16.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2746, 2926, 8838, 6738, 6562, 3638, 7502, 7269], 'generators': [1, 24, 128, 16], 'label': '384.12892.16.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.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: 53008398
{'ambient': '384.12892', '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.br1.b1', '8.bs1.b1', '8.bu1.b1'], 'contains': ['32.c1.a1', '32.t1.b1', '48.d1.b1'], 'core': '16.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2746, 2926, 8755, 7721, 6562, 3638, 6971, 7013], 'generators': [193, 24, 128, 16], 'label': '384.12892.16.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.h1.b1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.c1.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: 53008399
{'ambient': '384.12892', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.bt1.a1', '8.bv1.a1', '8.bw1.a1'], 'contains': ['32.b1.a1', '32.y1.a1', '48.bi1.a1'], 'core': '16.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3291, 6432, 8290, 4372, 6963, 4328, 9369, 4400], 'generators': [35, 216, 16, 128], 'label': '384.12892.16.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.a1', 'normal_contained_in': ['8.j1.a1'], 'normal_contains': ['32.b1.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: 53008400
{'ambient': '384.12892', '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.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.bt1.b1', '8.bv1.b1', '8.bw1.b1'], 'contains': ['32.b1.a1', '32.y1.b1', '48.bi1.b1'], 'core': '16.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3291, 6432, 7823, 4547, 6963, 4328, 9226, 4150], 'generators': [227, 216, 16, 128], 'label': '384.12892.16.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.i1.b1', 'normal_contained_in': ['8.j1.a1'], 'normal_contains': ['32.b1.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: 53008401
{'ambient': '384.12892', '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.u1.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.d1.a1', '32.m1.a1', '32.t1.a1', '32.t1.b1', '48.e1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7373, -1, 3127, -1, 3966, -1, 4136, -1], 'generators': [1, 16, 192, 128], 'label': '384.12892.16.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.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'}
id: 53008402
{'ambient': '384.12892', 'aut_centralizer_order': 384, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '16.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.z1.a1', '8.ba1.a1', '8.bb1.a1', '8.bc1.a1', '8.bd1.a1', '8.be1.a1'], 'contains': ['32.a1.a1', '32.e1.a1', '32.n1.a1', '32.u1.a1', '48.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9349, -1, 660, -1, 658, -1, 765, -1], 'generators': [21, 16, 192, 128], 'label': '384.12892.16.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.k1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53008403
{'ambient': '384.12892', 'aut_centralizer_order': 384, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '16.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.z1.a1', '8.ba1.a1', '8.bf1.a1', '8.bg1.a1', '8.bh1.a1', '8.bi1.a1'], 'contains': ['32.a1.a1', '32.f1.a1', '32.o1.a1', '32.v1.a1', '48.g1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9244, -1, 377, -1, 905, -1, 647, -1], 'generators': [309, 16, 192, 128], 'label': '384.12892.16.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.l1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 53008404
{'ambient': '384.12892', 'aut_centralizer_order': 384, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '8.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.u1.a1', '8.v1.a1', '8.bj1.a1', '8.bo1.a1', '8.bp1.a1', '8.bq1.a1'], 'contains': ['32.a1.a1', '32.i1.a1', '48.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7480, -1, 2906, -1, 3844, -1, 2450, -1], 'generators': [97, 16, 128, 192], 'label': '384.12892.16.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.m1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 53008405
{'ambient': '384.12892', 'aut_centralizer_order': 128, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 256, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.t1.a1', '8.y1.a1', '8.bk1.a1', '8.bm1.a1', '8.bo1.a1', '8.bp1.a1'], 'contains': ['32.a1.a1', '32.y1.a1', '32.y1.b1', '48.m1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6985, -1, 3296, -1, 4090, -1, 4808, -1], 'generators': [35, 192, 16, 128], 'label': '384.12892.16.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.n1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}

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.