LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-09-20T18:42:42.334145

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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [6, 4, 4], 'aut_gens': [[1, 2, 8, 16, 32], [5, 120, 92, 16, 103], [25, 56, 92, 16, 22], [29, 40, 76, 16, 74]], 'aut_group': '6144.hl', 'aut_hash': 6634475629184585473, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 20, 'aut_perms': [795862742061059294, 1645422199001689800, 1054057601297046978], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 3, 2], [2, 4, 4, 1], [4, 8, 6, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.\\GL(2,\\mathbb{Z}/4)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '96.195', 'autcentquo_hash': 195, 'autcentquo_nilpotent': False, 'autcentquo_order': 96, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 4], [4, 8, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '32.27', 'commutator_count': 1, 'commutator_label': '16.14', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 761, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 4], [4, 8, 1, 6], [4, 8, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 112, 'exponent': 4, 'exponents_of_order': [7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '8.5', 'hash': 761, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2, 1, 4], 'inner_gens': [[1, 10, 8, 16, 108], [9, 2, 8, 16, 120], [1, 2, 8, 16, 48], [1, 2, 8, 16, 32], [77, 74, 24, 16, 32]], 'inner_hash': 27, 'inner_nilpotent': True, 'inner_order': 32, 'inner_split': False, 'inner_tex': 'C_2^2\\wr C_2', 'inner_used': [1, 2, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [4, 4]], 'label': '128.761', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^4:Q8', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 26, 'number_divisions': 23, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 233, 'number_subgroups': 648, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 31], [4, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 3, 2, 2], 'outer_gen_pows': [4, 68, 0, 0, 1, 0, 0], 'outer_gens': [[17, 6, 8, 16, 111], [73, 78, 24, 16, 56], [1, 78, 8, 16, 116], [17, 2, 8, 16, 32], [1, 111, 84, 16, 6], [1, 6, 8, 16, 112], [1, 6, 8, 16, 124]], 'outer_group': '192.1472', 'outer_hash': 1472, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 8, 'outer_perms': [120, 16, 1, 7, 840, 11520, 16680], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'D_4\\times S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 7]], 'representations': {'PC': {'code': 304611416202824932492386, 'gens': [1, 2, 4, 5, 6], 'pres': [7, 2, 2, 2, 2, 2, 2, 2, 141, 36, 4541, 2532, 523, 278, 124, 1973]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083311105, 1075676673, 2346386634, 2211644610, 30540864, 1087570945, 1075152385]}, 'Perm': {'d': 16, 'gens': [14002613452800, 8395940068432, 7, 2789792421136, 40279687, 5167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4:Q_8', 'transitive_degree': 16, '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: 43448078
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 761, 'group_order': 128, 'label': '1A', 'order': 1, 'powers': [1], 'representative': 0, 'size': 1}
id: 43448089
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 761, 'group_order': 128, 'label': '2A', 'order': 2, 'powers': [1], 'representative': 16, 'size': 1}
id: 43448097
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 761, 'group_order': 128, 'label': '2B', 'order': 2, 'powers': [1], 'representative': 28, 'size': 1}
id: 43448098
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 761, 'group_order': 128, 'label': '2C', 'order': 2, 'powers': [1], 'representative': 12, 'size': 1}
id: 43448099
{'aut_label': '2D', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 761, 'group_order': 128, 'label': '2D', 'order': 2, 'powers': [1], 'representative': 8, 'size': 2}
id: 43448100
{'aut_label': '2D', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 761, 'group_order': 128, 'label': '2E', 'order': 2, 'powers': [1], 'representative': 68, 'size': 2}
id: 43448101
{'aut_label': '2D', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 761, 'group_order': 128, 'label': '2F', 'order': 2, 'powers': [1], 'representative': 76, 'size': 2}
id: 43448102
{'aut_label': '2G', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 761, 'group_order': 128, 'label': '2G', 'order': 2, 'powers': [1], 'representative': 64, 'size': 2}
id: 43448103
{'aut_label': '2G', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 761, 'group_order': 128, 'label': '2H', 'order': 2, 'powers': [1], 'representative': 4, 'size': 2}
id: 43448079
{'aut_label': '2G', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 761, 'group_order': 128, 'label': '2I', 'order': 2, 'powers': [1], 'representative': 72, 'size': 2}
id: 43448080
{'aut_label': '2J', 'centralizer': '4.a1', 'counter': 11, 'group_counter': 761, 'group_order': 128, 'label': '2J', 'order': 2, 'powers': [1], 'representative': 1, 'size': 4}
id: 43448081
{'aut_label': '2J', 'centralizer': '4.a1', 'counter': 12, 'group_counter': 761, 'group_order': 128, 'label': '2K', 'order': 2, 'powers': [1], 'representative': 65, 'size': 4}
id: 43448082
{'aut_label': '2J', 'centralizer': '4.a1', 'counter': 13, 'group_counter': 761, 'group_order': 128, 'label': '2L', 'order': 2, 'powers': [1], 'representative': 17, 'size': 4}
id: 43448083
{'aut_label': '2J', 'centralizer': '4.a1', 'counter': 14, 'group_counter': 761, 'group_order': 128, 'label': '2M', 'order': 2, 'powers': [1], 'representative': 81, 'size': 4}
id: 43448084
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 15, 'group_counter': 761, 'group_order': 128, 'label': '4A', 'order': 4, 'powers': [3], 'representative': 34, 'size': 8}
id: 43448085
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 16, 'group_counter': 761, 'group_order': 128, 'label': '4B', 'order': 4, 'powers': [4], 'representative': 33, 'size': 8}
id: 43448086
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 17, 'group_counter': 761, 'group_order': 128, 'label': '4C', 'order': 4, 'powers': [4], 'representative': 3, 'size': 8}
id: 43448087
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 18, 'group_counter': 761, 'group_order': 128, 'label': '4D', 'order': 4, 'powers': [4], 'representative': 98, 'size': 8}
id: 43448088
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 19, 'group_counter': 761, 'group_order': 128, 'label': '4E', 'order': 4, 'powers': [3], 'representative': 41, 'size': 8}
id: 43448090
{'aut_label': '4A', 'centralizer': '8.a1', 'counter': 20, 'group_counter': 761, 'group_order': 128, 'label': '4F', 'order': 4, 'powers': [3], 'representative': 67, 'size': 8}
id: 43448091
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 21, 'group_counter': 761, 'group_order': 128, 'label': '4G1', 'order': 4, 'powers': [8], 'representative': 32, 'size': 8}
id: 43448092
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 22, 'group_counter': 761, 'group_order': 128, 'label': '4G-1', 'order': 4, 'powers': [8], 'representative': 96, 'size': 8}
id: 43448093
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 23, 'group_counter': 761, 'group_order': 128, 'label': '4H1', 'order': 4, 'powers': [9], 'representative': 2, 'size': 8}
id: 43448094
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 24, 'group_counter': 761, 'group_order': 128, 'label': '4H-1', 'order': 4, 'powers': [9], 'representative': 6, 'size': 8}
id: 43448095
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 25, 'group_counter': 761, 'group_order': 128, 'label': '4I1', 'order': 4, 'powers': [10], 'representative': 35, 'size': 8}
id: 43448096
{'aut_label': '4G1', 'centralizer': '8.f1', 'counter': 26, 'group_counter': 761, 'group_order': 128, 'label': '4I-1', 'order': 4, 'powers': [10], 'representative': 43, '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: 107207
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1a', '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], 'schur_index': 1}
id: 107218
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1b', '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], 'schur_index': 1}
id: 107223
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1c', '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], 'schur_index': 1}
id: 107224
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1d', '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], 'schur_index': 1}
id: 107225
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1e', '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], 'schur_index': 1}
id: 107226
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1f', '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], 'schur_index': 1}
id: 107227
{'cdim': 1, 'counter': 7, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1g', '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], 'schur_index': 1}
id: 107228
{'cdim': 1, 'counter': 8, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.1h', '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], 'schur_index': 1}
id: 107229
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107208
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107209
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107210
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, 2, -2, 2, -2, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107211
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2], 'schur_index': 1}
id: 107212
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2f', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2], 'schur_index': 1}
id: 107213
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2g', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 107214
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2h', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 2, 2, -2, -2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 107215
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2i', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107216
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2j', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -4, 4, 4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107217
{'cdim': 2, 'counter': 19, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.2k', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107219
{'cdim': 4, 'counter': 20, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.4a', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107220
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.4b', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107221
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.4c', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 107222
{'cdim': 4, 'counter': 23, 'faithful': False, 'group': '128.761', 'group_order': 128, 'image': None, 'label': '128.761.4d', 'multiplicity': 1, 'nt': [8, 29], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 2, -2, -2, 2, 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: 104036
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 128, 'label': '128.761.1a', '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]]]}
id: 104047
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 64, 'label': '128.761.1b', '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]]]}
id: 104055
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 64, 'label': '128.761.1c', '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]]]}
id: 104056
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 64, 'label': '128.761.1d', '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]]]}
id: 104057
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 64, 'label': '128.761.1e', '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]]]}
id: 104058
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 64, 'label': '128.761.1f', '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]]]}
id: 104059
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 64, 'label': '128.761.1g', '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]]]}
id: 104060
{'center': '1.a1', 'center_index': 1, 'center_order': 128, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 64, 'label': '128.761.1h', '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]]]}
id: 104061
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104037
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104038
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104039
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104040
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]]]}
id: 104041
{'center': '4.b1', 'center_index': 4, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 16, 'label': '128.761.2f', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]]]}
id: 104042
{'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.c1', 'kernel_order': 16, 'label': '128.761.2g', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104043
{'center': '4.a1', 'center_index': 4, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.c1', 'kernel_order': 16, 'label': '128.761.2h', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104044
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2i1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]]]}
id: 104045
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2i2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]]]}
id: 104046
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2j1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104048
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2j2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104049
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2k1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]]]}
id: 104050
{'center': '4.c1', 'center_index': 4, 'center_order': 32, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 8, 'label': '128.761.2k2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]]]}
id: 104051
{'center': '32.a1', 'center_index': 32, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 2, 'label': '128.761.4a', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104052
{'center': '32.a1', 'center_index': 32, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 2, 'label': '128.761.4b', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104053
{'center': '32.a1', 'center_index': 32, 'center_order': 4, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 2, 'label': '128.761.4c', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 104054
{'center': '32.a1', 'center_index': 32, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '128.761', 'group_counter': 761, 'group_order': 128, 'image': None, 'image_isoclass': '64.138', 'image_order': 64, 'indicator': 1, 'kernel': '64.b1', 'kernel_order': 2, 'label': '128.761.4d', 'nt': [8, 29], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 8208882
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 128, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '128.761.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.761', 'subgroup_hash': 761, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:Q_8', 'supersolvable': True, 'sylow': 2}
id: 8208893
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 64, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208904
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
id: 8208915
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.224', 'subgroup_hash': 224, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:Q_8', 'supersolvable': True, 'sylow': 0}
id: 8208926
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
id: 8208934
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208935
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208936
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208937
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
id: 8208883
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 16, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208884
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, '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': ['D', 'Phi', 'U1', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 8208885
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 8208886
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 8208887
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208888
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208889
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208890
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 8208891
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 8208892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208894
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
id: 8208895
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 8208896
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208897
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208898
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208899
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208900
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208901
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208902
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208903
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208905
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208906
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208907
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208908
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 8208909
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208910
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 8208911
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208912
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.16.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 8208913
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.27', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'S', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208914
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.29', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 29, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208916
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '128.761.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.31', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2:C_2', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208917
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208918
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208919
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208920
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.761.32.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 8208921
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208922
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208923
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.i2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.i2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208924
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208925
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '128.761.32.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 8208927
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.761.32.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 8208928
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 2, 'counter': 51, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.761.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.74', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 74, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:Q_8', 'simple': True, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 8208929
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '128.761.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\wr C_2^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 8208930
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.761.64.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 8208931
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.761.64.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 8208932
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '128.761.64.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 8208933
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '128.761', 'ambient_counter': 761, 'ambient_order': 128, 'ambient_tex': 'C_2^4:Q_8', 'central': True, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 1, 'counter': 56, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '128.761.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '128.761', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 761, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'L3', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 8208882
{'ambient': '128.761', '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': '32.a1', 'complements': ['128.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3272, 3900, 3323, 4068], 'generators': [1, 2, 32], 'label': '128.761.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
id: 8208883
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '8.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.e1', '16.j1'], 'core': '8.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2554, 2592, 2598, 2705], 'generators': [3, 8, 16], 'label': '128.761.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '32.27', 'quotient_action_image': '8.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 8208884
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 28, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.b1', '16.c1', '16.l1'], 'core': '8.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5669, 5949, 5767, 6205], 'generators': [76, 8, 64, 16], 'label': '128.761.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208885
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '4.a1', 'complements': ['16.m1'], 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['16.c1', '16.f1', '16.o1'], 'core': '8.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8616, 8323, 8765, 8659], 'generators': [1, 76, 8, 16], 'label': '128.761.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '64.74', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208886
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '4.d1'], 'contains': ['16.a1', '16.d1', '16.f1', '16.g1', '16.i1', '16.i2'], 'core': '16.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7093, -1, 7216, -1], 'generators': [1, 12, 8, 16], 'label': '128.761.8.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.d1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208887
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '4.e1'], 'contains': ['16.a1', '16.e1'], 'core': '16.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1718, -1, 1748, -1], 'generators': [3, 72], 'label': '128.761.8.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.e1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 8208888
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '8.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '4.d1'], 'contains': ['16.a1', '16.h1', '16.k1'], 'core': '16.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4226, -1, 4299, -1], 'generators': [35, 12, 16], 'label': '128.761.8.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.f1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208889
{'ambient': '128.761', 'aut_centralizer_order': 16, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.e1'], 'contains': ['16.e1'], 'core': '32.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1081, -1, 1099, -1], 'generators': [33, 34], 'label': '128.761.8.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.g1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 8208890
{'ambient': '128.761', 'aut_centralizer_order': 16, 'aut_label': '8.g2', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '96.227', 'aut_weyl_index': 64, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1'], 'contains': ['16.e1', '16.m1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [369, -1, 375, -1], 'generators': [121, 34, 16], 'label': '128.761.8.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.g2', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g2', 'subgroup_fusion': None, 'weyl_group': '16.14'}
id: 8208891
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1'], 'contains': ['16.b1', '16.f1', '16.g1', '16.n1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7601, -1, 7732, -1], 'generators': [1, 76, 72, 16], 'label': '128.761.8.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.h1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208892
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1'], 'contains': ['16.b1', '16.h1'], 'core': '16.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5062, -1, 5149, -1], 'generators': [35, 76], 'label': '128.761.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.i1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 8208893
{'ambient': '128.761', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '512.6344809', 'aut_weyl_index': 12, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4066, 6689, 4129, 6977], 'generators': [1, 2, 64], 'label': '128.761.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 8208894
{'ambient': '128.761', 'aut_centralizer_order': 8, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['4.d1'], 'contains': ['16.i1', '16.j1', '16.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [3390, -1, 3449, -1], 'generators': [77, 78], 'label': '128.761.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '8.j1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208895
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['16.i1', '16.i2', '16.l1', '16.n1', '16.o1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [8109, -1, 8249, -1], 'generators': [1, 76, 8, 80], 'label': '128.761.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '8.k1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208896
{'ambient': '128.761', 'aut_centralizer_order': 512, 'aut_label': '16.a1', 'aut_quo_index': 4, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '8.b1', '8.d1', '8.e1', '8.f1'], 'contains': ['32.a1', '32.b1', '32.c1', '32.e1'], 'core': '16.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4554, 4161, 4633, 4341], 'generators': [12, 8, 16], 'label': '128.761.16.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1'], 'normal_contains': ['32.a1', '32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208897
{'ambient': '128.761', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.b1', '8.h1', '8.i1'], 'contains': ['32.b1', '32.c1', '32.h1'], 'core': '16.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5062, 5949, 5149, 6205], 'generators': [76, 72, 16], 'label': '128.761.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.b1'], 'normal_contains': ['32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '64.74', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208898
{'ambient': '128.761', 'aut_centralizer_order': 256, 'aut_label': '16.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1', '8.c1'], 'contains': ['32.b1', '32.j1'], 'core': '16.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6078, 7735, 6183, 8068], 'generators': [76, 8, 16], 'label': '128.761.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.c1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '64.74', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208899
{'ambient': '128.761', 'aut_centralizer_order': 192, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1'], 'contains': ['32.a1', '32.d1', '32.f1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6586, -1, 6699, -1], 'generators': [1, 12, 16], 'label': '128.761.16.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.d1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208900
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.e1', '8.g1', '8.g2'], 'contains': ['32.a1', '32.g1'], 'core': '32.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1353, -1, 1376, -1], 'generators': [3, 16], 'label': '128.761.16.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.e1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208901
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '8.d1', '8.h1'], 'contains': ['32.b1', '32.d1', '32.i1', '32.i2'], 'core': '32.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8616, -1, 8765, -1], 'generators': [1, 76, 16], 'label': '128.761.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.f1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208902
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.d1', '8.h1'], 'contains': ['32.c1', '32.d1', '32.k1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7093, -1, 7216, -1], 'generators': [1, 4, 16], 'label': '128.761.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.g1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208903
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '8.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.f1', '8.i1'], 'contains': ['32.c1', '32.l1'], 'core': '32.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [3879, -1, 3946, -1], 'generators': [35, 16], 'label': '128.761.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '16.h1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208904
{'ambient': '128.761', 'aut_centralizer_order': 4, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '512.418986', 'aut_weyl_index': 12, 'centralizer': '32.a1', 'complements': ['64.e1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3272, 3900, 3323, 4068], 'generators': [33, 2], 'label': '128.761.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
id: 8208905
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.d1', '8.j1', '8.k1'], 'contains': ['32.e1', '32.f1', '32.i1', '32.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7601, -1, 7732, -1], 'generators': [77, 12, 24], 'label': '128.761.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.i1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208906
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.i2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.d1', '8.k1'], 'contains': ['32.e1', '32.f1', '32.i2', '32.k1'], 'core': '64.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [8109, -1, 8249, -1], 'generators': [1, 12, 24], 'label': '128.761.16.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.i2', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208907
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.j1'], 'contains': ['32.e1', '32.g1'], 'core': '64.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [2196, -1, 2233, -1], 'generators': [3, 24], 'label': '128.761.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.j1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208908
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '8.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['8.f1', '8.j1'], 'contains': ['32.e1', '32.l1'], 'core': '64.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [3037, -1, 3090, -1], 'generators': [127, 68], 'label': '128.761.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1', 'old_label': '16.k1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208909
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.k1'], 'contains': ['32.e1', '32.h1', '32.j1'], 'core': '64.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [5570, -1, 5666, -1], 'generators': [76, 8, 80], 'label': '128.761.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.l1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208910
{'ambient': '128.761', 'aut_centralizer_order': 16, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.g2'], 'contains': ['32.g1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [542, -1, 551, -1], 'generators': [109, 110], 'label': '128.761.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.g2', 'old_label': '16.m1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208911
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.h1', '8.k1'], 'contains': ['32.h1', '32.i1', '32.i2', '32.k1'], 'core': '128.a1', 'coset_action_label': '16T347', 'count': 48, 'diagramx': [9123, -1, 9282, -1], 'generators': [1, 68, 80], 'label': '128.761.16.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.n1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208912
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '16.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '8.k1'], 'contains': ['32.i1', '32.i2', '32.j1'], 'core': '128.a1', 'coset_action_label': '16T333', 'count': 16, 'diagramx': [9631, -1, 9798, -1], 'generators': [1, 76, 24], 'label': '128.761.16.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '16.o1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208913
{'ambient': '128.761', 'aut_centralizer_order': 3072, 'aut_label': '32.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.d1', '16.e1'], 'contains': ['64.a1', '64.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4047, 3268, 4116, 3409], 'generators': [12, 16], 'label': '128.761.32.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1', '64.b1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '32.27', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.27', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208914
{'ambient': '128.761', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.f1'], 'contains': ['64.a1', '64.c1'], 'core': '32.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5570, 6842, 5666, 7136], 'generators': [76, 16], 'label': '128.761.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '64.74', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208915
{'ambient': '128.761', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1536.408633426', 'aut_weyl_index': 4, 'centralizer': '32.a1', 'complements': ['64.e1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.e1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2480, 1111, 2516, 1159], 'generators': [33, 34, 8, 64], 'label': '128.761.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '32.27', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
id: 8208916
{'ambient': '128.761', 'aut_centralizer_order': 1024, 'aut_label': '32.c1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.a1', '16.b1', '16.g1', '16.h1'], 'contains': ['64.a1', '64.d1'], 'core': '32.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4554, 5054, 4633, 5273], 'generators': [4, 16], 'label': '128.761.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.a1', '16.b1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '64.74', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208917
{'ambient': '128.761', 'aut_centralizer_order': 384, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.d1', '16.f1', '16.g1'], 'contains': ['64.a1', '64.e1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7601, -1, 7732, -1], 'generators': [1, 16], 'label': '128.761.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.d1', 'projective_image': '64.74', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208918
{'ambient': '128.761', 'aut_centralizer_order': 512, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '16.i1', '16.i2', '16.j1', '16.k1', '16.l1'], 'contains': ['64.b1', '64.c1', '64.d1'], 'core': '64.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5062, -1, 5149, -1], 'generators': [12, 24], 'label': '128.761.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.e1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208919
{'ambient': '128.761', 'aut_centralizer_order': 192, 'aut_label': '32.f1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '16.i1', '16.i2'], 'contains': ['64.b1', '64.e1'], 'core': '64.b1', 'coset_action_label': None, 'count': 16, 'diagramx': [7093, -1, 7216, -1], 'generators': [1, 12], 'label': '128.761.32.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.f1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208920
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '32.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.e1', '16.j1', '16.m1'], 'contains': ['64.b1'], 'core': '64.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [1774, -1, 1805, -1], 'generators': [3], 'label': '128.761.32.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1', 'old_label': '32.g1', 'projective_image': '64.138', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208921
{'ambient': '128.761', 'aut_centralizer_order': 256, 'aut_label': '32.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.b1', '16.l1', '16.n1'], 'contains': ['64.c1', '64.d1'], 'core': '128.a1', 'coset_action_label': '32T795', 'count': 12, 'diagramx': [6078, -1, 6183, -1], 'generators': [68, 80], 'label': '128.761.32.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.h1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208922
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '32.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.f1', '16.i1', '16.n1', '16.o1'], 'contains': ['64.c1', '64.e1'], 'core': '128.a1', 'coset_action_label': '32T758', 'count': 24, 'diagramx': [8616, -1, 8765, -1], 'generators': [1, 76], 'label': '128.761.32.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.i1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 8208923
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '32.i2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['16.f1', '16.i2', '16.n1', '16.o1'], 'contains': ['64.c1', '64.e1'], 'core': '128.a1', 'coset_action_label': '32T759', 'count': 24, 'diagramx': [9123, -1, 9282, -1], 'generators': [9, 76], 'label': '128.761.32.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.i2', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.i2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208924
{'ambient': '128.761', 'aut_centralizer_order': 256, 'aut_label': '32.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '16.l1', '16.o1'], 'contains': ['64.c1'], 'core': '128.a1', 'coset_action_label': '32T760', 'count': 4, 'diagramx': [6586, -1, 6699, -1], 'generators': [76, 24], 'label': '128.761.32.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.j1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208925
{'ambient': '128.761', 'aut_centralizer_order': 64, 'aut_label': '32.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.g1', '16.i1', '16.i2', '16.n1'], 'contains': ['64.d1', '64.e1'], 'core': '128.a1', 'coset_action_label': '32T794', 'count': 48, 'diagramx': [8109, -1, 8249, -1], 'generators': [1, 4], 'label': '128.761.32.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '32.k1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208926
{'ambient': '128.761', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 32, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '8.h1', '8.k1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7346, 8889, 7474, 9273], 'generators': [1, 76, 8, 16, 64], 'label': '128.761.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '32.27', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 8208927
{'ambient': '128.761', 'aut_centralizer_order': 128, 'aut_label': '32.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '8.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['16.h1', '16.k1'], 'contains': ['64.d1'], 'core': '128.a1', 'coset_action_label': '32T1551', 'count': 24, 'diagramx': [3569, -1, 3631, -1], 'generators': [111], 'label': '128.761.32.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.f1', 'old_label': '32.l1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208928
{'ambient': '128.761', 'aut_centralizer_order': 6144, 'aut_label': '64.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1'], 'contains': ['128.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5347, 4946, 5439, 5205], 'generators': [16], 'label': '128.761.64.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.74', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.74', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208929
{'ambient': '128.761', 'aut_centralizer_order': 3072, 'aut_label': '64.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '32.e1', '32.f1', '32.g1'], 'contains': ['128.a1'], 'core': '64.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4901, 3333, 4986, 3523], 'generators': [12], 'label': '128.761.64.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.a1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': '64.138', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.138', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208930
{'ambient': '128.761', 'aut_centralizer_order': 1024, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['32.b1', '32.e1', '32.h1', '32.i1', '32.i2', '32.j1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6238, -1, 6346, -1], 'generators': [76], 'label': '128.761.64.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.c1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208931
{'ambient': '128.761', 'aut_centralizer_order': 1024, 'aut_label': '64.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['32.c1', '32.e1', '32.h1', '32.k1', '32.l1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5792, -1, 5893, -1], 'generators': [4], 'label': '128.761.64.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '64.d1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208932
{'ambient': '128.761', 'aut_centralizer_order': 384, 'aut_label': '64.e1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '32.f1', '32.i1', '32.i2', '32.k1'], 'contains': ['128.a1'], 'core': '128.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [7854, -1, 7990, -1], 'generators': [1], 'label': '128.761.64.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '64.e1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208933
{'ambient': '128.761', 'aut_centralizer_order': None, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.b1', '64.c1', '64.d1', '64.e1'], 'contains': [], 'core': '128.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5792, 4139, 5893, 4341], 'generators': [], 'label': '128.761.128.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '128.a1', 'normal_contained_in': ['64.a1', '64.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '128.a1', 'projective_image': '128.761', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 8208934
{'ambient': '128.761', 'aut_centralizer_order': 16, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.e1'], 'core': '4.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2678, 1852, 2724, 1932], 'generators': [3, 8, 64], 'label': '128.761.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 8208935
{'ambient': '128.761', 'aut_centralizer_order': 16, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '16.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.b1', '8.f1', '8.i1'], 'core': '4.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5025, 5949, 5112, 6205], 'generators': [35, 76, 64], 'label': '128.761.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.b1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
id: 8208936
{'ambient': '128.761', 'aut_centralizer_order': 8, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '16.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.d1', '8.f1', '8.j1'], 'core': '8.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3861, -1, 3927, -1], 'generators': [1, 2, 16], 'label': '128.761.4.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.d1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 8208937
{'ambient': '128.761', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '32.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['2.c1'], 'contains': ['8.a1', '8.e1', '8.g1', '8.g2'], 'core': '8.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1718, -1, 1748, -1], 'generators': [33, 34, 8], 'label': '128.761.4.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '4.e1', 'projective_image': '32.27', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '16.14'}

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.