LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2026-09-22T11:08:47.761194

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [20, 4, 2], 'aut_gens': [[873460098142623179389602209644892650585571564852335, 383691507931091386758258565563740844961908370748160], [960905282869288884797521732780353381585780200703865, 645876609121925686719473288805375188095186504782529], [718944595352215069368417524179443946560110255947729, 881263432564956763403730670563312947243865183635904], [1048300395436943164069917074731095608143610245152775, 164021882476314236389125244727733696756166212322848]], 'aut_group': '960.10871', 'aut_hash': 10871, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 960, 'aut_permdeg': 40, 'aut_perms': [651484207202906980216756211559060320579762423006, 353775167343812031412650107009843352854852513094, 663658459281326222818834147010266121577253435560], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 20, 2, 1], [3, 20, 1, 1], [4, 30, 1, 2], [5, 24, 1, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 20, 4, 1], [8, 30, 4, 1], [10, 24, 1, 1], [10, 24, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.34', 'autcentquo_hash': 34, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 20, 2], [3, 20, 1], [4, 30, 2], [5, 24, 1], [6, 20, 7], [8, 30, 4], [10, 24, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '120.34', 'commutator_count': 1, 'commutator_label': '120.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '60.5'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 950, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['240.90', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 20, 1, 2], [3, 20, 1, 1], [4, 30, 1, 2], [5, 24, 1, 1], [6, 20, 1, 3], [6, 20, 2, 2], [8, 30, 2, 2], [10, 24, 1, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 57, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '240.189', 'hash': 950, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [3, 4], 'inner_gens': [[873460098142623179389602209644892650585571564852335, 1029251913462739648170227714034217169338081266330054], [705495111338243025415396094301641703980223705895465, 383691507931091386758258565563740844961908370748160]], 'inner_hash': 34, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'S_5', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [4, 10], [5, 4], [6, 6]], 'label': '480.950', 'linC_count': 12, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 4, 'linQ_dim': 9, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,5):C2^2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 24, 'number_divisions': 20, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 78, 'number_subgroups': 826, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 43], [3, 20], [4, 60], [5, 24], [6, 140], [8, 120], [10, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1186397458801114847900684359069942869305648233204687, 383691507931091386758258565563740844961908370748160], [1186397458801114847900684359069942869305648233204687, 826377542339693536611577113022497314854335057280849]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 6], [5, 4], [6, 2], [8, 2], [12, 2]], 'representations': {'Perm': {'d': 42, 'gens': [873460098142623179389602209644892650585571564852335, 383691507931091386758258565563740844961908370748160]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,5):C_2^2', 'transitive_degree': 80, '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: 105445189
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 950, 'group_order': 480, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
id: 105445200
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 950, 'group_order': 480, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 1, 'size': 1}
id: 105445206
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 950, 'group_order': 480, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 716792294760557442254470872548892758600862075419880, 'size': 1}
id: 105445207
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 950, 'group_order': 480, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 716792294760557442254470872548892758600862075419881, 'size': 1}
id: 105445208
{'aut_label': '2D', 'centralizer': '20.a1.a1', 'counter': 5, 'group_counter': 950, 'group_order': 480, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 12184121262635178935991840568944828090172486708110, 'size': 20}
id: 105445209
{'aut_label': '2D', 'centralizer': '20.a1.a1', 'counter': 6, 'group_counter': 950, 'group_order': 480, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 12184121262635178935991840568944828090172486708111, 'size': 20}
id: 105445210
{'aut_label': '3A', 'centralizer': '20.a1.a1', 'counter': 7, 'group_counter': 950, 'group_order': 480, 'label': '3A', 'order': 3, 'powers': [7, 1, 7], 'representative': 23201246737408819476459285156601496927581302337206, 'size': 20}
id: 105445211
{'aut_label': '4A', 'centralizer': '30.b1.a1', 'counter': 8, 'group_counter': 950, 'group_order': 480, 'label': '4A', 'order': 4, 'powers': [3, 8, 8], 'representative': 1301280964814827702693477468674371488369034554687464, 'size': 30}
id: 105445212
{'aut_label': '4B', 'centralizer': '30.b1.a1', 'counter': 9, 'group_counter': 950, 'group_order': 480, 'label': '4B', 'order': 4, 'powers': [3, 9, 9], 'representative': 547690105609458310110538198698055038333497179366705, 'size': 30}
id: 105445190
{'aut_label': '5A', 'centralizer': '24.a1.a1', 'counter': 10, 'group_counter': 950, 'group_order': 480, 'label': '5A', 'order': 5, 'powers': [10, 10, 1], 'representative': 298088457943006043464023388007340034115983134183264, 'size': 24}
id: 105445191
{'aut_label': '6A', 'centralizer': '20.a1.a1', 'counter': 11, 'group_counter': 950, 'group_order': 480, 'label': '6A', 'order': 6, 'powers': [7, 2, 11], 'representative': 18429333032579239268307109944456734508472692558871, 'size': 20}
id: 105445192
{'aut_label': '6B', 'centralizer': '20.a1.a1', 'counter': 12, 'group_counter': 950, 'group_order': 480, 'label': '6B', 'order': 6, 'powers': [7, 3, 12], 'representative': 80481273536896569201577763212366610699017433398230, 'size': 20}
id: 105445193
{'aut_label': '6A', 'centralizer': '20.a1.a1', 'counter': 13, 'group_counter': 950, 'group_order': 480, 'label': '6C', 'order': 6, 'powers': [7, 4, 13], 'representative': 80481273536896569201577763212366610699017433398231, 'size': 20}
id: 105445194
{'aut_label': '6D1', 'centralizer': '20.a1.a1', 'counter': 14, 'group_counter': 950, 'group_order': 480, 'label': '6D1', 'order': 6, 'powers': [7, 5, 15], 'representative': 9038028577059994829968420251182292617578620151968, 'size': 20}
id: 105445195
{'aut_label': '6D1', 'centralizer': '20.a1.a1', 'counter': 15, 'group_counter': 950, 'group_order': 480, 'label': '6D-1', 'order': 6, 'powers': [7, 5, 14], 'representative': 25453432998748066547911754896207636970822745025104, 'size': 20}
id: 105445196
{'aut_label': '6D1', 'centralizer': '20.a1.a1', 'counter': 16, 'group_counter': 950, 'group_order': 480, 'label': '6E1', 'order': 6, 'powers': [7, 6, 17], 'representative': 9038028577059994829968420251182292617578620151969, 'size': 20}
id: 105445197
{'aut_label': '6D1', 'centralizer': '20.a1.a1', 'counter': 17, 'group_counter': 950, 'group_order': 480, 'label': '6E-1', 'order': 6, 'powers': [7, 6, 16], 'representative': 25453432998748066547911754896207636970822745025105, 'size': 20}
id: 105445198
{'aut_label': '8A1', 'centralizer': '30.b1.a1', 'counter': 18, 'group_counter': 950, 'group_order': 480, 'label': '8A1', 'order': 8, 'powers': [8, 18, 19], 'representative': 858049745959147796665790358097988220184566718729200, 'size': 30}
id: 105445199
{'aut_label': '8A1', 'centralizer': '30.b1.a1', 'counter': 19, 'group_counter': 950, 'group_order': 480, 'label': '8A-1', 'order': 8, 'powers': [8, 19, 18], 'representative': 628882806634392034767218356114330898957643233358870, 'size': 30}
id: 105445201
{'aut_label': '8A1', 'centralizer': '30.b1.a1', 'counter': 20, 'group_counter': 950, 'group_order': 480, 'label': '8B1', 'order': 8, 'powers': [8, 20, 21], 'representative': 171446884758745307545816759124044753500869933412511, 'size': 30}
id: 105445202
{'aut_label': '8A1', 'centralizer': '30.b1.a1', 'counter': 21, 'group_counter': 950, 'group_order': 480, 'label': '8B-1', 'order': 8, 'powers': [8, 21, 20], 'representative': 979666301168786737757751678378819022174204589983465, 'size': 30}
id: 105445203
{'aut_label': '10A', 'centralizer': '24.a1.a1', 'counter': 22, 'group_counter': 950, 'group_order': 480, 'label': '10A', 'order': 10, 'powers': [10, 22, 2], 'representative': 674465925891770207874026031506164562469562625460985, 'size': 24}
id: 105445204
{'aut_label': '10B', 'centralizer': '24.a1.a1', 'counter': 23, 'group_counter': 950, 'group_order': 480, 'label': '10B', 'order': 10, 'powers': [10, 23, 3], 'representative': 409695761216731000010918662431309469578341186401200, 'size': 24}
id: 105445205
{'aut_label': '10A', 'centralizer': '24.a1.a1', 'counter': 24, 'group_counter': 950, 'group_order': 480, 'label': '10C', 'order': 10, 'powers': [10, 24, 4], 'representative': 669482846146094732738897464760208425350473332724895, 'size': 24}

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: 3440212
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.1a', '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], 'schur_index': 1}
id: 3440223
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.1b', '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], 'schur_index': 1}
id: 3440225
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.1c', '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], 'schur_index': 1}
id: 3440226
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.1d', '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], 'schur_index': 1}
id: 3440227
{'cdim': 4, 'counter': 5, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4a', 'multiplicity': 1, 'nt': [5, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 2, 2, 1, 0, 0, -1, -1, -1, -1, 1, -1, 1, 1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
id: 3440228
{'cdim': 4, 'counter': 6, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4b', 'multiplicity': 1, 'nt': [10, 12], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, 1, 0, 0, -1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
id: 3440229
{'cdim': 4, 'counter': 7, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4c', 'multiplicity': 1, 'nt': [10, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, 2, 1, 0, 0, -1, -1, 1, 1, -1, -1, 1, -1, 0, 0, 0, 0, 1, -1, 1], 'schur_index': 1}
id: 3440230
{'cdim': 4, 'counter': 8, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4d', 'multiplicity': 1, 'nt': [10, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 2, -2, 1, 0, 0, -1, 1, -1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 1, -1, 1], 'schur_index': 1}
id: 3440231
{'cdim': 4, 'counter': 9, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4e', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, -2, 0, 0, -1, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0, 0, 1, 1, -1], 'schur_index': 2}
id: 3440213
{'cdim': 4, 'counter': 10, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4f', 'multiplicity': 1, 'nt': [120, 0], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -2, 0, 0, -1, 0, 0, 0, 2, 0, 2, -2, 0, 0, 0, 0, -1, 1, 1], 'schur_index': 2}
id: 3440216
{'cdim': 5, 'counter': 13, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.5a', 'multiplicity': 1, 'nt': [6, 14], 'qdim': 5, 'qvalues': [5, 5, 5, 5, -1, -1, -1, 1, 1, 0, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 3440217
{'cdim': 5, 'counter': 14, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.5b', 'multiplicity': 1, 'nt': [10, 13], 'qdim': 5, 'qvalues': [5, 5, 5, 5, 1, 1, -1, 1, 1, 0, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 3440218
{'cdim': 5, 'counter': 15, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.5c', 'multiplicity': 1, 'nt': [12, 123], 'qdim': 5, 'qvalues': [5, -5, 5, -5, -1, 1, -1, 1, -1, 0, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
id: 3440219
{'cdim': 5, 'counter': 16, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.5d', 'multiplicity': 1, 'nt': [12, 123], 'qdim': 5, 'qvalues': [5, -5, 5, -5, 1, -1, -1, 1, -1, 0, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
id: 3440220
{'cdim': 6, 'counter': 17, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.6a', 'multiplicity': 1, 'nt': [20, 30], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, 0, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
id: 3440221
{'cdim': 6, 'counter': 18, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.6b', 'multiplicity': 1, 'nt': [20, 65], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 0, 0, 0, -2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, -1], 'schur_index': 1}
id: 3440214
{'cdim': 4, 'counter': 11, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4g', 'multiplicity': 2, 'nt': [40, 172], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, 0, -2, -2, 0, 0, 0, 0, 2, 2, -2], 'schur_index': 1}
id: 3440215
{'cdim': 4, 'counter': 12, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.4h', 'multiplicity': 2, 'nt': [40, 172], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 2, 0, 0, -2, 0, 0, 0, -2, 0, -2, 2, 0, 0, 0, 0, -2, 2, 2], 'schur_index': 1}
id: 3440222
{'cdim': 6, 'counter': 19, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.6c', 'multiplicity': 2, 'nt': [40, 172], 'qdim': 12, 'qvalues': [12, -12, -12, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2], 'schur_index': 1}
id: 3440224
{'cdim': 6, 'counter': 20, 'faithful': False, 'group': '480.950', 'group_order': 480, 'image': None, 'label': '480.950.6d', 'multiplicity': 2, 'nt': [40, 172], 'qdim': 12, 'qvalues': [12, 12, -12, -12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2], '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: 4851287
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 480, 'label': '480.950.1a', '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]]]}
id: 4851298
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 240, 'label': '480.950.1b', '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]]]}
id: 4851304
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 240, 'label': '480.950.1c', '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]]]}
id: 4851305
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 480, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 240, 'label': '480.950.1d', '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]]]}
id: 4851306
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 5, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.950.4a', 'nt': [5, 5], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 4851307
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 6, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.950.4b', 'nt': [10, 12], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 4851308
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 7, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.189', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 2, 'label': '480.950.4c', 'nt': [10, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 4851309
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 8, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.189', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 2, 'label': '480.950.4d', 'nt': [10, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
id: 4851310
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 9, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': -1, 'kernel': '240.a1.b1', 'kernel_order': 2, 'label': '480.950.4e', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
id: 4851288
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 10, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': -1, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.950.4f', 'nt': [120, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 4851289
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 11, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 2, 'label': '480.950.4g1', 'nt': [40, 172], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
id: 4851290
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 12, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 2, 'label': '480.950.4g2', 'nt': [40, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
id: 4851291
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 13, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.950.4h1', 'nt': [40, 172], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 4851292
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 14, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.950.4h2', 'nt': [40, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
id: 4851293
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 15, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.950.5a', 'nt': [6, 14], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 4851294
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 16, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.950.5b', 'nt': [10, 13], 'q_character': None, 'values': [[[5, 0]], [[5, 0]], [[5, 0]], [[5, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 4851295
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 17, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.189', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 2, 'label': '480.950.5c', 'nt': [12, 123], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 4851296
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 18, 'cyclotomic_n': 1, 'dim': 5, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.189', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 2, 'label': '480.950.5d', 'nt': [12, 123], 'q_character': None, 'values': [[[5, 0]], [[-5, 0]], [[5, 0]], [[-5, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 4851297
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '120.34', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 4, 'label': '480.950.6a', 'nt': [20, 30], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 4851299
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.189', 'image_order': 240, 'indicator': 1, 'kernel': '240.b1.a1', 'kernel_order': 2, 'label': '480.950.6b', 'nt': [20, 65], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
id: 4851300
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 21, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 2, 'label': '480.950.6c1', 'nt': [40, 172], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
id: 4851301
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 22, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.b1', 'kernel_order': 2, 'label': '480.950.6c2', 'nt': [40, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
id: 4851302
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 23, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.950.6d1', 'nt': [40, 172], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 4851303
{'center': '120.a1.a1', 'center_index': 120, 'center_order': 4, 'counter': 24, 'cyclotomic_n': 8, 'dim': 6, 'faithful': False, 'field': [2, 0, 1], 'group': '480.950', 'group_counter': 950, 'group_order': 480, 'image': None, 'image_isoclass': '240.90', 'image_order': 240, 'indicator': 0, 'kernel': '240.a1.a1', 'kernel_order': 2, 'label': '480.950.6d2', 'nt': [40, 2], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[1, 0]], [[-1, 0]], [[-1, 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: 58655574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 480, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '480.950.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.950', 'subgroup_hash': 950, 'subgroup_order': 480, 'subgroup_tex': '\\SL(2,5):C_2^2', 'supersolvable': False, 'sylow': 0}
id: 58655585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 240, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.950.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.94', 'subgroup_hash': 94, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times \\SL(2,5)', 'supersolvable': False, 'sylow': 0}
id: 58655596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 240, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '480.950.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.90', 'subgroup_hash': 90, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
id: 58655607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 240, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '480.950.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.90', 'subgroup_hash': 90, 'subgroup_order': 240, 'subgroup_tex': '\\SL(2,5):C_2', 'supersolvable': False, 'sylow': 0}
id: 58655618
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 120, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.950.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': True, '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': False, 'special_labels': ['D', 'PC', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '120.5', 'subgroup_hash': 5, 'subgroup_order': 120, 'subgroup_tex': '\\SL(2,5)', 'supersolvable': False, 'sylow': 0}
id: 58655629
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '480.950.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.189', 'subgroup_hash': 189, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times \\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 58655640
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.6.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.32', 'subgroup_hash': 32, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:C_8', 'supersolvable': True, 'sylow': 0}
id: 58655650
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.10.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
id: 58655651
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.32', 'subgroup_hash': 32, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times \\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 58655575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 58655576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.10.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.29', 'subgroup_hash': 29, 'subgroup_order': 48, 'subgroup_tex': '\\GL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 58655577
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655578
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.3', 'subgroup_hash': 3, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
id: 58655579
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.3', 'subgroup_hash': 3, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
id: 58655580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '480.950.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, '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': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 2}
id: 58655581
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655582
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
id: 58655583
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 58655586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 58655587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 58655588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
id: 58655589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.3', 'subgroup_hash': 3, 'subgroup_order': 24, 'subgroup_tex': '\\SL(2,3)', 'supersolvable': False, 'sylow': 0}
id: 58655590
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 58655591
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655592
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
id: 58655594
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 58655595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, '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: 58655597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 58655598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 58655599
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 58655600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.30.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '30.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
id: 58655601
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655602
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655603
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 58655604
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 58655605
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655606
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655608
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
id: 58655609
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 58655610
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
id: 58655611
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655612
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
id: 58655613
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 58655614
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 58655615
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 58655616
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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: 58655617
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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: 58655619
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 58655620
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 58655621
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
id: 58655622
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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: 58655623
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 58655624
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.60.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 58655625
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, '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: 58655626
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 58655627
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.80.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 58655628
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 58655630
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 58655631
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.80.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
id: 58655632
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 58655633
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.80.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
id: 58655634
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '480.950.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, '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': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 58655635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '480.950.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_5', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'S', 'U0', 'C2'], '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: 58655636
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.120.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655639
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '480.950.120.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655641
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655642
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, '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: 58655643
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '480.950.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
id: 58655644
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '480.950.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.90', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 90, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 58655645
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '480.950.240.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.90', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 90, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2', 'simple': True, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 58655646
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 2, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '480.950.240.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.189', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 189, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_5', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], '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: 58655647
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.240.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, '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: 58655648
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '480.950.240.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '240.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 240, '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: 58655649
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '480.950', 'ambient_counter': 950, 'ambient_order': 480, 'ambient_tex': '\\SL(2,5):C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 1, 'counter': 78, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '480.950.480.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '480.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '480.950', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 950, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\SL(2,5):C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C4'], '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: 58655574
{'ambient': '480.950', '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': '120.a1.a1', 'complements': ['480.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '5.a1.a1', '6.a1.a1', '10.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4997, 6273, 6584, 4194, 4426, 4237, 4965, 3918], 'generators': [235651537567254845405764561743860186231063668263865, 1, 956585943079938762807472150995146934072166698245521, 716792294760557442254470872548892758600862075419881], 'label': '480.950.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 58655575
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 20, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.f1.a1', '30.e1.a1', '40.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4413, -1, 5883, -1, 5914, -1, 5424, -1], 'generators': [292557596686905534223201606408708978150060523223054, 480866617086047616678182767008641048689239693846000, 1127264949751373683958359644629655238862694430761408, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 58655576
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '48.48', 'aut_weyl_index': 20, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.f1.a1', '30.e1.b1', '40.e1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4413, -1, 6875, -1, 5914, -1, 5931, -1], 'generators': [480866617086047616678182767008641048689239693846000, 1010981736211329344691992626021944897949607341472881, 1127264949751373683958359644629655238862694430761408, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.10.c1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 58655577
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '60.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8339, -1, 8412, -1, 418, -1, 300, -1], 'generators': [442999200286521059294786354848256530527962572807008, 789153521835325048590367505500094269122332526016704, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.12.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655578
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '60.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9059, -1, 8888, -1, 1221, -1, 876, -1], 'generators': [716792294760557442254470872548892758600862075419880, 911039014768093878868092056576607333259874866188654, 1021834788607556582837829297498268518260702261709024, 1116919375541533841997677361283935615376955132575950], 'label': '480.950.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655579
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '6.a1.a1'], 'contains': ['24.b1.a1', '60.f1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9059, -1, 9291, -1, 1221, -1, 1355, -1], 'generators': [716792294760557442254470872548892758600862075419880, 911039014768093878868092056576607333259874866188654, 269961270339745678442940314921078626793246537529985, 1116919375541533841997677361283935615376955132575950], 'label': '480.950.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.b1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655580
{'ambient': '480.950', 'aut_centralizer_order': 1, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '64.226', 'aut_weyl_index': 15, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.c1.a1', '30.d1.a1', '30.d1.b1', '30.e1.a1', '30.e1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6824, -1, 7280, -1, 3657, -1, 3410, -1], 'generators': [292557596686905534223201606408708978150060523223054, 480866617086047616678182767008641048689239693846000, 385147547852846740609771464011774573041418289458526, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655581
{'ambient': '480.950', 'aut_centralizer_order': 6, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['40.a1.a1', '40.a1.b1', '40.c1.a1', '40.d1.a1', '40.d1.b1', '60.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [786, -1, 1525, -1, 9590, -1, 9046, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1, 542315455125022342332476192707293981307824410806368, 716792294760557442254470872548892758600862075419881], 'label': '480.950.20.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655582
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id: 58655583
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '24.14', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.f1.a1', '40.g1.a1', '60.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [4530, -1, 5496, -1, 6346, -1, 5823, -1], 'generators': [1046450592059321610886933944173651861850951517107169, 431555331418158156369713230910311172789922481136886, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655584
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '10.a1.a1'], 'contains': ['40.d1.a1', '40.e1.a1', '40.f1.a1', '60.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3201, -1, 4504, -1, 7497, -1, 6649, -1], 'generators': [748616464605151307937313748912851594821171432265920, 292557596686905534223201606408708978150060523223054, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.d1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655585
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '240.189', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['240.c1.b1', '240.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.b1.a1', '12.a1.a1', '20.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5818, 7960, 6791, 8300, 3511, 6899, 4075, 7753], 'generators': [895279187594821988880112138954456167147316150631904, 693047798377598605388492537248532577724994302008865, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '120.34', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 58655586
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '10.a1.a1'], 'contains': ['40.d1.b1', '40.e1.b1', '40.f1.a1', '60.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3201, -1, 5064, -1, 7497, -1, 7019, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 95465631605261042941128131848255151193898657249945, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.20.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.d1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655587
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['40.d1.a1', '40.e1.b1', '40.g1.a1', '60.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2738, -1, 3801, -1, 8013, -1, 7760, -1], 'generators': [292557596686905534223201606408708978150060523223054, 95465631605261042941128131848255151193898657249945, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.20.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655588
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '24.14', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1'], 'contains': ['40.d1.b1', '40.e1.a1', '40.g1.a1', '60.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2738, -1, 3422, -1, 8013, -1, 7390, -1], 'generators': [748616464605151307937313748912851594821171432265920, 1010981736211329344691992626021944897949607341472881, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.20.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '20.e1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655589
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.b1.a1', '10.c1.a1', '10.c1.b1'], 'contains': ['60.g1.a1', '80.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5164, -1, 6295, -1, 4864, -1, 4759, -1], 'generators': [716792294760557442254470872548892758600862075419880, 1024624528931577947488565935571604392720219037958566, 50171025853727777429212403812529356424413085704470, 510198799479422222947367341336538420861781254482824], 'label': '480.950.20.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.f1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 58655590
{'ambient': '480.950', 'aut_centralizer_order': 20, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.2', 'aut_weyl_index': 120, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.a1.a1', '48.a1.b1', '48.b1.a1', '120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8334, -1, 8063, -1, 968, -1, 1263, -1], 'generators': [442999200286521059294786354848256530527962572807008, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.24.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 58655591
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '20.3', 'aut_weyl_index': 48, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1'], 'contains': ['48.b1.a1', '120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9633, -1, 9783, -1, 2203, -1, 2149, -1], 'generators': [442999200286521059294786354848256530527962572807008, 716792294760557442254470872548892758600862075419880, 789153521835325048590367505500094269122332526016704], 'label': '480.950.24.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655592
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '40.12', 'aut_weyl_index': 24, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1'], 'contains': ['48.b1.a1', '120.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8979, -1, 9478, -1, 1687, -1, 1778, -1], 'generators': [442999200286521059294786354848256530527962572807008, 716792294760557442254470872548892758600862075419880, 122969256638068636595909372092418946468336196362487], 'label': '480.950.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655593
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '32.49', 'aut_weyl_index': 30, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.c1.a1', '60.c1.b1', '60.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4499, -1, 5106, -1, 5492, -1, 5210, -1], 'generators': [292557596686905534223201606408708978150060523223054, 385147547852846740609771464011774573041418289458526, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655594
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.f1.a1', '60.f1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8208, -1, 8139, -1, 2153, -1, 2024, -1], 'generators': [385147547852846740609771464011774573041418289458526, 1, 925510243291654117890086777403221121612568996985809, 716792294760557442254470872548892758600862075419881], 'label': '480.950.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655595
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id: 58655596
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '240.189', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['240.a1.a1', '240.a1.b1', '240.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.c1.a1', '12.b1.a1', '20.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4997, 1854, 6119, 4194, 4426, 1607, 4731, 3918], 'generators': [846028547347866553381280831496145422308962616745168, 1118012910674999646975210150207547183937260824474960, 716792294760557442254470872548892758600862075419880], 'label': '480.950.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '240.189', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 58655597
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.c1.a1', '60.e1.a1', '60.f1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6049, -1, 6964, -1, 2809, -1, 2495, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1268673416966049349475834941699208169680221764659065, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.30.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.d1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655598
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1'], 'contains': ['60.c1.b1', '60.e1.a1', '60.f1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6049, -1, 6637, -1, 2809, -1, 2890, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 1268673416966049349475834941699208169680221764659065, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.30.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.d1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655599
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '60.f1.a1', '60.g1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7620, -1, 7750, -1, 4134, -1, 3841, -1], 'generators': [292557596686905534223201606408708978150060523223054, 480866617086047616678182767008641048689239693846000, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.30.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655600
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '16.11', 'aut_weyl_index': 60, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.b1', '15.a1.a1'], 'contains': ['60.c1.b1', '60.f1.b1', '60.g1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7620, -1, 8782, -1, 4134, -1, 4236, -1], 'generators': [480866617086047616678182767008641048689239693846000, 1010981736211329344691992626021944897949607341472881, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.30.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.e1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655601
{'ambient': '480.950', 'aut_centralizer_order': 6, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1'], 'contains': ['80.a1.a1', '80.c1.a1', '80.c1.b1', '120.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [297, -1, 196, -1, 9669, -1, 9762, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1, 542315455125022342332476192707293981307824410806368], 'label': '480.950.40.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655602
{'ambient': '480.950', 'aut_centralizer_order': 6, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1'], 'contains': ['80.a1.b1', '80.c1.a1', '80.c1.b1', '120.b1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 20, 'diagramx': [297, -1, 649, -1, 9669, -1, 9215, -1], 'generators': [292557596686905534223201606408708978150060523223054, 542315455125022342332476192707293981307824410806368, 716792294760557442254470872548892758600862075419881], 'label': '480.950.40.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '40.a1.b1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655603
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.a1', '80.d1.a1', '80.d1.b1', '120.b1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [820, -1, 1182, -1, 9085, -1, 8795, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1127264949751373683958359644629655238862694430761408, 1], 'label': '480.950.40.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.b1.a1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 58655604
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1'], 'contains': ['80.a1.b1', '80.d1.a1', '80.d1.b1', '120.b1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 20, 'diagramx': [820, -1, 1688, -1, 9085, -1, 8505, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1127264949751373683958359644629655238862694430761408, 716792294760557442254470872548892758600862075419881], 'label': '480.950.40.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '40.b1.b1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 58655605
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '80.a1.b1', '80.b1.a1', '120.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2390, -1, 3465, -1, 6873, -1, 6081, -1], 'generators': [1024624528931577947488565935571604392720219037958566, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.40.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655606
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.d1.a1', '20.e1.a1'], 'contains': ['80.b1.a1', '80.c1.a1', '120.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1344, -1, 2320, -1, 8501, -1, 6918, -1], 'generators': [292557596686905534223201606408708978150060523223054, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655607
{'ambient': '480.950', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '240.189', 'aut_weyl_index': 4, 'centralizer': '120.a1.a1', 'complements': ['240.c1.a1', '240.a1.a1', '240.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '10.c1.b1', '12.b1.b1', '20.d1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4997, 1854, 7334, 1247, 4426, 1607, 5203, 1165], 'generators': [716792294760557442254470872548892758600862075419880, 235651537567254845405764561743860186231063668263865, 956585943079938762807472150995146934072166698245521], 'label': '480.950.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '240.189', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 58655608
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.d1.b1', '20.e1.b1'], 'contains': ['80.b1.a1', '80.c1.b1', '120.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1344, -1, 3012, -1, 8501, -1, 8087, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 716792294760557442254470872548892758600862075419880, 542315455125022342332476192707293981307824410806368], 'label': '480.950.40.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.d1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655609
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '20.b1.a1', '20.d1.a1', '20.e1.b1'], 'contains': ['80.b1.a1', '80.d1.a1', '120.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1867, -1, 2666, -1, 7457, -1, 6500, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1127264949751373683958359644629655238862694430761408, 716792294760557442254470872548892758600862075419880], 'label': '480.950.40.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.e1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655610
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.b1', '20.b1.a1', '20.d1.b1', '20.e1.a1'], 'contains': ['80.b1.a1', '80.d1.b1', '120.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1867, -1, 4064, -1, 7457, -1, 7338, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 1127264949751373683958359644629655238862694430761408, 716792294760557442254470872548892758600862075419880], 'label': '480.950.40.e1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.e1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655611
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '20.c1.a1', '20.d1.a1', '20.d1.b1'], 'contains': ['80.b1.a1', '120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [5148, -1, 5802, -1, 5313, -1, 4961, -1], 'generators': [319892353530926604445456947054085882197166029582750, 716792294760557442254470872548892758600862075419880, 431555331418158156369713230910311172789922481136886], 'label': '480.950.40.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.f1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655612
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '12.4', 'aut_weyl_index': 80, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '20.e1.a1', '20.e1.b1'], 'contains': ['80.b1.a1', '120.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3538, -1, 4337, -1, 5830, -1, 5331, -1], 'generators': [445780718056637058871576836454153707102382862816401, 319892353530926604445456947054085882197166029582750, 716792294760557442254470872548892758600862075419880], 'label': '480.950.40.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '40.g1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655613
{'ambient': '480.950', 'aut_centralizer_order': 20, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1'], 'contains': ['96.a1.a1', '240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8279, -1, 8632, -1, 1709, -1, 1795, -1], 'generators': [426445142574562157261255856047921354952341659253215, 1], 'label': '480.950.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 58655614
{'ambient': '480.950', 'aut_centralizer_order': 20, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1'], 'contains': ['96.a1.a1', '240.a1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8279, -1, 8925, -1, 1709, -1, 1440, -1], 'generators': [716792294760557442254470872548892758600862075419881, 442999200286521059294786354848256530527962572807009], 'label': '480.950.48.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.a1.b1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 58655615
{'ambient': '480.950', 'aut_centralizer_order': 40, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['96.a1.a1', '240.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9778, -1, 9850, -1, 2203, -1, 2149, -1], 'generators': [442999200286521059294786354848256530527962572807008, 716792294760557442254470872548892758600862075419880], 'label': '480.950.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 58655616
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.b1.b1', '120.c1.a1', '120.c1.b1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3508, -1, 2627, -1, 7890, -1, 7648, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.60.a1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655617
{'ambient': '480.950', 'aut_centralizer_order': 16, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.c1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1'], 'contains': ['120.a1.a1', '120.d1.a1', '120.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6105, -1, 6315, -1, 4056, -1, 3478, -1], 'generators': [1, 716792294760557442254470872548892758600862075419881, 1232295639045787252339960316374130381712724465203961], 'label': '480.950.60.b1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655618
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '120.34', 'aut_weyl_index': 8, 'centralizer': '120.a1.a1', 'complements': ['120.b1.a1', '120.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['20.f1.a1', '24.b1.a1', '40.f1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5818, 5449, 7128, 4269, 2793, 4172, 4075, 4835], 'generators': [895279187594821988880112138954456167147316150631904, 977388224277852628071748937199590603449235085757680, 716792294760557442254470872548892758600862075419880], 'label': '480.950.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '240.189', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
id: 58655619
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.a1', '30.a1.a1', '30.d1.a1', '30.e1.a1'], 'contains': ['120.c1.a1', '120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5008, -1, 5246, -1, 4639, -1, 4187, -1], 'generators': [292557596686905534223201606408708978150060523223054, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.60.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655620
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.d1.b1', '30.a1.a1', '30.d1.b1', '30.e1.b1'], 'contains': ['120.c1.b1', '120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5008, -1, 5872, -1, 4639, -1, 4478, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.60.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.c1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655621
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1.a1', '20.e1.b1', '30.a1.a1'], 'contains': ['120.c1.a1', '120.c1.b1', '120.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [3931, -1, 4654, -1, 6289, -1, 5662, -1], 'generators': [292557596686905534223201606408708978150060523223054, 804823342775640176693004337497981658731077735358415, 716792294760557442254470872548892758600862075419880], 'label': '480.950.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.a1.a1', 'old_label': '60.d1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 58655622
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '8.3', 'aut_weyl_index': 120, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.c1.a1', '30.d1.a1', '30.d1.b1'], 'contains': ['120.d1.a1', '120.e1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6629, -1, 6905, -1, 3068, -1, 3060, -1], 'generators': [716792294760557442254470872548892758600862075419880, 50171025853727777429212403812529356424413085704470, 1232295639045787252339960316374130381712724465203961], 'label': '480.950.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.e1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
id: 58655623
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '30.b1.a1', '30.d1.b1', '30.e1.a1'], 'contains': ['120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8988, -1, 7536, -1, 2664, -1, 2479, -1], 'generators': [1325318920530865849365258730554128388157086743970486, 385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880], 'label': '480.950.60.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.f1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655624
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': 30, 'aut_weyl_group': '4.2', 'aut_weyl_index': 240, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '30.b1.a1', '30.d1.a1', '30.e1.b1'], 'contains': ['120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8988, -1, 8043, -1, 2664, -1, 2769, -1], 'generators': [385147547852846740609771464011774573041418289458526, 716792294760557442254470872548892758600862075419880, 925510243291654117890086777403221121612568996985809], 'label': '480.950.60.f1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.f1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655625
{'ambient': '480.950', 'aut_centralizer_order': 8, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '24.12', 'aut_weyl_index': 40, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.a1', '30.c1.a1', '30.e1.a1', '30.e1.b1'], 'contains': ['120.d1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7293, -1, 9261, -1, 3472, -1, 3897, -1], 'generators': [716792294760557442254470872548892758600862075419880, 50171025853727777429212403812529356424413085704470, 510198799479422222947367341336538420861781254482824], 'label': '480.950.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.g1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 58655626
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.b1.a1', '40.c1.a1'], 'contains': ['160.a1.a1', '240.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [1022, -1, 1794, -1, 7098, -1, 7410, -1], 'generators': [1024624528931577947488565935571604392720219037958566, 1], 'label': '480.950.80.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655627
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '40.b1.b1', '40.c1.a1'], 'contains': ['160.a1.a1', '240.a1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 10, 'diagramx': [1022, -1, 2427, -1, 7098, -1, 7120, -1], 'generators': [1024624528931577947488565935571604392720219037958566, 716792294760557442254470872548892758600862075419881], 'label': '480.950.80.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '80.a1.b1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655628
{'ambient': '480.950', 'aut_centralizer_order': 48, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1.a1', '40.c1.a1', '40.d1.a1', '40.d1.b1', '40.e1.a1', '40.e1.b1', '40.f1.a1', '40.g1.a1'], 'contains': ['160.a1.a1', '240.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2507, -1, 4034, -1, 6234, -1, 6169, -1], 'generators': [716792294760557442254470872548892758600862075419880, 1024624528931577947488565935571604392720219037958566], 'label': '480.950.80.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655629
{'ambient': '480.950', 'aut_centralizer_order': 1, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '192.1472', 'aut_weyl_index': 5, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.b1.a1', '10.c1.a1', '10.c1.b1', '15.a1.a1', '20.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4399, -1, 6378, -1, 5347, -1, 5863, -1], 'generators': [292557596686905534223201606408708978150060523223054, 480866617086047616678182767008641048689239693846000, 1127264949751373683958359644629655238862694430761408, 385147547852846740609771464011774573041418289458526, 1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.5.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
id: 58655630
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.b1', '40.d1.a1'], 'contains': ['160.a1.a1', '240.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [222, -1, 150, -1, 8457, -1, 8610, -1], 'generators': [292557596686905534223201606408708978150060523223054, 542315455125022342332476192707293981307824410806368], 'label': '480.950.80.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '80.c1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655631
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.a1.b1', '40.d1.b1'], 'contains': ['160.a1.a1', '240.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [222, -1, 423, -1, 8457, -1, 9231, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 542315455125022342332476192707293981307824410806368], 'label': '480.950.80.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '80.c1.b1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655632
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 160, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '40.b1.b1', '40.e1.a1'], 'contains': ['160.a1.a1', '240.c1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [624, -1, 1188, -1, 7502, -1, 7700, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1127264949751373683958359644629655238862694430761408], 'label': '480.950.80.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '80.d1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 58655633
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '6.1', 'aut_weyl_index': 160, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '40.b1.b1', '40.e1.b1'], 'contains': ['160.a1.a1', '240.c1.b1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [624, -1, 1555, -1, 7502, -1, 7990, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 1127264949751373683958359644629655238862694430761408], 'label': '480.950.80.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1.a1', 'old_label': '80.d1.b1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
id: 58655634
{'ambient': '480.950', 'aut_centralizer_order': 40, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 240, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.a1.b1', '48.b1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9734, -1, 8925, -1, 2203, -1, 1972, -1], 'generators': [426445142574562157261255856047921354952341659253214], 'label': '480.950.96.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
id: 58655635
{'ambient': '480.950', 'aut_centralizer_order': 480, 'aut_label': '120.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.c1.a1', '60.a1.a1', '60.b1.a1'], 'contains': ['240.a1.a1', '240.a1.b1', '240.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4097, 7960, 4903, 7016, 5801, 6899, 5859, 7282], 'generators': [1, 716792294760557442254470872548892758600862075419881], 'label': '480.950.120.a1.a1', 'mobius_quo': 2, 'mobius_sub': 60, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['240.a1.b1', '240.a1.a1', '240.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '120.34', 'quotient_action_image': '1.1', 'quotient_action_kernel': '120.34', 'quotient_action_kernel_order': 120, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655636
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '40.b1.a1', '60.a1.a1'], 'contains': ['240.a1.a1', '240.c1.a1', '240.c1.b1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1626, -1, 602, -1, 7934, -1, 8921, -1], 'generators': [292557596686905534223201606408708978150060523223054, 1], 'label': '480.950.120.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655637
{'ambient': '480.950', 'aut_centralizer_order': 12, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.b1', '40.b1.b1', '60.a1.a1'], 'contains': ['240.a1.b1', '240.c1.a1', '240.c1.b1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 20, 'diagramx': [1626, -1, 1162, -1, 7934, -1, 8300, -1], 'generators': [292557596686905534223201606408708978150060523223054, 716792294760557442254470872548892758600862075419881], 'label': '480.950.120.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '120.b1.b1', 'projective_image': '240.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655638
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.a1', '40.e1.a1', '60.a1.a1', '60.c1.a1', '60.d1.a1'], 'contains': ['240.b1.a1', '240.c1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3331, -1, 3133, -1, 6666, -1, 6479, -1], 'generators': [292557596686905534223201606408708978150060523223054, 716792294760557442254470872548892758600862075419880], 'label': '480.950.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655639
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.d1.b1', '40.e1.b1', '60.a1.a1', '60.c1.b1', '60.d1.a1'], 'contains': ['240.b1.a1', '240.c1.b1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [3331, -1, 4471, -1, 6666, -1, 6810, -1], 'generators': [1010981736211329344691992626021944897949607341472881, 716792294760557442254470872548892758600862075419880], 'label': '480.950.120.c1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '120.c1.b1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655640
{'ambient': '480.950', 'aut_centralizer_order': 1, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '160.207', 'aut_weyl_index': 6, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.b1.b1', '30.b1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8475, -1, 8412, -1, 1524, -1, 1355, -1], 'generators': [263044386887473842495128639202504675044690276156785, 1330167095375282552375989396341561782716441971781129, 1, 716792294760557442254470872548892758600862075419881, 1021834788607556582837829297498268518260702261709024], 'label': '480.950.6.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
id: 58655641
{'ambient': '480.950', 'aut_centralizer_order': 32, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.f1.a1', '60.b1.a1', '60.c1.a1', '60.c1.b1', '60.e1.a1', '60.f1.a1', '60.f1.b1', '60.g1.a1'], 'contains': ['240.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6411, -1, 7157, -1, 3764, -1, 3688, -1], 'generators': [716792294760557442254470872548892758600862075419880, 510198799479422222947367341336538420861781254482824], 'label': '480.950.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.d1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655642
{'ambient': '480.950', 'aut_centralizer_order': 32, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': 15, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '30.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.g1.a1', '60.b1.a1', '60.d1.a1', '60.e1.a1'], 'contains': ['240.b1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5103, -1, 6065, -1, 4937, -1, 4759, -1], 'generators': [716792294760557442254470872548892758600862075419880, 1232295639045787252339960316374130381712724465203961], 'label': '480.950.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '120.e1.a1', 'projective_image': '240.189', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655643
{'ambient': '480.950', 'aut_centralizer_order': 48, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '2.1', 'aut_weyl_index': 480, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '80.a1.b1', '80.b1.a1', '80.c1.a1', '80.c1.b1', '80.d1.a1', '80.d1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [724, -1, 2061, -1, 7098, -1, 7700, -1], 'generators': [1024624528931577947488565935571604392720219037958566], 'label': '480.950.160.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 58655644
{'ambient': '480.950', 'aut_centralizer_order': 480, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1'], 'contains': ['480.a1.a1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2889, 8146, 2380, 6940, 6447, 6899, 7410, 6671], 'generators': [1], 'label': '480.950.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['120.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '240.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.90', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655645
{'ambient': '480.950', 'aut_centralizer_order': 480, 'aut_label': '240.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '80.a1.b1', '120.a1.a1', '120.b1.b1'], 'contains': ['480.a1.a1'], 'core': '240.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2889, 8146, 2627, 8753, 6447, 6899, 7120, 8365], 'generators': [716792294760557442254470872548892758600862075419881], 'label': '480.950.240.a1.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '240.a1.b1', 'normal_contained_in': ['120.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.b1', 'projective_image': '240.90', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.90', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.a1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655646
{'ambient': '480.950', 'aut_centralizer_order': 960, 'aut_label': '240.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '80.b1.a1', '120.a1.a1', '120.c1.a1', '120.c1.b1', '120.d1.a1', '120.e1.a1'], 'contains': ['480.a1.a1'], 'core': '240.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4097, 5449, 5026, 5126, 5801, 4562, 6012, 4976], 'generators': [716792294760557442254470872548892758600862075419880], 'label': '480.950.240.b1.a1', 'mobius_quo': -1, 'mobius_sub': -120, 'normal_closure': '240.b1.a1', 'normal_contained_in': ['4.a1.a1', '120.a1.a1'], 'normal_contains': ['480.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.b1.a1', 'projective_image': '240.189', 'quotient_action_image': '1.1', 'quotient_action_kernel': '240.189', 'quotient_action_kernel_order': 240, 'quotient_fusion': None, 'short_label': '240.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655647
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.a1', '80.d1.a1', '120.b1.a1', '120.b1.b1', '120.c1.a1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1626, -1, 466, -1, 7502, -1, 7994, -1], 'generators': [292557596686905534223201606408708978150060523223054], 'label': '480.950.240.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '240.c1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655648
{'ambient': '480.950', 'aut_centralizer_order': 24, 'aut_label': '240.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '1.1', 'aut_weyl_index': 960, 'centralizer': '20.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.c1.b1', '80.d1.b1', '120.b1.a1', '120.b1.b1', '120.c1.b1'], 'contains': ['480.a1.a1'], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1626, -1, 1468, -1, 7502, -1, 8292, -1], 'generators': [1010981736211329344691992626021944897949607341472881], 'label': '480.950.240.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1.a1', 'old_label': '240.c1.b1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '240.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655649
{'ambient': '480.950', 'aut_centralizer_order': None, 'aut_label': '480.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '160.a1.a1', '240.a1.a1', '240.a1.b1', '240.b1.a1', '240.c1.a1', '240.c1.b1'], 'contains': [], 'core': '480.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2889, 6797, 2380, 6940, 6447, 5731, 7410, 6671], 'generators': [], 'label': '480.950.480.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '480.a1.a1', 'normal_contained_in': ['240.a1.b1', '240.a1.a1', '240.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '480.a1.a1', 'projective_image': '480.950', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '480.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 58655650
{'ambient': '480.950', 'aut_centralizer_order': 1, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '96.209', 'aut_weyl_index': 10, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '20.d1.a1', '20.d1.b1', '20.e1.a1', '20.e1.b1', '30.a1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2884, -1, 4517, -1, 7497, -1, 7019, -1], 'generators': [748616464605151307937313748912851594821171432265920, 292557596686905534223201606408708978150060523223054, 1, 542315455125022342332476192707293981307824410806368, 716792294760557442254470872548892758600862075419881], 'label': '480.950.10.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
id: 58655651
{'ambient': '480.950', 'aut_centralizer_order': 4, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '48.48', 'aut_weyl_index': 20, 'centralizer': '120.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.f1.a1', '30.c1.a1', '40.c1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5164, -1, 6378, -1, 4864, -1, 4671, -1], 'generators': [1024624528931577947488565935571604392720219037958566, 50171025853727777429212403812529356424413085704470, 1, 716792294760557442254470872548892758600862075419881, 1232295639045787252339960316374130381712724465203961], 'label': '480.950.10.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '120.34', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}

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.