LMFDB - Abstract group data

Formats: - HTML - YAML - JSON - 2025-10-04T14:39:55.668646

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 20, 4, 4, 2, 4, 4, 2], 'aut_gens': [[1, 2, 16], [161, 10, 272], [81, 50, 16], [253, 210, 144], [85, 314, 144], [89, 106, 304], [249, 258, 48], [13, 50, 304], [13, 190, 304]], 'aut_group': None, 'aut_hash': 5919243039148427669, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5120, 'aut_permdeg': 96, 'aut_perms': [375315022060181409552564828706875017875839248007786020427899977320319995812818828527659623779144473075512936037512597694250667887232222776646454684025, 304800887597729080994202113583221095892485863541985083147151511707687070733182041131743652338032392883299033088138704077594507834771159587351976084632, 861955497483123264038702426172977405008344606380384948695502444215299290459577328992219432958192972330493978135624346502859031469119763906053616856313, 27632090472713345794445708987398749149753759897383157777248871669162043396459218888214140568046484309048392667863953428295986700191887908853037754364, 651806683666346692304103902955178510037753679211880032608877579232494490536180402782751573004697427934646674092038729501763729647371822123858010698865, 48060191131529940784816011737267923523048183902315002517195550802422592974854852604589617999235539192911486155408410779831527181991980185014141166880, 367889952892351897295686242962695223096761600846957280789150128596962408656151023551342453826030421658037667286201359253998167872605662140133826109400, 108334273590702305370885015245451464681859952881106891381997839895198914015519249739916732220062764769242406407564691448057711593651123548849484818848], 'aut_phi_ratio': 40.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [5, 2, 2, 1], [8, 20, 4, 2], [10, 2, 2, 3], [20, 4, 2, 4], [20, 4, 4, 1], [20, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_5:(C_2\\times C_4\\times C_2^2.C_2^5)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '320.1638', 'autcentquo_hash': 1638, 'autcentquo_nilpotent': False, 'autcentquo_order': 320, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 2, 4], [4, 4, 1], [4, 8, 2], [5, 2, 2], [8, 20, 8], [10, 2, 6], [20, 4, 12], [20, 8, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '80.19', 'commutator_count': 2, 'commutator_label': '40.9', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 105, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [5, 2, 2, 1], [8, 20, 4, 2], [10, 2, 2, 3], [20, 4, 2, 4], [20, 4, 4, 1], [20, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 40, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '20.4', 'hash': 105, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 10], 'inner_gens': [[1, 94, 176], [245, 2, 304], [161, 34, 16]], 'inner_hash': 19, 'inner_nilpotent': False, 'inner_order': 80, 'inner_split': True, 'inner_tex': 'C_{10}.D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 26], [4, 13]], 'label': '320.105', 'linC_count': 320, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 44, 'linQ_dim': 12, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C20.D8', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 22, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 47, 'number_divisions': 24, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 64, 'number_subgroups': 174, 'old_label': None, 'order': 320, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [4, 28], [5, 4], [8, 160], [10, 12], [20, 112]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[169, 2, 16], [1, 170, 16], [81, 2, 176], [1, 82, 176], [1, 2, 272]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [127, 39916800, 362880, 5040, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [4, 9], [8, 6], [16, 1]], 'representations': {'PC': {'code': 74588068770217504492828973201849434115, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -5, 1120, 1317, 36, 254, 58, 6164, 5331, 102, 6060, 124, 6285]}, 'GLZN': {'d': 2, 'p': 105, 'gens': [33960739, 82191446, 5136169, 87979576, 1159831, 90854147, 85785094]}, 'Perm': {'d': 21, 'gens': [2690128182443022727, 4886141055427548720, 7940368848461374800, 10493555889062096640, 12414935000230963200, 12414935001350206800, 37]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{20}.D_8', 'transitive_degree': 320, '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: 103767107
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 105, 'group_order': 320, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 103767118
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 105, 'group_order': 320, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 160, 'size': 1}
id: 103767129
{'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 105, 'group_order': 320, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 8, 'size': 1}
id: 103767140
{'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 105, 'group_order': 320, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 168, 'size': 1}
id: 103767149
{'aut_label': '4A', 'centralizer': '2.c1.a1', 'counter': 5, 'group_counter': 105, 'group_order': 320, 'label': '4A', 'order': 4, 'powers': [2, 5], 'representative': 80, 'size': 2}
id: 103767150
{'aut_label': '4B', 'centralizer': '2.c1.a1', 'counter': 6, 'group_counter': 105, 'group_order': 320, 'label': '4B', 'order': 4, 'powers': [2, 6], 'representative': 88, 'size': 2}
id: 103767151
{'aut_label': '4C', 'centralizer': '2.b1.a1', 'counter': 7, 'group_counter': 105, 'group_order': 320, 'label': '4C', 'order': 4, 'powers': [3, 7], 'representative': 4, 'size': 2}
id: 103767152
{'aut_label': '4D', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 105, 'group_order': 320, 'label': '4D', 'order': 4, 'powers': [3, 8], 'representative': 164, 'size': 2}
id: 103767153
{'aut_label': '4E', 'centralizer': '4.a1.a1', 'counter': 9, 'group_counter': 105, 'group_order': 320, 'label': '4E', 'order': 4, 'powers': [4, 9], 'representative': 84, 'size': 4}
id: 103767108
{'aut_label': '4F', 'centralizer': '8.d1.a1', 'counter': 10, 'group_counter': 105, 'group_order': 320, 'label': '4F', 'order': 4, 'powers': [2, 10], 'representative': 1, 'size': 8}
id: 103767109
{'aut_label': '4F', 'centralizer': '8.d1.b1', 'counter': 11, 'group_counter': 105, 'group_order': 320, 'label': '4G', 'order': 4, 'powers': [2, 11], 'representative': 81, 'size': 8}
id: 103767110
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 12, 'group_counter': 105, 'group_order': 320, 'label': '5A1', 'order': 5, 'powers': [13, 1], 'representative': 64, 'size': 2}
id: 103767111
{'aut_label': '5A1', 'centralizer': '2.a1.a1', 'counter': 13, 'group_counter': 105, 'group_order': 320, 'label': '5A2', 'order': 5, 'powers': [12, 1], 'representative': 128, 'size': 2}
id: 103767112
{'aut_label': '8A1', 'centralizer': '20.f1.a1', 'counter': 14, 'group_counter': 105, 'group_order': 320, 'label': '8A1', 'order': 8, 'powers': [7, 17], 'representative': 290, 'size': 20}
id: 103767113
{'aut_label': '8A1', 'centralizer': '20.f1.a1', 'counter': 15, 'group_counter': 105, 'group_order': 320, 'label': '8A-1', 'order': 8, 'powers': [7, 16], 'representative': 302, 'size': 20}
id: 103767114
{'aut_label': '8A1', 'centralizer': '20.f1.a1', 'counter': 16, 'group_counter': 105, 'group_order': 320, 'label': '8A3', 'order': 8, 'powers': [7, 15], 'representative': 294, 'size': 20}
id: 103767115
{'aut_label': '8A1', 'centralizer': '20.f1.a1', 'counter': 17, 'group_counter': 105, 'group_order': 320, 'label': '8A-3', 'order': 8, 'powers': [7, 14], 'representative': 298, 'size': 20}
id: 103767116
{'aut_label': '8B1', 'centralizer': '20.d1.a1', 'counter': 18, 'group_counter': 105, 'group_order': 320, 'label': '8B1', 'order': 8, 'powers': [5, 21], 'representative': 243, 'size': 20}
id: 103767117
{'aut_label': '8B1', 'centralizer': '20.d1.a1', 'counter': 19, 'group_counter': 105, 'group_order': 320, 'label': '8B-1', 'order': 8, 'powers': [5, 20], 'representative': 3, 'size': 20}
id: 103767119
{'aut_label': '8B1', 'centralizer': '20.d1.a1', 'counter': 20, 'group_counter': 105, 'group_order': 320, 'label': '8B3', 'order': 8, 'powers': [5, 19], 'representative': 163, 'size': 20}
id: 103767120
{'aut_label': '8B1', 'centralizer': '20.d1.a1', 'counter': 21, 'group_counter': 105, 'group_order': 320, 'label': '8B-3', 'order': 8, 'powers': [5, 18], 'representative': 83, 'size': 20}
id: 103767121
{'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 22, 'group_counter': 105, 'group_order': 320, 'label': '10A1', 'order': 10, 'powers': [12, 2], 'representative': 32, 'size': 2}
id: 103767122
{'aut_label': '10A1', 'centralizer': '2.a1.a1', 'counter': 23, 'group_counter': 105, 'group_order': 320, 'label': '10A3', 'order': 10, 'powers': [13, 2], 'representative': 96, 'size': 2}
id: 103767123
{'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 24, 'group_counter': 105, 'group_order': 320, 'label': '10B1', 'order': 10, 'powers': [12, 3], 'representative': 136, 'size': 2}
id: 103767124
{'aut_label': '10B1', 'centralizer': '2.a1.a1', 'counter': 25, 'group_counter': 105, 'group_order': 320, 'label': '10B3', 'order': 10, 'powers': [13, 3], 'representative': 72, 'size': 2}
id: 103767125
{'aut_label': '10C1', 'centralizer': '2.a1.a1', 'counter': 26, 'group_counter': 105, 'group_order': 320, 'label': '10C1', 'order': 10, 'powers': [12, 4], 'representative': 40, 'size': 2}
id: 103767126
{'aut_label': '10C1', 'centralizer': '2.a1.a1', 'counter': 27, 'group_counter': 105, 'group_order': 320, 'label': '10C3', 'order': 10, 'powers': [13, 4], 'representative': 104, 'size': 2}
id: 103767127
{'aut_label': '20A1', 'centralizer': '4.a1.a1', 'counter': 28, 'group_counter': 105, 'group_order': 320, 'label': '20A1', 'order': 20, 'powers': [22, 5], 'representative': 16, 'size': 4}
id: 103767128
{'aut_label': '20A1', 'centralizer': '4.a1.a1', 'counter': 29, 'group_counter': 105, 'group_order': 320, 'label': '20A3', 'order': 20, 'powers': [23, 5], 'representative': 48, 'size': 4}
id: 103767130
{'aut_label': '20B1', 'centralizer': '4.a1.a1', 'counter': 30, 'group_counter': 105, 'group_order': 320, 'label': '20B1', 'order': 20, 'powers': [22, 6], 'representative': 24, 'size': 4}
id: 103767131
{'aut_label': '20B1', 'centralizer': '4.a1.a1', 'counter': 31, 'group_counter': 105, 'group_order': 320, 'label': '20B3', 'order': 20, 'powers': [23, 6], 'representative': 56, 'size': 4}
id: 103767132
{'aut_label': '20C1', 'centralizer': '4.a1.a1', 'counter': 32, 'group_counter': 105, 'group_order': 320, 'label': '20C1', 'order': 20, 'powers': [24, 7], 'representative': 68, 'size': 4}
id: 103767133
{'aut_label': '20C1', 'centralizer': '4.a1.a1', 'counter': 33, 'group_counter': 105, 'group_order': 320, 'label': '20C3', 'order': 20, 'powers': [25, 7], 'representative': 132, 'size': 4}
id: 103767134
{'aut_label': '20D1', 'centralizer': '4.a1.a1', 'counter': 34, 'group_counter': 105, 'group_order': 320, 'label': '20D1', 'order': 20, 'powers': [25, 8], 'representative': 36, 'size': 4}
id: 103767135
{'aut_label': '20D1', 'centralizer': '4.a1.a1', 'counter': 35, 'group_counter': 105, 'group_order': 320, 'label': '20D3', 'order': 20, 'powers': [24, 8], 'representative': 100, 'size': 4}
id: 103767136
{'aut_label': '20E1', 'centralizer': '4.a1.a1', 'counter': 36, 'group_counter': 105, 'group_order': 320, 'label': '20E1', 'order': 20, 'powers': [26, 9], 'representative': 20, 'size': 4}
id: 103767137
{'aut_label': '20E1', 'centralizer': '4.a1.a1', 'counter': 37, 'group_counter': 105, 'group_order': 320, 'label': '20E-1', 'order': 20, 'powers': [26, 9], 'representative': 28, 'size': 4}
id: 103767138
{'aut_label': '20E1', 'centralizer': '4.a1.a1', 'counter': 38, 'group_counter': 105, 'group_order': 320, 'label': '20E3', 'order': 20, 'powers': [27, 9], 'representative': 212, 'size': 4}
id: 103767139
{'aut_label': '20E1', 'centralizer': '4.a1.a1', 'counter': 39, 'group_counter': 105, 'group_order': 320, 'label': '20E-3', 'order': 20, 'powers': [27, 9], 'representative': 52, 'size': 4}
id: 103767141
{'aut_label': '20F1', 'centralizer': '8.d1.a1', 'counter': 40, 'group_counter': 105, 'group_order': 320, 'label': '20F1', 'order': 20, 'powers': [22, 10], 'representative': 65, 'size': 8}
id: 103767142
{'aut_label': '20F1', 'centralizer': '8.d1.a1', 'counter': 41, 'group_counter': 105, 'group_order': 320, 'label': '20F-1', 'order': 20, 'powers': [22, 10], 'representative': 257, 'size': 8}
id: 103767143
{'aut_label': '20F1', 'centralizer': '8.d1.a1', 'counter': 42, 'group_counter': 105, 'group_order': 320, 'label': '20F3', 'order': 20, 'powers': [23, 10], 'representative': 33, 'size': 8}
id: 103767144
{'aut_label': '20F1', 'centralizer': '8.d1.a1', 'counter': 43, 'group_counter': 105, 'group_order': 320, 'label': '20F-3', 'order': 20, 'powers': [23, 10], 'representative': 129, 'size': 8}
id: 103767145
{'aut_label': '20F1', 'centralizer': '8.d1.b1', 'counter': 44, 'group_counter': 105, 'group_order': 320, 'label': '20G1', 'order': 20, 'powers': [22, 11], 'representative': 17, 'size': 8}
id: 103767146
{'aut_label': '20F1', 'centralizer': '8.d1.b1', 'counter': 45, 'group_counter': 105, 'group_order': 320, 'label': '20G-1', 'order': 20, 'powers': [22, 11], 'representative': 145, 'size': 8}
id: 103767147
{'aut_label': '20F1', 'centralizer': '8.d1.b1', 'counter': 46, 'group_counter': 105, 'group_order': 320, 'label': '20G3', 'order': 20, 'powers': [23, 11], 'representative': 49, 'size': 8}
id: 103767148
{'aut_label': '20F1', 'centralizer': '8.d1.b1', 'counter': 47, 'group_counter': 105, 'group_order': 320, 'label': '20G-3', 'order': 20, 'powers': [23, 11], 'representative': 133, 'size': 8}

Column	Type
cdim	integer
counter	smallint
faithful	boolean
group	text
group_order	numeric
image	text
label	text
multiplicity	smallint
nt	integer[]
qdim	integer
qvalues	integer[]
schur_index	smallint

gps_qchar • Show schema

id: 2465933
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 2465944
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2465950
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
id: 2465951
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
id: 2465952
{'cdim': 1, 'counter': 5, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, -2, -2, 2, -2, -2, -2, 2, 2, 2, 2, -2], 'schur_index': 1}
id: 2465953
{'cdim': 1, 'counter': 6, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, -2, -2, -2, -2, 2], 'schur_index': 1}
id: 2465954
{'cdim': 2, 'counter': 7, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465955
{'cdim': 2, 'counter': 8, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465956
{'cdim': 2, 'counter': 9, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2c', 'multiplicity': 2, 'nt': [5, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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: 2465934
{'cdim': 2, 'counter': 10, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2d', 'multiplicity': 2, 'nt': [8, 6], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, -4, 0, 4, 0, 0, 0, 0, -4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465935
{'cdim': 2, 'counter': 11, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2e', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, 4, 0, 0, 0, 4, -4, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465936
{'cdim': 2, 'counter': 12, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2f', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, 4, -4, 0, -4, 0, 0, 0, 0, 4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465937
{'cdim': 2, 'counter': 13, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2g', 'multiplicity': 2, 'nt': [10, 3], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, -4, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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: 2465938
{'cdim': 2, 'counter': 14, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2h', 'multiplicity': 2, 'nt': [16, 14], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, -4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, -4, -4, 4, 0, 0, 0, -4, 4, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465939
{'cdim': 2, 'counter': 15, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2i', 'multiplicity': 2, 'nt': [20, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, -4, 4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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': 2}
id: 2465940
{'cdim': 2, 'counter': 16, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2j', 'multiplicity': 2, 'nt': [20, 2], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -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': 2}
id: 2465943
{'cdim': 4, 'counter': 19, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4a', 'multiplicity': 1, 'nt': [16, 40], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465941
{'cdim': 2, 'counter': 17, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2k', 'multiplicity': 4, 'nt': [20, 7], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -8, -8, 8, 8, -8, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465942
{'cdim': 2, 'counter': 18, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.2l', 'multiplicity': 4, 'nt': [20, 7], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, -8, -8, -8, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, 2, -2, -2, 2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
id: 2465945
{'cdim': 4, 'counter': 20, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4b', 'multiplicity': 2, 'nt': [40, 31], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 8, -8, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 0, 0, 0, -2, 2, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465946
{'cdim': 4, 'counter': 21, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4c', 'multiplicity': 2, 'nt': [40, 32], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, 2, 0, -2, 0, 0, 0, 0, 2, -2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465947
{'cdim': 4, 'counter': 22, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4d', 'multiplicity': 2, 'nt': [40, 49], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 2, 2, -2, 2, 0, 2, 0, 0, 0, 0, -2, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465948
{'cdim': 4, 'counter': 23, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4e', 'multiplicity': 2, 'nt': [80, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, -8, 8, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, 2, 2, -2, 0, 0, 0, 2, -2, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
id: 2465949
{'cdim': 4, 'counter': 24, 'faithful': False, 'group': '320.105', 'group_order': 320, 'image': None, 'label': '320.105.4f', 'multiplicity': 4, 'nt': [80, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

Column	Type
center	text
center_index	numeric
center_order	numeric
counter	smallint
cyclotomic_n	integer
dim	integer
faithful	boolean
field	numeric[]
group	text
group_counter	integer
group_order	numeric
image	text
image_isoclass	text
image_order	numeric
indicator	smallint
kernel	text
kernel_order	numeric
label	text
nt	integer[]
q_character	text
values	jsonb

gps_char • Show schema

id: 3173205
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 320, 'label': '320.105.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3173216
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 160, 'label': '320.105.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3173227
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 160, 'label': '320.105.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
id: 3173238
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 160, 'label': '320.105.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
id: 3173247
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 80, 'label': '320.105.1e1', 'nt': [4, 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, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 3173248
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 80, 'label': '320.105.1e2', 'nt': [4, 2], '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, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 3173249
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 320, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 80, 'label': '320.105.1f1', 'nt': [4, 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, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[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: 3173250
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id: 3173251
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 80, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 40, 'label': '320.105.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173206
{'center': '4.a1.a1', 'center_index': 4, 'center_order': 80, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 40, 'label': '320.105.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173207
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 32, 'label': '320.105.2c1', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]]]}
id: 3173208
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '10.1', 'image_order': 10, 'indicator': 1, 'kernel': '10.a1.a1', 'kernel_order': 32, 'label': '320.105.2c2', 'nt': [5, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]]]}
id: 3173209
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 40, 'counter': 13, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.b1.a1', 'kernel_order': 20, 'label': '320.105.2d1', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173210
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 40, 'counter': 14, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.7', 'image_order': 16, 'indicator': 1, 'kernel': '16.b1.a1', 'kernel_order': 20, 'label': '320.105.2d2', 'nt': [8, 6], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173211
{'center': '8.b1.a1', 'center_index': 8, 'center_order': 40, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 20, 'label': '320.105.2e1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173212
{'center': '8.b1.a1', 'center_index': 8, 'center_order': 40, 'counter': 16, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 20, 'label': '320.105.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173213
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 40, 'counter': 17, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 20, 'label': '320.105.2f1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173214
{'center': '8.a1.a1', 'center_index': 8, 'center_order': 40, 'counter': 18, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1.a1', 'kernel_order': 20, 'label': '320.105.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173215
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 19, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 16, 'label': '320.105.2g1', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]]]}
id: 3173217
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 20, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '20.4', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 16, 'label': '320.105.2g2', 'nt': [10, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]]]}
id: 3173218
{'center': '8.b1.a1', 'center_index': 8, 'center_order': 40, 'counter': 21, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.9', 'image_order': 16, 'indicator': -1, 'kernel': '16.e1.a1', 'kernel_order': 20, 'label': '320.105.2h1', 'nt': [16, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173219
{'center': '8.b1.a1', 'center_index': 8, 'center_order': 40, 'counter': 22, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [-2, 0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '16.9', 'image_order': 16, 'indicator': -1, 'kernel': '16.e1.a1', 'kernel_order': 20, 'label': '320.105.2h2', 'nt': [16, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173220
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 23, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.b1.b1', 'kernel_order': 16, 'label': '320.105.2i1', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]]]}
id: 3173221
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 24, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.b1.b1', 'kernel_order': 16, 'label': '320.105.2i2', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]]]}
id: 3173222
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id: 3173223
{'center': '10.a1.a1', 'center_index': 10, 'center_order': 32, 'counter': 26, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '20.1', 'image_order': 20, 'indicator': -1, 'kernel': '20.b1.a1', 'kernel_order': 16, 'label': '320.105.2j2', 'nt': [20, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]]]}
id: 3173224
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 27, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.b1.a1', 'kernel_order': 8, 'label': '320.105.2k1', 'nt': [20, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]]]}
id: 3173225
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 28, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.b1.a1', 'kernel_order': 8, 'label': '320.105.2k2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]]]}
id: 3173226
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 29, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.b1.a1', 'kernel_order': 8, 'label': '320.105.2k3', 'nt': [20, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]]]}
id: 3173228
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 30, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.b1.a1', 'kernel_order': 8, 'label': '320.105.2k4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]]]}
id: 3173229
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 31, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 8, 'label': '320.105.2l1', 'nt': [20, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]]]}
id: 3173230
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 32, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 8, 'label': '320.105.2l2', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 2], [-1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 2], [1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]]]}
id: 3173231
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 33, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 8, 'label': '320.105.2l3', 'nt': [20, 7], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[-1, 2], [1, -2]]]}
id: 3173232
{'center': '20.a1.a1', 'center_index': 20, 'center_order': 16, 'counter': 34, 'cyclotomic_n': 5, 'dim': 2, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '40.8', 'image_order': 40, 'indicator': 0, 'kernel': '40.a1.a1', 'kernel_order': 8, 'label': '320.105.2l4', 'nt': [20, 4], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 2], [1, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 2], [1, -2]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 2], [-1, -2]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 2], [1, -2]], [[-1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[-1, 2], [1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[-1, 0], [-2, 1], [-1, 2], [-1, -2]], [[-1, 2], [1, -2]], [[1, 2], [-1, -2]], [[1, 0], [2, 1], [1, 2], [1, -2]], [[1, 2], [-1, -2]]]}
id: 3173233
{'center': '16.a1.a1', 'center_index': 16, 'center_order': 20, 'counter': 35, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '32.8', 'image_order': 32, 'indicator': -1, 'kernel': '32.c1.a1', 'kernel_order': 10, 'label': '320.105.4a', 'nt': [16, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173234
{'center': '40.b1.a1', 'center_index': 40, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.17', 'image_order': 80, 'indicator': 1, 'kernel': '80.d1.a1', 'kernel_order': 4, 'label': '320.105.4b1', 'nt': [40, 31], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173235
{'center': '40.b1.a1', 'center_index': 40, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.17', 'image_order': 80, 'indicator': 1, 'kernel': '80.d1.a1', 'kernel_order': 4, 'label': '320.105.4b2', 'nt': [40, 31], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173236
{'center': '40.a1.a1', 'center_index': 40, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.15', 'image_order': 80, 'indicator': 1, 'kernel': '80.b1.a1', 'kernel_order': 4, 'label': '320.105.4c1', 'nt': [40, 32], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173237
{'center': '40.a1.a1', 'center_index': 40, 'center_order': 8, 'counter': 39, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.15', 'image_order': 80, 'indicator': 1, 'kernel': '80.b1.a1', 'kernel_order': 4, 'label': '320.105.4c2', 'nt': [40, 32], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173239
{'center': '40.a1.a1', 'center_index': 40, 'center_order': 8, 'counter': 40, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.16', 'image_order': 80, 'indicator': -1, 'kernel': '80.c1.a1', 'kernel_order': 4, 'label': '320.105.4d1', 'nt': [40, 49], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173240
{'center': '40.a1.a1', 'center_index': 40, 'center_order': 8, 'counter': 41, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.16', 'image_order': 80, 'indicator': -1, 'kernel': '80.c1.a1', 'kernel_order': 4, 'label': '320.105.4d2', 'nt': [40, 49], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173241
{'center': '40.b1.a1', 'center_index': 40, 'center_order': 8, 'counter': 42, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.18', 'image_order': 80, 'indicator': -1, 'kernel': '80.e1.a1', 'kernel_order': 4, 'label': '320.105.4e1', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173242
{'center': '40.b1.a1', 'center_index': 40, 'center_order': 8, 'counter': 43, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [-1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '80.18', 'image_order': 80, 'indicator': -1, 'kernel': '80.e1.a1', 'kernel_order': 4, 'label': '320.105.4e2', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173243
{'center': '80.a1.a1', 'center_index': 80, 'center_order': 4, 'counter': 44, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '160.43', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 2, 'label': '320.105.4f1', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [2, -2]], [[0, 0]], [[2, 0], [4, 1], [2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1], [-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173244
{'center': '80.a1.a1', 'center_index': 80, 'center_order': 4, 'counter': 45, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '160.43', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 2, 'label': '320.105.4f2', 'nt': [80, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2], [2, -2]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[-2, 2], [-2, -2]], [[2, 2], [-2, -2]], [[0, 0]], [[-2, 0], [-4, 1], [-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1], [2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173245
{'center': '80.a1.a1', 'center_index': 80, 'center_order': 4, 'counter': 46, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '160.43', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 2, 'label': '320.105.4f3', 'nt': [80, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[-2, 0], [-4, 1], [-2, 2], [-2, -2]], [[0, 0]], [[-2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1], [2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
id: 3173246
{'center': '80.a1.a1', 'center_index': 80, 'center_order': 4, 'counter': 47, 'cyclotomic_n': 5, 'dim': 4, 'faithful': False, 'field': [1, -1, 1, -1, 1], 'group': '320.105', 'group_counter': 105, 'group_order': 320, 'image': None, 'image_isoclass': '160.43', 'image_order': 160, 'indicator': 0, 'kernel': '160.c1.a1', 'kernel_order': 2, 'label': '320.105.4f4', 'nt': [80, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2], [-2, -2]], [[2, 2], [2, -2]], [[-2, 2], [-2, -2]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 0], [4, 1], [2, 2], [2, -2]], [[0, 0]], [[2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1], [-2, 2], [-2, -2]], [[0, 0]], [[0, 0]], [[-2, 2], [2, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}

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

gps_subgroup_search • Show schema

id: 51693260
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 320, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '320.105.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '320.105', 'subgroup_hash': 105, 'subgroup_order': 320, 'subgroup_tex': 'C_{20}.D_8', 'supersolvable': True, 'sylow': 0}
id: 51693271
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 160, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '160.189', 'subgroup_hash': 189, 'subgroup_order': 160, 'subgroup_tex': 'C_{20}:Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693282
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 160, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '160.11', 'subgroup_hash': 11, 'subgroup_order': 160, 'subgroup_tex': 'C_{20}:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693293
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 160, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '160.11', 'subgroup_hash': 11, 'subgroup_order': 160, 'subgroup_tex': 'C_{20}:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693304
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 80, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.20', 'subgroup_hash': 20, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693315
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 80, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693321
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 80, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693322
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 40, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.47', 'subgroup_hash': 47, 'subgroup_order': 80, 'subgroup_tex': 'Q_8\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 51693323
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.9', 'subgroup_hash': 9, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693261
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 40, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.22', 'subgroup_hash': 22, 'subgroup_order': 80, 'subgroup_tex': 'C_4:C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693262
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 40, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.9', 'subgroup_hash': 9, 'subgroup_order': 80, 'subgroup_tex': 'C_{10}:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693263
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '320.105.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '64.13', 'subgroup_hash': 13, 'subgroup_order': 64, 'subgroup_tex': 'C_4.D_8', 'supersolvable': True, 'sylow': 2}
id: 51693264
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 40, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693265
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 40, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693266
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 40, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693267
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693268
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 20, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693269
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693270
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693272
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 20, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.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': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.11', 'subgroup_hash': 11, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693273
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 20, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.1', 'subgroup_hash': 1, 'subgroup_order': 40, 'subgroup_tex': 'C_5:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693274
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': True, 'core_order': 32, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_5', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693275
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693276
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '32.12', 'subgroup_hash': 12, 'subgroup_order': 32, 'subgroup_tex': 'C_4:C_8', 'supersolvable': True, 'sylow': 0}
id: 51693277
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 20, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2', 'C4'], 'split': False, '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: 51693278
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 20, 'counter': 26, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693279
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 20, 'counter': 27, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693280
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 20, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693281
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 20, 'counter': 29, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.9', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693283
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 30, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693284
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 10, 'counter': 31, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.16.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693285
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 10, 'counter': 32, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.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': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 51693286
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
id: 51693287
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 51693288
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 16, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.20.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 51693289
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693290
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.20.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 51693291
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.20.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
id: 51693292
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.20.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 51693294
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 10, 'counter': 40, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.9', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 51693295
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 10, 'counter': 41, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 51693296
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 10, 'counter': 42, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 51693297
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 8, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51693298
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51693299
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': True, 'core_order': 8, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 51693300
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.40.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 51693301
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.40.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 51693302
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.40.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693303
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.40.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 51693305
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 4, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '320.105.40.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
id: 51693306
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.40.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
id: 51693307
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 5, 'counter': 52, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '320.105.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.D_8', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
id: 51693308
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 320, 'characteristic': True, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '320.105.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.19', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 19, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.D_4', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 51693309
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 4, 'counter': 54, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.80.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.15', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693310
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 4, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.80.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693311
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 4, 'counter': 56, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.80.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8:D_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693312
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': True, 'core_order': 4, 'counter': 57, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.80.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.18', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5:Q_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693313
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.80.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693314
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.80.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693316
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '320.105.80.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
id: 51693317
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 320, 'characteristic': True, 'core_order': 2, 'counter': 61, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.160.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '160.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.D_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 51693318
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 320, 'characteristic': True, 'core_order': 2, 'counter': 62, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.160.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '160.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}.Q_{16}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 51693319
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 320, 'characteristic': True, 'core_order': 2, 'counter': 63, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '320.105.160.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '160.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '160.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 51693320
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '320.105', 'ambient_counter': 105, 'ambient_order': 320, 'ambient_tex': 'C_{20}.D_8', 'central': True, 'central_factor': False, 'centralizer_order': 320, 'characteristic': True, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '320.105.320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '320.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '320.105', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 105, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}.D_8', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}

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

gps_subgroup_data • Show schema

id: 51693260
{'ambient': '320.105', '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': '80.a1.a1', 'complements': ['320.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7737, 4767, 4739, 6415, 5723, 5221, 6020, 4003], 'generators': [1, 160, 92, 80, 2, 64, 168], 'label': '320.105.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '80.19', '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': '80.19'}
id: 51693261
{'ambient': '320.105', 'aut_centralizer_order': 40, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.196', 'aut_weyl_index': 80, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.d1.a1', '8.d1.b1', '20.e1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7737, -1, 5977, -1, 7424, -1, 5605, -1], 'generators': [1, 64, 8, 172, 160], 'label': '320.105.4.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 51693262
{'ambient': '320.105', 'aut_centralizer_order': 16, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '160.236', 'aut_weyl_index': 32, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '20.f1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9779, -1, 1313, -1, 9017, -1, 9116, -1], 'generators': [2, 4, 8, 160, 64], 'label': '320.105.4.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.f1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
id: 51693263
{'ambient': '320.105', 'aut_centralizer_order': 4, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 20, 'centralizer': '80.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [8209, -1, 4605, -1, 5322, -1, 6375, -1], 'generators': [1, 2], 'label': '320.105.5.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': '80.19', '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': '16.3'}
id: 51693264
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.a1', '4.d1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '40.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2322, 1797, 9119, 1325, 2475, 2594, 1486, 7805], 'generators': [168, 64, 160, 80], 'label': '320.105.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.a1', '16.b1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693265
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.e1.a1', '4.f1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.e1.a1', '40.b1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8341, 8260, 1415, 4855, 8300, 7263, 8513, 5404], 'generators': [172, 64, 8, 160], 'label': '320.105.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '16.e1.a1', '16.d1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693266
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '8.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 320, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['16.a1.a1', '16.g1.a1', '40.c1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4388, 4529, 2695, 7030, 6390, 4548, 7299, 3106], 'generators': [92, 64, 168, 160], 'label': '320.105.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['16.a1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693267
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 320, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.c1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '40.d1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5361, -1, 5501, -1, 4944, -1, 4321, -1], 'generators': [1, 64, 160, 168], 'label': '320.105.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693268
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '16.10', 'aut_weyl_index': 320, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.c1.a1', '4.e1.a1'], 'contains': ['16.a1.a1', '16.f1.b1', '40.d1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5361, -1, 6580, -1, 4944, -1, 5126, -1], 'generators': [81, 64, 160, 168], 'label': '320.105.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.b1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693269
{'ambient': '320.105', 'aut_centralizer_order': 40, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 160, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.b1.a1', '16.f1.a1', '16.f1.b1', '40.e1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1427, -1, 8319, -1, 1627, -1, 2227, -1], 'generators': [1, 64, 160, 80], 'label': '320.105.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.e1.a1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693270
{'ambient': '320.105', 'aut_centralizer_order': 16, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 64, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1'], 'contains': ['16.b1.a1', '40.f1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [221, -1, 9803, -1, 209, -1, 183, -1], 'generators': [3, 160, 64, 80], 'label': '320.105.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '8.f1.a1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
id: 51693271
{'ambient': '320.105', 'aut_centralizer_order': 20, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.27144', 'aut_weyl_index': 20, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1', '4.e1.a1', '10.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6812, 3140, 4467, 7956, 6130, 6799, 5669, 2667], 'generators': [1, 160, 80, 64, 92, 168], 'label': '320.105.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
id: 51693272
{'ambient': '320.105', 'aut_centralizer_order': 40, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '32.25', 'aut_weyl_index': 160, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.c1.a1', '16.f1.a1', '16.f1.b1', '40.g1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3218, -1, 7588, -1, 4096, -1, 2904, -1], 'generators': [1, 64, 160, 248], 'label': '320.105.8.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.g1.a1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693273
{'ambient': '320.105', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 64, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.d1.a1', '40.h1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9761, -1, 197, -1, 9791, -1, 9817, -1], 'generators': [2, 8, 64, 4], 'label': '320.105.8.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '8.h1.a1', 'projective_image': '160.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': '10.1'}
id: 51693274
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '64.226', 'aut_weyl_index': 80, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.b1.b1', '20.c1.a1', '20.e1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7355, 3687, 4419, 8816, 5769, 8234, 6247, 1910], 'generators': [1, 92, 80], 'label': '320.105.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['20.a1.a1', '20.b1.a1', '20.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '80.19', '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': '16.3'}
id: 51693275
{'ambient': '320.105', 'aut_centralizer_order': 32, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '32.46', 'aut_weyl_index': 160, 'centralizer': '40.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.f1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [9164, -1, 1964, -1, 8158, -1, 8336, -1], 'generators': [2, 80], 'label': '320.105.10.b1.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.b1.a1', 'projective_image': '80.19', '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': '8.3'}
id: 51693276
{'ambient': '320.105', 'aut_centralizer_order': 32, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': 5, 'aut_weyl_group': '32.46', 'aut_weyl_index': 160, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.d1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6353, -1, 4909, -1, 3373, -1, 4963, -1], 'generators': [3, 92], 'label': '320.105.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '80.19', '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': '8.3'}
id: 51693277
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1280, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '80.a1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4872, 6827, 4312, 3132, 5627, 4250, 5975, 6404], 'generators': [168, 64, 160], 'label': '320.105.16.a1.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.b1.a1', '8.a1.a1', '8.c1.a1'], 'normal_contains': ['32.c1.a1', '32.b1.a1', '32.a1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693278
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '16.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['32.a1.a1', '80.b1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [448, 796, 9119, 376, 1571, 1358, 1323, 8851], 'generators': [80, 160, 64], 'label': '320.105.16.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': '160.39', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693279
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '80.c1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1505, 1797, 8650, 1325, 3243, 386, 2430, 9673], 'generators': [248, 160, 64], 'label': '320.105.16.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['32.a1.a1', '80.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': '160.39', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693280
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '16.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.h1.a1'], 'contains': ['32.b1.a1', '80.d1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8878, 9693, 875, 5437, 8870, 9614, 8810, 5227], 'generators': [12, 8, 64], 'label': '320.105.16.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.b1.a1', '80.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': '160.42', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693281
{'ambient': '320.105', 'aut_centralizer_order': 640, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['32.b1.a1', '80.e1.a1'], 'core': '16.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8120, 8260, 1750, 4488, 7604, 8643, 8375, 4404], 'generators': [172, 8, 64], 'label': '320.105.16.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': ['8.b1.a1'], 'normal_contains': ['32.b1.a1', '80.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.e1.a1', 'projective_image': '160.42', 'quotient_action_image': '4.2', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693282
{'ambient': '320.105', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 8, 'centralizer': '40.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '10.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8998, 6121, 2225, 6415, 7729, 3907, 8020, 4003], 'generators': [2, 64, 4, 160, 80, 8], 'label': '320.105.2.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': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.8'}
id: 51693283
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '80.f1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2030, -1, 7433, -1, 4147, -1, 3220, -1], 'generators': [1, 160, 64], 'label': '320.105.16.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.f1.a1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693284
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.e1.a1', '8.g1.a1'], 'contains': ['32.a1.a1', '80.f1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2030, -1, 7903, -1, 4147, -1, 4010, -1], 'generators': [81, 160, 64], 'label': '320.105.16.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.f1.b1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693285
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1'], 'contains': ['32.c1.a1', '80.g1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4119, -1, 2422, -1, 7107, -1, 7269, -1], 'generators': [92, 168, 64], 'label': '320.105.16.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.g1.a1', 'projective_image': '160.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693286
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '20.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6192, 5108, 3106, 6286, 7085, 5905, 7906, 4255], 'generators': [92, 80], 'label': '320.105.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': -10, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.b1.a1', '40.a1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693287
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '20.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 160, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.d1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6710, 3254, 3772, 8106, 5667, 8676, 5758, 1910], 'generators': [1, 92], 'label': '320.105.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.b1.a1', '10.a1.a1'], 'normal_contains': ['40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
id: 51693288
{'ambient': '320.105', 'aut_centralizer_order': 80, 'aut_label': '20.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '32.27', 'aut_weyl_index': 160, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '10.a1.a1'], 'contains': ['40.c1.a1', '40.d1.b1'], 'core': '20.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6710, 3254, 4850, 9096, 5667, 8676, 6667, 1051], 'generators': [81, 92], 'label': '320.105.20.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': ['4.b1.b1', '10.a1.a1'], 'normal_contains': ['40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.b1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
id: 51693289
{'ambient': '320.105', 'aut_centralizer_order': 160, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 320, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.d1.a1', '40.d1.b1', '40.e1.a1', '40.g1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3815, -1, 6622, -1, 3322, -1, 3580, -1], 'generators': [1, 168, 80], 'label': '320.105.20.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '80.19', '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': '8.5'}
id: 51693290
{'ambient': '320.105', 'aut_centralizer_order': 64, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.5', 'aut_weyl_index': 640, 'centralizer': '20.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '40.f1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2317, -1, 9787, -1, 853, -1, 746, -1], 'generators': [3, 168], 'label': '320.105.20.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.c1.a1', 'old_label': '20.d1.a1', 'projective_image': '80.19', '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': '2.1'}
id: 51693291
{'ambient': '320.105', 'aut_centralizer_order': 160, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '16.11', 'aut_weyl_index': 320, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '10.a1.a1'], 'contains': ['40.b1.a1', '40.d1.a1', '40.d1.b1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7260, -1, 5545, -1, 7576, -1, 6212, -1], 'generators': [1, 172], 'label': '320.105.20.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '20.e1.a1', 'projective_image': '80.19', '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': '8.5'}
id: 51693292
{'ambient': '320.105', 'aut_centralizer_order': 64, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.5', 'aut_weyl_index': 640, 'centralizer': '20.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '10.b1.a1'], 'contains': ['40.b1.a1', '40.h1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9404, -1, 812, -1, 9147, -1, 9254, -1], 'generators': [2, 160], 'label': '320.105.20.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '20.f1.a1', 'projective_image': '80.19', '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': '2.1'}
id: 51693293
{'ambient': '320.105', 'aut_centralizer_order': 8, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '640.21483', 'aut_weyl_index': 8, 'centralizer': '40.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '10.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5403, 4767, 5432, 5134, 4192, 5221, 4963, 5114], 'generators': [3, 64, 8, 80, 92, 160], 'label': '320.105.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.8'}
id: 51693294
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '32.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1280, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.c1.a1', '16.f1.a1', '16.f1.b1'], 'contains': ['64.a1.a1', '160.a1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1529, 1797, 7769, 646, 3695, 2097, 3220, 8552], 'generators': [160, 64], 'label': '320.105.32.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.c1.a1', '16.b1.a1'], 'normal_contains': ['64.a1.a1', '160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '160.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693295
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '32.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1280, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.e1.a1'], 'contains': ['64.a1.a1', '160.b1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7313, 7554, 2684, 4145, 7288, 7605, 8217, 6235], 'generators': [8, 64], 'label': '320.105.32.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.e1.a1', '16.d1.a1'], 'normal_contains': ['64.a1.a1', '160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '160.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.12', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693296
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '32.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1280, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '160.c1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4573, 5689, 3965, 3197, 6791, 4250, 6361, 7057], 'generators': [168, 64], 'label': '320.105.32.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '160.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '160.43', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.12', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693297
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '40.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.c1.a1', '20.d1.a1'], 'contains': ['80.a1.a1', '80.b1.a1', '80.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2716, 2298, 9045, 1431, 2610, 2594, 1877, 7805], 'generators': [168, 80], 'label': '320.105.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '80.c1.a1', '80.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.4', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693298
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '40.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1', '20.e1.a1', '20.f1.a1'], 'contains': ['80.a1.a1', '80.d1.a1', '80.e1.a1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8269, 7987, 1713, 6577, 8237, 7406, 7822, 3358], 'generators': [172, 160], 'label': '320.105.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '80.e1.a1', '80.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '80.19', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.4', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693299
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '40.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.a1.a1', '20.b1.a1', '20.b1.b1'], 'contains': ['80.a1.a1', '80.g1.a1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5696, 4278, 3425, 8041, 6475, 5905, 6716, 2088], 'generators': [92, 160], 'label': '320.105.40.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': ['8.c1.a1', '20.a1.a1', '20.b1.a1', '20.b1.b1'], 'normal_contains': ['80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693300
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '20.b1.a1', '20.c1.a1', '20.e1.a1'], 'contains': ['80.a1.a1', '80.f1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6508, -1, 5166, -1, 4780, -1, 4563, -1], 'generators': [1, 168], 'label': '320.105.40.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.d1.a1', 'projective_image': '80.19', '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': '4.2'}
id: 51693301
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '20.b1.b1', '20.c1.a1', '20.e1.a1'], 'contains': ['80.a1.a1', '80.f1.b1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6508, -1, 5891, -1, 4780, -1, 5234, -1], 'generators': [81, 168], 'label': '320.105.40.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '40.d1.b1', 'projective_image': '80.19', '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': '4.2'}
id: 51693302
{'ambient': '320.105', 'aut_centralizer_order': 160, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 640, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '20.c1.a1'], 'contains': ['80.b1.a1', '80.f1.a1', '80.f1.b1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1641, -1, 7610, -1, 2023, -1, 2825, -1], 'generators': [1, 80], 'label': '320.105.40.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '40.e1.a1', 'projective_image': '160.39', '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': '4.2'}
id: 51693303
{'ambient': '320.105', 'aut_centralizer_order': 64, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '20.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '20.d1.a1'], 'contains': ['80.b1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [985, -1, 9803, -1, 853, -1, 746, -1], 'generators': [3], 'label': '320.105.40.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.d1.a1', 'old_label': '40.f1.a1', 'projective_image': '160.39', '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': '1.1'}
id: 51693304
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '16.10', 'aut_weyl_index': 320, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '20.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5086, 4767, 2492, 5651, 6491, 4978, 7704, 4666], 'generators': [92, 64, 168, 80, 160], 'label': '320.105.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normal_contains': ['8.b1.a1', '8.a1.a1', '8.c1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 51693305
{'ambient': '320.105', 'aut_centralizer_order': 160, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 640, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '20.c1.a1'], 'contains': ['80.c1.a1', '80.f1.a1', '80.f1.b1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3367, -1, 7226, -1, 3695, -1, 3615, -1], 'generators': [1, 248], 'label': '320.105.40.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '40.g1.a1', 'projective_image': '160.39', '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': '4.2'}
id: 51693306
{'ambient': '320.105', 'aut_centralizer_order': 64, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1280, 'centralizer': '20.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '20.f1.a1'], 'contains': ['80.d1.a1'], 'core': '80.d1.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9404, -1, 812, -1, 9322, -1, 9254, -1], 'generators': [2], 'label': '320.105.40.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.f1.a1', 'old_label': '40.h1.a1', 'projective_image': '160.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693307
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1280, 'centralizer': '2.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'contains': ['320.a1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3415, 4358, 4792, 2336, 6768, 4250, 6183, 7057], 'generators': [64], 'label': '320.105.64.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.c1.a1', '32.b1.a1', '32.a1.a1'], 'normal_contains': ['320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '320.105', 'quotient_action_image': '2.1', 'quotient_action_kernel': '32.35', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693308
{'ambient': '320.105', 'aut_centralizer_order': 5120, 'aut_label': '80.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1', '40.d1.a1', '40.d1.b1'], 'contains': ['160.a1.a1', '160.b1.a1', '160.c1.a1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5510, 5018, 4472, 2949, 5695, 5188, 5941, 5441], 'generators': [168, 160], 'label': '320.105.80.a1.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.b1.a1', '40.a1.a1', '40.c1.a1'], 'normal_contains': ['160.c1.a1', '160.b1.a1', '160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '80.19', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.19', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693309
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '80.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '40.a1.a1', '40.e1.a1', '40.f1.a1'], 'contains': ['160.a1.a1'], 'core': '80.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1111, 307, 9190, 560, 2023, 2980, 1877, 7805], 'generators': [80], 'label': '320.105.80.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.b1.a1', 'normal_contained_in': ['16.b1.a1', '40.a1.a1'], 'normal_contains': ['160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.b1.a1', 'projective_image': '160.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.6', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693310
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '80.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '40.a1.a1', '40.g1.a1'], 'contains': ['160.a1.a1'], 'core': '80.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1916, 1991, 8591, 1335, 3243, 1214, 2627, 9299], 'generators': [248], 'label': '320.105.80.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1.a1', 'normal_contained_in': ['16.c1.a1', '40.a1.a1'], 'normal_contains': ['160.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.c1.a1', 'projective_image': '160.39', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.4', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693311
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '80.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '40.b1.a1', '40.h1.a1'], 'contains': ['160.b1.a1'], 'core': '80.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8669, 9409, 1072, 5329, 8554, 8488, 8711, 4722], 'generators': [12], 'label': '320.105.80.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.d1.a1', 'normal_contained_in': ['16.d1.a1', '40.b1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.d1.a1', 'projective_image': '160.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.6', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693312
{'ambient': '320.105', 'aut_centralizer_order': 2560, 'aut_label': '80.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '40.b1.a1'], 'contains': ['160.b1.a1'], 'core': '80.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7749, 7987, 1713, 6104, 7740, 6722, 7822, 4050], 'generators': [172], 'label': '320.105.80.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.e1.a1', 'normal_contained_in': ['16.e1.a1', '40.b1.a1'], 'normal_contains': ['160.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.e1.a1', 'projective_image': '160.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.4', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693313
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '8.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '40.d1.a1', '40.e1.a1', '40.g1.a1'], 'contains': ['160.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2472, -1, 7082, -1, 4147, -1, 3615, -1], 'generators': [1], 'label': '320.105.80.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '80.f1.a1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693314
{'ambient': '320.105', 'aut_centralizer_order': 320, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '8.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.b1', '40.d1.b1', '40.e1.a1', '40.g1.a1'], 'contains': ['160.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2472, -1, 7689, -1, 4147, -1, 3970, -1], 'generators': [81], 'label': '320.105.80.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '80.f1.b1', 'projective_image': '160.39', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693315
{'ambient': '320.105', 'aut_centralizer_order': 20, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 40, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '20.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6071, 2219, 3372, 7427, 5034, 6799, 4321, 3125], 'generators': [1, 64, 168, 92, 160], 'label': '320.105.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
id: 51693316
{'ambient': '320.105', 'aut_centralizer_order': 1280, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 2560, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '40.c1.a1'], 'contains': ['160.c1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4902, -1, 3425, -1, 6339, -1, 6756, -1], 'generators': [92], 'label': '320.105.80.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '80.g1.a1', 'projective_image': '160.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 51693317
{'ambient': '320.105', 'aut_centralizer_order': 5120, 'aut_label': '160.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '80.a1.a1', '80.b1.a1', '80.c1.a1', '80.f1.a1', '80.f1.b1'], 'contains': ['320.a1.a1'], 'core': '160.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2197, 1991, 7689, 1335, 3921, 2980, 3615, 7805], 'generators': [160], 'label': '320.105.160.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '160.a1.a1', 'normal_contained_in': ['32.a1.a1', '80.a1.a1', '80.c1.a1', '80.b1.a1'], 'normal_contains': ['320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.a1.a1', 'projective_image': '160.39', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.39', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693318
{'ambient': '320.105', 'aut_centralizer_order': 5120, 'aut_label': '160.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '80.a1.a1', '80.d1.a1', '80.e1.a1'], 'contains': ['320.a1.a1'], 'core': '160.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7313, 6997, 2380, 4413, 7288, 6722, 7822, 5441], 'generators': [8], 'label': '320.105.160.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '160.b1.a1', 'normal_contained_in': ['32.b1.a1', '80.a1.a1', '80.e1.a1', '80.d1.a1'], 'normal_contains': ['320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.b1.a1', 'projective_image': '160.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.42', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693319
{'ambient': '320.105', 'aut_centralizer_order': 5120, 'aut_label': '160.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 5120, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '80.a1.a1', '80.g1.a1'], 'contains': ['320.a1.a1'], 'core': '160.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4788, 5018, 4274, 2949, 6350, 5044, 6538, 6385], 'generators': [168], 'label': '320.105.160.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '160.c1.a1', 'normal_contained_in': ['32.c1.a1', '80.a1.a1'], 'normal_contains': ['320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '160.c1.a1', 'projective_image': '160.43', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.43', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693320
{'ambient': '320.105', 'aut_centralizer_order': None, 'aut_label': '320.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': ['64.a1.a1', '160.a1.a1', '160.b1.a1', '160.c1.a1'], 'contains': [], 'core': '320.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4513, 4676, 4413, 2627, 6576, 4647, 6361, 6721], 'generators': [], 'label': '320.105.320.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '320.a1.a1', 'normal_contained_in': ['64.a1.a1', '160.c1.a1', '160.b1.a1', '160.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '320.a1.a1', 'projective_image': '320.105', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 51693321
{'ambient': '320.105', 'aut_centralizer_order': 20, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 40, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '8.d1.b1', '20.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6071, 2219, 4264, 9624, 5034, 6799, 6889, 696], 'generators': [81, 64, 168, 92, 160], 'label': '320.105.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '20.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
id: 51693322
{'ambient': '320.105', 'aut_centralizer_order': 40, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '64.196', 'aut_weyl_index': 80, 'centralizer': '16.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.g1.a1', '20.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3373, -1, 7118, -1, 4096, -1, 3501, -1], 'generators': [1, 80, 64, 168, 160], 'label': '320.105.4.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
id: 51693323
{'ambient': '320.105', 'aut_centralizer_order': 16, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '160.236', 'aut_weyl_index': 32, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '20.d1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2185, -1, 9531, -1, 1667, -1, 1116, -1], 'generators': [3, 80, 160, 168, 64], 'label': '320.105.4.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.d1.a1', 'projective_image': '80.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
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.