LMFDB - Abstract group data

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

gps_groups • Show schema

{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '800.948', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [12, 4, 4, 8, 8, 20, 20], 'aut_gens': [[1, 2, 16, 160], [1, 11, 185, 1248], [801, 811, 824, 576], [9, 3, 857, 1248], [801, 95, 1016, 1248], [9, 83, 377, 1152], [9, 90, 721, 1504], [9, 2, 312, 1184]], 'aut_group': None, 'aut_hash': 2048208238781551685, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 491520, 'aut_permdeg': 56, 'aut_perms': [661871485034650194783841381935856665153976665324495660539202318636021575193, 647965519063767735608864223846308643204783831595941583907902005565373025676, 670408411410868003556551235787358522300790548438365356069563457017860647168, 671814863551634088814670741516797759690266355583097330458484571241857075588, 101315715449574605870262687623987216497691606097773398080844715524927280227, 166241419330442031358754101333671017505427426314907193327549769365206589892, 113391277619925086428789264834061676289566798197339144072845731239697916898], 'aut_phi_ratio': 768.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 4, 1], [4, 1, 4, 2], [4, 2, 4, 1], [5, 1, 24, 1], [8, 2, 16, 1], [10, 1, 24, 3], [10, 1, 96, 1], [10, 2, 96, 1], [20, 1, 96, 2], [20, 2, 96, 1], [40, 2, 384, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^7.C_2^5.S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 120, 'autcent_group': None, 'autcent_hash': 6144963880117411462, 'autcent_nilpotent': False, 'autcent_order': 245760, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times C_2^5.C_2^3\\times \\GL(2,5)', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [4, 1, 8], [4, 2, 4], [5, 1, 24], [8, 2, 16], [10, 1, 168], [10, 2, 96], [20, 1, 192], [20, 2, 96], [40, 2, 384]], 'center_label': '400.201', 'center_order': 400, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5495, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['32.5', 1], ['5.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [4, 1, 2, 4], [4, 2, 2, 2], [5, 1, 4, 6], [8, 2, 4, 4], [10, 1, 4, 42], [10, 2, 4, 24], [20, 1, 8, 24], [20, 2, 8, 12], [40, 2, 16, 24]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2604, 'exponent': 40, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '200.52', 'hash': 5495, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2, 1], 'inner_gens': [[1, 2, 16, 160], [1, 2, 816, 160], [1, 802, 16, 160], [1, 2, 16, 160]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 800], [2, 200]], 'label': '1600.5495', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C10^2.OD16', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 1000, 'number_divisions': 154, 'number_normal_subgroups': 456, 'number_subgroup_autclasses': 126, 'number_subgroup_classes': 808, 'number_subgroups': 1160, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 15], [4, 16], [5, 24], [8, 32], [10, 360], [20, 384], [40, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 120, 'outer_gen_orders': [12, 4, 4, 8, 8, 20, 20], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 11, 185, 1248], [801, 811, 824, 576], [9, 3, 857, 1248], [801, 95, 1016, 1248], [9, 83, 377, 1152], [9, 90, 721, 1504], [9, 2, 312, 1184]], 'outer_group': None, 'outer_hash': 8904253135100398360, 'outer_nilpotent': False, 'outer_order': 122880, 'outer_permdeg': 2560, 'outer_perms': 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'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^7.C_2^3.S_5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 8, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 54], [8, 48], [16, 36]], 'representations': {'PC': {'code': 103311048191623904324434133043, 'gens': [1, 2, 5, 7], 'pres': [8, -2, -2, -2, -2, -2, -5, -2, -5, 41, 66, 16332, 116, 166]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [681481, 29644075, 30666285, 44811689, 44295681, 6133257, 16016551, 685345]}, 'Perm': {'d': 24, 'gens': [28207315931062913568000, 55083347173188659001600, 55083347173182392064000, 13412044800, 82261660440517189632000, 55083347171874717696000, 1451520, 96]}}, 'schur_multiplier': [2, 2, 2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 40], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}^2.\\OD_{16}', 'transitive_degree': 800, '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: 122395850
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 5495, 'group_order': 1600, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
id: 122395962
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 5495, 'group_order': 1600, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 800, 'size': 1}
id: 122396073
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 5495, 'group_order': 1600, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 808, 'size': 1}
id: 122396184
{'aut_label': '2C', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 5495, 'group_order': 1600, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1, 'size': 1}
id: 122396295
{'aut_label': '2C', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 5495, 'group_order': 1600, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 801, 'size': 1}
id: 122396406
{'aut_label': '2C', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 5495, 'group_order': 1600, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 9, 'size': 1}
id: 122396517
{'aut_label': '2C', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 5495, 'group_order': 1600, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 809, 'size': 1}
id: 122396628
{'aut_label': '2G', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 5495, 'group_order': 1600, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 8, 'size': 1}
id: 122396739
{'aut_label': '2H', 'centralizer': '2.a1', 'counter': 9, 'group_counter': 5495, 'group_order': 1600, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 80, 'size': 2}
id: 122395851
{'aut_label': '2H', 'centralizer': '2.a1', 'counter': 10, 'group_counter': 5495, 'group_order': 1600, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 88, 'size': 2}
id: 122395863
{'aut_label': '2H', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 5495, 'group_order': 1600, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 81, 'size': 2}
id: 122395874
{'aut_label': '2H', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 5495, 'group_order': 1600, 'label': '2K', 'order': 2, 'powers': [1, 12], 'representative': 89, 'size': 2}
id: 122395885
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 13, 'group_counter': 5495, 'group_order': 1600, 'label': '4A1', 'order': 4, 'powers': [8, 13], 'representative': 5, 'size': 1}
id: 122395896
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 14, 'group_counter': 5495, 'group_order': 1600, 'label': '4A-1', 'order': 4, 'powers': [8, 14], 'representative': 13, 'size': 1}
id: 122395907
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{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 982, 'group_counter': 5495, 'group_order': 1600, 'label': '40W-17', 'order': 40, 'powers': [507, 62], 'representative': 703, 'size': 2}
id: 122396832
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 983, 'group_counter': 5495, 'group_order': 1600, 'label': '40W19', 'order': 40, 'powers': [506, 63], 'representative': 471, 'size': 2}
id: 122396833
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 984, 'group_counter': 5495, 'group_order': 1600, 'label': '40W-19', 'order': 40, 'powers': [505, 64], 'representative': 1307, 'size': 2}
id: 122396834
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 985, 'group_counter': 5495, 'group_order': 1600, 'label': '40X1', 'order': 40, 'powers': [513, 61], 'representative': 403, 'size': 2}
id: 122396835
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 986, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-1', 'order': 40, 'powers': [514, 62], 'representative': 1375, 'size': 2}
id: 122396836
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 987, 'group_counter': 5495, 'group_order': 1600, 'label': '40X3', 'order': 40, 'powers': [515, 63], 'representative': 247, 'size': 2}
id: 122396837
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 988, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-3', 'order': 40, 'powers': [516, 64], 'representative': 731, 'size': 2}
id: 122396838
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 989, 'group_counter': 5495, 'group_order': 1600, 'label': '40X7', 'order': 40, 'powers': [517, 62], 'representative': 735, 'size': 2}
id: 122396840
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 990, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-7', 'order': 40, 'powers': [518, 61], 'representative': 243, 'size': 2}
id: 122396841
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 991, 'group_counter': 5495, 'group_order': 1600, 'label': '40X9', 'order': 40, 'powers': [519, 61], 'representative': 1363, 'size': 2}
id: 122396842
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 992, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-9', 'order': 40, 'powers': [520, 62], 'representative': 415, 'size': 2}
id: 122396843
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 993, 'group_counter': 5495, 'group_order': 1600, 'label': '40X11', 'order': 40, 'powers': [520, 63], 'representative': 407, 'size': 2}
id: 122396844
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 994, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-11', 'order': 40, 'powers': [519, 64], 'representative': 1371, 'size': 2}
id: 122396845
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 995, 'group_counter': 5495, 'group_order': 1600, 'label': '40X13', 'order': 40, 'powers': [518, 64], 'representative': 251, 'size': 2}
id: 122396846
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 996, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-13', 'order': 40, 'powers': [517, 63], 'representative': 727, 'size': 2}
id: 122396847
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 997, 'group_counter': 5495, 'group_order': 1600, 'label': '40X17', 'order': 40, 'powers': [516, 61], 'representative': 723, 'size': 2}
id: 122396848
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 998, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-17', 'order': 40, 'powers': [515, 62], 'representative': 255, 'size': 2}
id: 122396849
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 999, 'group_counter': 5495, 'group_order': 1600, 'label': '40X19', 'order': 40, 'powers': [514, 63], 'representative': 1367, 'size': 2}
id: 122395853
{'aut_label': '40A1', 'centralizer': '2.b1', 'counter': 1000, 'group_counter': 5495, 'group_order': 1600, 'label': '40X-19', 'order': 40, 'powers': [513, 64], 'representative': 411, 'size': 2}

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: 7109823
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id: 7109889
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id: 7109900
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id: 7109902
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id: 7109903
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id: 7109904
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id: 7109905
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id: 7109906
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id: 7109907
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id: 7109908
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id: 7109913
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id: 7109914
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id: 7109915
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id: 7109916
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id: 7109917
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id: 7109884
{'cdim': 2, 'counter': 154, 'faithful': False, 'group': '1600.5495', 'group_order': 1600, 'image': None, 'label': '1600.5495.2ap', 'multiplicity': 8, 'nt': [40, 15], 'qdim': 16, 'qvalues': [16, 16, 16, -16, 16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, -4, -4, 16, -4, -4, 16, -4, -4, -4, -4, 16, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 16, -4, -4, -4, 4, -4, 4, 16, 4, -4, -4, 4, -4, 4, 4, -4, 4, -16, 4, 4, -16, 4, -16, 4, 16, -4, 4, -4, -4, 4, -16, -4, -4, -16, -16, -4, -4, 4, 4, -4, -4, -4, -4, 4, -4, -4, -4, 4, -4, 4, 4, -4, 16, -4, -4, -4, 4, 4, 4, 4, 4, 4, 4, -4, -4, 4, 4, -4, 4, 4, 16, -4, 4, -4, 4, -4, 4, 4, 4, -4, -4, 4, 16, 4, 16, -4, 4, 4, 4, 4, -16, -4, -4, 4, -16, -4, 16, 4, 4, 4, 4, 16, 4, 4, 4, -16, 4, -4, -4, -4, -4, -4, 4, -16, -4, -4, 4, 4, -4, 16, -16, 4, -4, 4, 4, -4, -16, -4, 4, 4, -4, 4, 16, 4, 4, -4, -4, 4, -4, 16, 4, 4, 4, 4, 4, -16, 4, -4, -4, 4, 4, -16, -4, 4, 4, -16, 4, -16, 4, 4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}

group 1600.5495 does not appear in gps_char

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: 78017338
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 400, 'characteristic': True, 'core_order': 1600, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '1600.5495.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1600.5495', 'subgroup_hash': 5495, 'subgroup_order': 1600, 'subgroup_tex': 'C_{10}^2.\\OD_{16}', 'supersolvable': True, 'sylow': 0}
id: 78017376
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 800, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '800.1185', 'subgroup_hash': 1185, 'subgroup_order': 800, 'subgroup_tex': 'C_2^2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017387
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 800, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.948', 'subgroup_hash': 948, 'subgroup_order': 800, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 400, 'characteristic': False, 'core_order': 800, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1600.5495.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.367', 'subgroup_hash': 367, 'subgroup_order': 800, 'subgroup_tex': 'C_{10}^2:C_8', 'supersolvable': True, 'sylow': 0}
id: 78017409
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 400, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', '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': '400.221', 'subgroup_hash': 221, 'subgroup_order': 400, 'subgroup_tex': 'C_2^2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017420
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 400, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U1', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.201', 'subgroup_hash': 201, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017431
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 400, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', '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': '400.201', 'subgroup_hash': 201, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017442
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 400, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, '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': '400.201', 'subgroup_hash': 201, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017453
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 400, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.201', 'subgroup_hash': 201, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017339
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 400, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '400.111', 'subgroup_hash': 111, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017350
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 200, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '400.201', 'subgroup_hash': 201, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017361
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 200, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '400.111', 'subgroup_hash': 111, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 400, 'characteristic': False, 'core_order': 320, 'counter': 13, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1600.5495.5.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '320.907', 'subgroup_hash': 907, 'subgroup_order': 320, 'subgroup_tex': 'C_2^3:C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017370
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 200, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', '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': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.52', 'subgroup_hash': 52, 'subgroup_order': 200, 'subgroup_tex': 'C_2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017371
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 200, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.52', 'subgroup_hash': 52, 'subgroup_order': 200, 'subgroup_tex': 'C_2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017372
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 200, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017373
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 200, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017374
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 200, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017375
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 200, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.52', 'subgroup_hash': 52, 'subgroup_order': 200, 'subgroup_tex': 'C_2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017377
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 200, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017378
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.52', 'subgroup_hash': 52, 'subgroup_order': 200, 'subgroup_tex': 'C_2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017379
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.52', 'subgroup_hash': 52, 'subgroup_order': 200, 'subgroup_tex': 'C_2\\times C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017380
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017381
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017382
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '200.37', 'subgroup_hash': 37, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017383
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '200.17', 'subgroup_hash': 17, 'subgroup_order': 200, 'subgroup_tex': 'C_5\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017384
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 160, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.10.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '160.228', 'subgroup_hash': 228, 'subgroup_order': 160, 'subgroup_tex': 'C_2^3\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017385
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 160, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.10.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '160.190', 'subgroup_hash': 190, 'subgroup_order': 160, 'subgroup_tex': 'C_2^2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 400, 'characteristic': False, 'core_order': 160, 'counter': 29, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1600.5495.10.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '10.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '160.48', 'subgroup_hash': 48, 'subgroup_order': 160, 'subgroup_tex': 'C_2^2:C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017388
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 100, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017389
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 100, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017390
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 100, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017391
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 100, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017392
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 100, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017393
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 100, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.f1', 'outer_equivalence': True, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.8', 'subgroup_hash': 8, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017394
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 100, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.8', 'subgroup_hash': 8, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017395
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 50, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017396
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 50, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017397
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 50, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.16', 'subgroup_hash': 16, 'subgroup_order': 100, 'subgroup_tex': 'C_{10}^2', 'supersolvable': True, 'sylow': 0}
id: 78017399
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 50, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.8', 'subgroup_hash': 8, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017400
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 80, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.52', 'subgroup_hash': 52, 'subgroup_order': 80, 'subgroup_tex': 'C_2^3\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017401
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 80, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017402
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 80, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017403
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 80, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017404
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 80, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017405
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 80, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.20.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '20.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '80.23', 'subgroup_hash': 23, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017406
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 40, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.20.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.45', 'subgroup_hash': 45, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 40, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.20.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '20.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '80.23', 'subgroup_hash': 23, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 400, 'characteristic': True, 'core_order': 64, 'counter': 49, 'cyclic': False, 'direct': True, 'hall': 2, 'label': '1600.5495.25.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '25.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '25.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 25, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.87', 'subgroup_hash': 87, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:C_8', 'supersolvable': True, 'sylow': 2}
id: 78017410
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 50, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.36', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017411
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 50, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.37', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017412
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 50, 'counter': 52, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1600.5495.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017413
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 50, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.22', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 22, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017414
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 25, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017415
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 40, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017416
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 40, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017417
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 40, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', '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: 78017418
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 40, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{10}', '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: 78017419
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 40, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', '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: 78017421
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 40, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017422
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 40, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.40.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times 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: 78017423
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.40.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.40.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.14', 'subgroup_hash': 14, 'subgroup_order': 40, 'subgroup_tex': 'C_2^2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017425
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.40.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.40.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017427
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.40.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017428
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.40.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
id: 78017429
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 32, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.50.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '50.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '50.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 50, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017430
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 32, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.50.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '50.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '50.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 50, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': 36, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
id: 78017432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': True, 'centralizer_order': 400, 'characteristic': False, 'core_order': 32, 'counter': 70, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1600.5495.50.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '50.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '50.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 50, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.5', 'subgroup_hash': 5, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:C_8', 'supersolvable': True, 'sylow': 0}
id: 78017433
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 25, 'counter': 71, 'cyclic': False, 'direct': True, 'hall': 5, 'label': '1600.5495.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.87', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 87, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
id: 78017434
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.80.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 78017435
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.80.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.23', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 78017436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 20, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.80.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.23', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 78017437
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.80.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.24', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 24, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times \\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 78017438
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.80.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.21', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 78017439
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 77, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.80.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.21', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_{20}', '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: 78017440
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 20, 'counter': 78, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.80.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '80.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_{10}', '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: 78017441
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 10, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.80.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017443
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 10, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.80.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017444
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 10, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.80.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017445
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 10, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.80.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
id: 78017446
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
id: 78017447
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 16, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017448
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 16, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017449
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 16, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017450
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 16, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017451
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 16, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.100.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '100.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '100.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 100, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 78017452
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.100.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
id: 78017454
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.100.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, '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: 78017455
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 10, 'counter': 91, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '160.190', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 190, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': ['C6'], '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: 78017456
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 10, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.160.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '160.191', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 191, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times \\OD_{16}', '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: 78017457
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 10, 'counter': 93, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1600.5495.160.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '160.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2:C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017458
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 10, 'counter': 94, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.160.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '160.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '160.176', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 176, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 160, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_{20}', '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: 78017459
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 5, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.160.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
id: 78017460
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 78017461
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 8, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 78017462
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 8, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{20}', '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: 78017463
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 8, 'counter': 99, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.52', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 52, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 78017340
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 8, 'counter': 100, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{20}', '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: 78017341
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.17', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 78017342
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 8, 'counter': 102, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.200.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '200.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '200.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 200, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4\\times C_5^2', '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: 78017343
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.200.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 78017344
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.200.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
id: 78017345
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.200.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, '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: 78017346
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.200.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, '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: 78017347
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.200.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, '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: 78017348
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.200.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, '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: 78017349
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 5, 'counter': 109, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1600.5495.320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '320.907', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 907, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:C_{40}', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
id: 78017351
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 4, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.400.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.201', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 201, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017352
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.400.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.111', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 111, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017353
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.400.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.111', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 111, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017354
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.400.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.112', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 112, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\OD_{16}\\times C_5^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017355
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 4, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.5495.400.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.109', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017356
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 4, 'counter': 115, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.400.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.109', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 109, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2:C_4', '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: 78017357
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 4, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.400.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.202', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 202, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_{10}^2', '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: 78017358
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.400.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017359
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 2, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.400.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017360
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.5495.400.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
id: 78017362
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.400.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 400, '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: 78017363
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 2, 'counter': 121, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.800.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '800.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '800.948', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 948, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}\\times C_{40}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], '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: 78017364
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 2, 'counter': 122, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.800.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '800.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '800.949', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 949, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8:C_{10}^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 78017365
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1600.5495.800.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '800.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '800.367', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 367, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2:C_8', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 78017366
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 2, 'counter': 124, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.5495.800.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '800.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '800.934', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 934, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 78017367
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.5495.800.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
id: 78017368
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.5495', 'ambient_counter': 5495, 'ambient_order': 1600, 'ambient_tex': 'C_{10}^2.\\OD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1600.5495.1600.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1600.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1600.5495', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5495, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1600, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}^2.\\OD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'L2', 'D2', 'C8'], '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: 78017338
{'ambient': '1600.5495', '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': '4.b1', 'complements': ['1600.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '5.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1210, 1957, 7699, 6723], 'generators': [1, 320, 800, 80, 4, 8, 2, 32], 'label': '1600.5495.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '5.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '4.2', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017427
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.l1', '20.e1', '20.g1'], 'contains': ['80.g1', '80.j1', '80.k1', '200.l1'], 'core': '80.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [2937, -1, 6316, -1], 'generators': [81, 320, 8, 4], 'label': '1600.5495.40.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.l1', 'projective_image': '80.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017339
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '4.f1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '3840.x', 'aut_weyl_index': 128, 'centralizer': '2.b1', 'complements': ['400.i1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.d1', '8.m1', '20.f1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [1522, 1565, 8012, 7133], 'generators': [3, 8, 32, 320, 800, 4], 'label': '1600.5495.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.d1', '20.f1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017340
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '200.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['40.e1', '100.c1', '100.d1', '100.e1'], 'contains': ['400.a1', '400.k1'], 'core': '200.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [4159, 4370, 6631, 6964], 'generators': [85, 800], 'label': '1600.5495.200.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '200.e1', 'normal_contained_in': ['40.e1', '100.c1', '100.d1', '100.e1'], 'normal_contains': ['400.a1'], 'normalizer': '1.a1', 'old_label': '200.e1', 'projective_image': '400.201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '100.16', 'quotient_action_kernel_order': 100, 'quotient_fusion': None, 'short_label': '200.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017341
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': ['8.m1'], 'conjugacy_class_count': 4, 'contained_in': ['40.f1', '100.a1'], 'contains': ['400.b1', '400.c1', '400.i1'], 'core': '200.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [8086, 7446, 3489, 3734], 'generators': [1, 80, 800], 'label': '1600.5495.200.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '200.f1', 'normal_contained_in': ['40.f1', '100.a1'], 'normal_contains': ['400.b1', '400.c1'], 'normalizer': '1.a1', 'old_label': '200.f1', 'projective_image': '400.111', 'quotient_action_image': '2.1', 'quotient_action_kernel': '100.8', 'quotient_action_kernel_order': 100, 'quotient_fusion': None, 'short_label': '200.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017342
{'ambient': '1600.5495', 'aut_centralizer_order': 30720, 'aut_label': '200.g1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['40.g1', '100.b1', '100.g1', '100.h1'], 'contains': ['400.e1', '400.f1', '400.g1'], 'core': '200.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [1835, 1903, 7701, 7900], 'generators': [1, 4], 'label': '1600.5495.200.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '200.g1', 'normal_contained_in': ['40.g1', '100.b1'], 'normal_contains': ['400.e1', '400.f1', '400.g1'], 'normalizer': '1.a1', 'old_label': '200.g1', 'projective_image': '200.38', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.38', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017343
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.h1', '100.a1'], 'contains': ['400.d1', '400.h1', '400.i1'], 'core': '400.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [7352, -1, 3312, -1], 'generators': [1, 808, 80], 'label': '1600.5495.200.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '200.h1', 'projective_image': '400.112', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017344
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.i1', '100.a1', '100.g1'], 'contains': ['400.e1', '400.i1', '400.j1'], 'core': '400.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [5521, -1, 5075, -1], 'generators': [1, 8, 80], 'label': '1600.5495.200.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '200.i1', 'projective_image': '400.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017345
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.3', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.j1', '100.c1', '100.g1'], 'contains': ['400.e1', '400.k1'], 'core': '400.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [4675, -1, 6044, -1], 'generators': [1, 84], 'label': '1600.5495.200.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '200.j1', 'projective_image': '400.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017346
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.k1', '100.d1', '100.g1'], 'contains': ['400.f1', '400.j1', '400.k1'], 'core': '400.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [3801, -1, 6338, -1], 'generators': [5, 80], 'label': '1600.5495.200.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '200.k1', 'projective_image': '400.109', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017347
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.l1', '100.e1', '100.g1'], 'contains': ['400.g1', '400.j1', '400.k1'], 'core': '400.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [2761, -1, 7115, -1], 'generators': [81, 4], 'label': '1600.5495.200.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '200.l1', 'projective_image': '400.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017348
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '200.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.m1', '100.f1', '100.h1'], 'contains': ['400.g1'], 'core': '400.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [854, -1, 9458, -1], 'generators': [3], 'label': '1600.5495.200.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '100.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '200.m1', 'projective_image': '400.202', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017349
{'ambient': '1600.5495', 'aut_centralizer_order': 20480, 'aut_label': '320.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': ['5.a1'], 'conjugacy_class_count': 6, 'contained_in': ['64.a1', '160.a1', '160.b1', '160.c1', '160.d1', '160.e1'], 'contains': ['1600.a1'], 'core': '320.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8988, 8435, 2761, 3160], 'generators': [320], 'label': '1600.5495.320.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '320.a1', 'normal_contained_in': ['64.a1', '160.a1', '160.b1', '160.c1', '160.d1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '320.a1', 'projective_image': '320.907', 'quotient_action_image': '1.1', 'quotient_action_kernel': '320.907', 'quotient_action_kernel_order': 320, 'quotient_fusion': None, 'short_label': '320.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017350
{'ambient': '1600.5495', 'aut_centralizer_order': 8, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '7680.h', 'aut_weyl_index': 64, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['8.g1', '8.i1', '8.j1', '8.k1', '8.l1', '20.g1'], 'core': '8.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [4497, -1, 4130, -1], 'generators': [1, 8, 80, 32, 4, 320], 'label': '1600.5495.4.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.g1', 'projective_image': '8.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017351
{'ambient': '1600.5495', 'aut_centralizer_order': 491520, 'aut_label': '400.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['80.a1', '200.a1', '200.b1', '200.c1', '200.d1', '200.e1'], 'contains': ['800.a1', '800.b1', '800.d1'], 'core': '400.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4927, 5139, 5429, 5919], 'generators': [8, 800], 'label': '1600.5495.400.a1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '400.a1', 'normal_contained_in': ['80.a1', '200.a1', '200.b1', '200.c1', '200.d1', '200.e1'], 'normal_contains': ['800.a1', '800.b1', '800.d1'], 'normalizer': '1.a1', 'old_label': '400.a1', 'projective_image': '400.201', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.201', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017352
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '400.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['80.b1', '200.a1', '200.f1'], 'contains': ['800.a1', '800.c1'], 'core': '400.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8711, 7442, 3666, 3886], 'generators': [1, 800], 'label': '1600.5495.400.b1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '400.b1', 'normal_contained_in': ['80.b1', '200.a1', '200.f1'], 'normal_contains': ['800.a1', '800.c1'], 'normalizer': '1.a1', 'old_label': '400.b1', 'projective_image': '400.111', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.111', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017353
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '400.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '2.a1', 'complements': ['4.h1'], 'conjugacy_class_count': 4, 'contained_in': ['80.c1', '200.b1', '200.f1'], 'contains': ['800.a1', '800.e1'], 'core': '400.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [8109, 7763, 3843, 4167], 'generators': [81, 800], 'label': '1600.5495.400.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '400.c1', 'normal_contained_in': ['80.c1', '200.b1', '200.f1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '400.c1', 'projective_image': '800.948', 'quotient_action_image': '2.1', 'quotient_action_kernel': '200.37', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '400.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017354
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '400.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['80.d1', '200.a1', '200.h1'], 'contains': ['800.b1', '800.c1'], 'core': '400.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [7458, 6971, 3135, 3603], 'generators': [1, 808], 'label': '1600.5495.400.d1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '400.d1', 'normal_contained_in': ['80.d1', '200.a1'], 'normal_contains': ['800.b1', '800.c1'], 'normalizer': '1.a1', 'old_label': '400.d1', 'projective_image': '400.112', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.112', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017355
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '400.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['80.e1', '200.a1', '200.g1', '200.i1', '200.j1'], 'contains': ['800.c1', '800.d1'], 'core': '400.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [5579, 5461, 5075, 5636], 'generators': [1, 8], 'label': '1600.5495.400.e1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '400.e1', 'normal_contained_in': ['80.e1', '200.a1', '200.g1'], 'normal_contains': ['800.c1', '800.d1'], 'normalizer': '1.a1', 'old_label': '400.e1', 'projective_image': '400.109', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.109', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017356
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '400.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['80.f1', '200.c1', '200.g1', '200.k1'], 'contains': ['800.d1'], 'core': '400.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [3413, 3221, 6338, 6634], 'generators': [5], 'label': '1600.5495.400.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '400.f1', 'normal_contained_in': ['80.f1', '200.c1', '200.g1'], 'normal_contains': ['800.d1'], 'normalizer': '1.a1', 'old_label': '400.f1', 'projective_image': '400.109', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.109', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017357
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '400.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['80.g1', '200.d1', '200.g1', '200.l1', '200.m1'], 'contains': ['800.d1'], 'core': '400.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [2017, 2103, 7408, 7239], 'generators': [4], 'label': '1600.5495.400.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '400.g1', 'normal_contained_in': ['80.g1', '200.d1', '200.g1'], 'normal_contains': ['800.d1'], 'normalizer': '1.a1', 'old_label': '400.g1', 'projective_image': '400.202', 'quotient_action_image': '1.1', 'quotient_action_kernel': '400.202', 'quotient_action_kernel_order': 400, 'quotient_fusion': None, 'short_label': '400.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017358
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '400.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.h1', '200.b1', '200.h1'], 'contains': ['800.b1', '800.e1'], 'core': '800.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7241, -1, 3312, -1], 'generators': [81, 808], 'label': '1600.5495.400.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '200.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '400.h1', 'projective_image': '800.949', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017359
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '400.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['80.i1', '200.f1', '200.h1', '200.i1'], 'contains': ['800.c1', '800.e1'], 'core': '800.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [7822, -1, 3489, -1], 'generators': [1, 80], 'label': '1600.5495.400.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '200.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '400.i1', 'projective_image': '800.367', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017360
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '400.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.j1', '200.b1', '200.i1', '200.k1', '200.l1'], 'contains': ['800.d1', '800.e1'], 'core': '800.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [5144, -1, 5252, -1], 'generators': [81, 8], 'label': '1600.5495.400.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '200.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '400.j1', 'projective_image': '800.934', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017361
{'ambient': '1600.5495', 'aut_centralizer_order': 8, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '7680.h', 'aut_weyl_index': 64, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1'], 'contains': ['8.g1', '8.m1', '20.h1'], 'core': '8.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [896, -1, 7602, -1], 'generators': [1, 8, 32, 320, 2, 4], 'label': '1600.5495.4.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.h1', 'projective_image': '8.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017362
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '400.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 245760, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.k1', '200.e1', '200.j1', '200.k1', '200.l1'], 'contains': ['800.d1'], 'core': '800.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [4165, -1, 6113, -1], 'generators': [85], 'label': '1600.5495.400.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '200.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '400.k1', 'projective_image': '800.934', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017363
{'ambient': '1600.5495', 'aut_centralizer_order': 491520, 'aut_label': '800.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['160.a1', '400.a1', '400.b1', '400.c1'], 'contains': ['1600.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8109, 7537, 3722, 4099], 'generators': [800], 'label': '1600.5495.800.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '800.a1', 'normal_contained_in': ['160.a1', '400.a1', '400.b1', '400.c1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '800.a1', 'projective_image': '800.948', 'quotient_action_image': '1.1', 'quotient_action_kernel': '800.948', 'quotient_action_kernel_order': 800, 'quotient_fusion': None, 'short_label': '800.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017364
{'ambient': '1600.5495', 'aut_centralizer_order': 491520, 'aut_label': '800.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['160.b1', '400.a1', '400.d1', '400.h1'], 'contains': ['1600.a1'], 'core': '800.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7241, 6971, 3256, 3851], 'generators': [808], 'label': '1600.5495.800.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '800.b1', 'normal_contained_in': ['160.b1', '400.a1', '400.d1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '800.b1', 'projective_image': '800.949', 'quotient_action_image': '1.1', 'quotient_action_kernel': '800.949', 'quotient_action_kernel_order': 800, 'quotient_fusion': None, 'short_label': '800.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017365
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '800.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '1.a1', 'complements': ['2.c1'], 'conjugacy_class_count': 4, 'contained_in': ['160.c1', '400.b1', '400.d1', '400.e1', '400.i1'], 'contains': ['1600.a1'], 'core': '800.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7898, 7254, 3411, 3603], 'generators': [1], 'label': '1600.5495.800.c1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '800.c1', 'normal_contained_in': ['160.c1', '400.b1', '400.d1', '400.e1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '800.c1', 'projective_image': '800.367', 'quotient_action_image': '1.1', 'quotient_action_kernel': '800.367', 'quotient_action_kernel_order': 800, 'quotient_fusion': None, 'short_label': '800.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017366
{'ambient': '1600.5495', 'aut_centralizer_order': 491520, 'aut_label': '800.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['160.d1', '400.a1', '400.e1', '400.f1', '400.g1', '400.j1', '400.k1'], 'contains': ['1600.a1'], 'core': '800.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [5035, 5300, 5340, 5777], 'generators': [8], 'label': '1600.5495.800.d1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '800.d1', 'normal_contained_in': ['160.d1', '400.a1', '400.e1', '400.f1', '400.g1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '800.d1', 'projective_image': '800.934', 'quotient_action_image': '1.1', 'quotient_action_kernel': '800.934', 'quotient_action_kernel_order': 800, 'quotient_fusion': None, 'short_label': '800.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017367
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '800.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 491520, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.e1', '400.c1', '400.h1', '400.i1', '400.j1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7708, -1, 3566, -1], 'generators': [81], 'label': '1600.5495.800.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '400.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '800.e1', 'projective_image': '1600.5495', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017368
{'ambient': '1600.5495', 'aut_centralizer_order': None, 'aut_label': '1600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['320.a1', '800.a1', '800.b1', '800.c1', '800.d1', '800.e1'], 'contains': [], 'core': '1600.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7804, 7254, 3489, 3851], 'generators': [], 'label': '1600.5495.1600.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1600.a1', 'normal_contained_in': ['320.a1', '800.a1', '800.b1', '800.c1', '800.d1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1600.a1', 'projective_image': '1600.5495', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1600.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017369
{'ambient': '1600.5495', 'aut_centralizer_order': 20, 'aut_label': '5.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': None, 'aut_weyl_index': 120, 'centralizer': '4.b1', 'complements': ['320.a1'], 'conjugacy_class_count': 6, 'contained_in': ['1.a1'], 'contains': ['10.a1', '10.b1', '10.c1', '25.a1'], 'core': '5.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [260, 471, 8474, 7958], 'generators': [1, 800, 80, 320, 2, 8, 4], 'label': '1600.5495.5.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['10.a1', '10.b1', '10.c1', '25.a1'], 'normalizer': '1.a1', 'old_label': '5.a1', 'projective_image': '20.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '5.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017370
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['16.a1', '16.b1', '16.d1', '16.e1', '40.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7300, 7184, 2043, 1271], 'generators': [1, 800, 32, 8, 320], 'label': '1600.5495.8.a1', 'mobius_quo': -40, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['16.a1', '16.b1', '16.d1', '16.e1', '40.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '8.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017371
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.c1', '16.h1', '16.j1', '40.b1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6329, 6462, 2440, 1904], 'generators': [81, 800, 32, 8, 320], 'label': '1600.5495.8.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.c1', '40.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017372
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '8.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.d1'], 'contains': ['16.a1', '16.f1', '40.c1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3629, 4637, 4881, 3834], 'generators': [5, 32, 320, 800, 8], 'label': '1600.5495.8.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.d1'], 'normal_contains': ['16.a1', '16.f1', '40.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '8.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017373
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '8.d1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.e1', '4.f1'], 'contains': ['16.a1', '16.g1', '40.d1'], 'core': '8.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2294, 2531, 6892, 5774], 'generators': [4, 32, 320, 800, 8], 'label': '1600.5495.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1', '4.e1', '4.f1'], 'normal_contains': ['16.a1', '16.g1', '40.d1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '8.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017374
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '8.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.k1', '40.e1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [5233, 5578, 4061, 3180], 'generators': [85, 32, 320, 800, 8], 'label': '1600.5495.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '40.e1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '16.10', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017375
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.f1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '3840.g', 'aut_weyl_index': 128, 'centralizer': '2.a1', 'complements': ['200.m1'], 'conjugacy_class_count': 4, 'contained_in': ['4.a1'], 'contains': ['16.b1', '16.c1', '16.i1', '40.f1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [8787, 8462, 1039, 638], 'generators': [1, 800, 32, 80, 320], 'label': '1600.5495.8.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.b1', '16.c1', '40.f1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '16.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017376
{'ambient': '1600.5495', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.g1', '10.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3447, 3648, 4989, 4804], 'generators': [1, 320, 80, 800, 4, 8, 32], 'label': '1600.5495.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '10.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017377
{'ambient': '1600.5495', 'aut_centralizer_order': 64, 'aut_label': '8.g1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.g1', '4.h1'], 'contains': ['16.e1', '16.f1', '16.g1', '40.g1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [3128, 3743, 5688, 4487], 'generators': [1, 32, 320, 4, 8], 'label': '1600.5495.8.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': ['4.b1'], 'normal_contains': ['16.e1', '16.f1', '16.g1', '40.g1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '8.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017378
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3840.g', 'aut_weyl_index': 128, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1'], 'contains': ['16.d1', '16.h1', '16.i1', '40.h1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [7785, -1, 569, -1], 'generators': [1, 880, 32, 808, 320], 'label': '1600.5495.8.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.h1', 'projective_image': '16.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017379
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3840.g', 'aut_weyl_index': 128, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.g1'], 'contains': ['16.e1', '16.i1', '16.j1', '40.i1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [6814, -1, 1646, -1], 'generators': [1, 80, 32, 8, 320], 'label': '1600.5495.8.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.i1', 'projective_image': '16.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017380
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '3840.g', 'aut_weyl_index': 128, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '4.g1'], 'contains': ['16.e1', '16.k1', '40.j1'], 'core': '16.e1', 'coset_action_label': None, 'count': 4, 'diagramx': [5735, -1, 3241, -1], 'generators': [1, 32, 320, 84, 8], 'label': '1600.5495.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.j1', 'projective_image': '16.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017381
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.g1'], 'contains': ['16.f1', '16.j1', '16.k1', '40.k1'], 'core': '16.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [4632, -1, 3651, -1], 'generators': [5, 32, 320, 80, 8], 'label': '1600.5495.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.k1', 'projective_image': '16.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017382
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.g1'], 'contains': ['16.g1', '16.j1', '16.k1', '40.l1'], 'core': '16.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [4130, -1, 4471, -1], 'generators': [81, 32, 320, 4, 8], 'label': '1600.5495.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '8.l1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017383
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1920.240757', 'aut_weyl_index': 256, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '4.h1'], 'contains': ['16.g1', '40.m1'], 'core': '16.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [1558, -1, 8407, -1], 'generators': [3, 320, 4, 32, 8], 'label': '1600.5495.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.m1', 'projective_image': '16.11', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017384
{'ambient': '1600.5495', 'aut_centralizer_order': 160, 'aut_label': '10.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '512.7532443', 'aut_weyl_index': 960, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '5.a1'], 'contains': ['20.a1', '20.b1', '20.c1', '20.d1', '20.e1', '20.g1', '50.a1'], 'core': '10.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2334, 2385, 6489, 6489], 'generators': [1, 8, 80, 800, 4, 320], 'label': '1600.5495.10.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1', 'normal_contained_in': ['2.a1', '5.a1'], 'normal_contains': ['20.a1', '20.b1', '20.c1', '20.d1', '20.e1', '50.a1'], 'normalizer': '1.a1', 'old_label': '10.a1', 'projective_image': '20.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017385
{'ambient': '1600.5495', 'aut_centralizer_order': 160, 'aut_label': '10.b1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '256.27015', 'aut_weyl_index': 1920, 'centralizer': '2.b1', 'complements': ['160.e1'], 'conjugacy_class_count': 12, 'contained_in': ['2.b1', '5.a1'], 'contains': ['20.b1', '20.f1', '20.h1', '50.b1'], 'core': '10.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [402, 471, 8822, 8512], 'generators': [1, 8, 800, 320, 2, 4], 'label': '1600.5495.10.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1', 'normal_contained_in': ['2.b1', '5.a1'], 'normal_contains': ['20.b1', '20.f1', '50.b1'], 'normalizer': '1.a1', 'old_label': '10.b1', 'projective_image': '20.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017386
{'ambient': '1600.5495', 'aut_centralizer_order': 80, 'aut_label': '10.c1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '256.27015', 'aut_weyl_index': 1920, 'centralizer': '4.b1', 'complements': ['160.e1', '160.c1'], 'conjugacy_class_count': 24, 'contained_in': ['2.c1', '5.a1'], 'contains': ['20.e1', '20.f1', '50.c1'], 'core': '10.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [993, 1201, 8420, 7872], 'generators': [81, 8, 320, 4, 2, 800], 'label': '1600.5495.10.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.c1', 'normal_contained_in': ['2.c1', '5.a1'], 'normal_contains': ['20.e1', '20.f1', '50.c1'], 'normalizer': '1.a1', 'old_label': '10.c1', 'projective_image': '40.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017387
{'ambient': '1600.5495', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '2.b1', 'complements': ['800.e1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.f1', '4.h1', '10.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [896, 1491, 7956, 7133], 'generators': [1, 4, 800, 32, 2, 8, 320], 'label': '1600.5495.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.f1', '10.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017388
{'ambient': '1600.5495', 'aut_centralizer_order': 1024, 'aut_label': '16.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'contains': ['32.a1', '32.b1', '32.d1', '80.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6716, 7469, 2541, 2293], 'generators': [8, 32, 320, 800], 'label': '1600.5495.16.a1', 'mobius_quo': 10, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1'], 'normal_contains': ['32.a1', '32.b1', '32.d1', '80.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '16.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017389
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '16.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.f1'], 'contains': ['32.a1', '32.c1', '80.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9349, 9039, 804, 531], 'generators': [1, 32, 320, 800], 'label': '1600.5495.16.b1', 'mobius_quo': 10, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.f1'], 'normal_contains': ['32.a1', '32.c1', '80.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '16.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.5', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017390
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': ['100.h1'], 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '8.f1'], 'contains': ['32.a1', '32.e1', '80.c1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [8647, 8611, 1039, 906], 'generators': [81, 32, 320, 800], 'label': '1600.5495.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.f1'], 'normal_contains': ['32.a1', '80.c1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '32.36', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017391
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '16.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.h1'], 'contains': ['32.b1', '32.c1', '80.d1'], 'core': '16.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [8072, 7905, 98, 157], 'generators': [801, 32, 320, 808], 'label': '1600.5495.16.d1', 'mobius_quo': 10, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.a1'], 'normal_contains': ['32.b1', '32.c1', '80.d1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '16.6', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.6', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017392
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '16.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.g1', '8.i1', '8.j1'], 'contains': ['32.c1', '32.d1', '80.e1'], 'core': '16.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [7278, 7042, 2071, 1918], 'generators': [1, 32, 320, 8], 'label': '1600.5495.16.e1', 'mobius_quo': 10, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.a1', '8.g1'], 'normal_contains': ['32.c1', '32.d1', '80.e1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '16.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017393
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '16.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.g1', '8.k1'], 'contains': ['32.d1', '80.f1'], 'core': '16.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [4366, 4735, 4557, 4312], 'generators': [5, 320, 8, 32], 'label': '1600.5495.16.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.f1', 'normal_contained_in': ['8.c1', '8.g1'], 'normal_contains': ['32.d1', '80.f1'], 'normalizer': '1.a1', 'old_label': '16.f1', 'projective_image': '16.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.3', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017394
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '16.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.g1', '8.l1', '8.m1'], 'contains': ['32.d1', '80.g1'], 'core': '16.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [3379, 3793, 5964, 4873], 'generators': [4, 320, 8, 32], 'label': '1600.5495.16.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.g1', 'normal_contained_in': ['8.d1', '8.g1'], 'normal_contains': ['32.d1', '80.g1'], 'normalizer': '1.a1', 'old_label': '16.g1', 'projective_image': '16.11', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.11', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017395
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.h1'], 'contains': ['32.b1', '32.e1', '80.h1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7785, -1, 333, -1], 'generators': [881, 32, 320, 808], 'label': '1600.5495.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.h1', 'projective_image': '32.37', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017396
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.f1', '8.h1', '8.i1'], 'contains': ['32.c1', '32.e1', '80.i1'], 'core': '32.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [8943, -1, 569, -1], 'generators': [1, 32, 320, 80], 'label': '1600.5495.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.i1', 'projective_image': '32.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017397
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.i1', '8.k1', '8.l1'], 'contains': ['32.d1', '32.e1', '80.j1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [6428, -1, 2306, -1], 'generators': [81, 32, 320, 8], 'label': '1600.5495.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.j1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017398
{'ambient': '1600.5495', 'aut_centralizer_order': 4, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '4.b1', 'complements': ['800.e1', '800.c1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '10.c1'], 'core': '2.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1522, 2420, 7445, 6318], 'generators': [81, 800, 32, 320, 2, 8, 4], 'label': '1600.5495.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '10.c1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017399
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '960.5693', 'aut_weyl_index': 512, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.j1', '8.k1', '8.l1'], 'contains': ['32.d1', '80.k1'], 'core': '32.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [5199, -1, 4205, -1], 'generators': [85, 320, 8, 32], 'label': '1600.5495.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '16.k1', 'projective_image': '32.22', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017400
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '20.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 3840, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '10.a1'], 'contains': ['40.a1', '40.b1', '40.f1', '40.h1', '40.i1', '100.a1'], 'core': '20.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5977, 5795, 2837, 2537], 'generators': [1, 80, 800, 8, 320], 'label': '1600.5495.20.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1', 'normal_contained_in': ['4.a1', '10.a1'], 'normal_contains': ['40.a1', '40.b1', '40.f1', '100.a1'], 'normalizer': '1.a1', 'old_label': '20.a1', 'projective_image': '40.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017401
{'ambient': '1600.5495', 'aut_centralizer_order': 1280, 'aut_label': '20.b1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '64.260', 'aut_weyl_index': 7680, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '10.a1', '10.b1'], 'contains': ['40.a1', '40.c1', '40.d1', '40.g1', '100.b1'], 'core': '20.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1885, 2162, 7693, 7683], 'generators': [1, 800, 320, 4, 8], 'label': '1600.5495.20.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.b1', 'normal_contained_in': ['4.b1', '10.a1', '10.b1'], 'normal_contains': ['40.a1', '40.c1', '40.d1', '40.g1', '100.b1'], 'normalizer': '1.a1', 'old_label': '20.b1', 'projective_image': '20.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '20.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017402
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '20.c1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '128.1031', 'aut_weyl_index': 3840, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '10.a1'], 'contains': ['40.a1', '40.e1', '40.j1', '100.c1'], 'core': '20.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [4914, 4924, 5284, 5131], 'generators': [1, 800, 320, 84, 8], 'label': '1600.5495.20.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.c1', 'normal_contained_in': ['4.c1', '10.a1'], 'normal_contains': ['40.a1', '40.e1', '100.c1'], 'normalizer': '1.a1', 'old_label': '20.c1', 'projective_image': '40.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017403
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '20.d1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '64.260', 'aut_weyl_index': 7680, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['4.d1', '10.a1'], 'contains': ['40.b1', '40.c1', '40.e1', '40.k1', '100.d1'], 'core': '20.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [3872, 3904, 6489, 6417], 'generators': [5, 800, 320, 80, 8], 'label': '1600.5495.20.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.d1', 'normal_contained_in': ['4.d1', '10.a1'], 'normal_contains': ['40.b1', '40.c1', '40.e1', '100.d1'], 'normalizer': '1.a1', 'old_label': '20.d1', 'projective_image': '40.9', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017404
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '20.e1', 'aut_quo_index': 3, 'aut_stab_index': 12, 'aut_weyl_group': '64.260', 'aut_weyl_index': 7680, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['4.e1', '10.a1', '10.c1'], 'contains': ['40.b1', '40.d1', '40.e1', '40.l1', '100.e1'], 'core': '20.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [2370, 2884, 7296, 7050], 'generators': [81, 800, 320, 4, 8], 'label': '1600.5495.20.e1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.e1', 'normal_contained_in': ['4.e1', '10.a1', '10.c1'], 'normal_contains': ['40.b1', '40.d1', '40.e1', '100.e1'], 'normalizer': '1.a1', 'old_label': '20.e1', 'projective_image': '40.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017405
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '20.f1', 'aut_quo_index': 3, 'aut_stab_index': 24, 'aut_weyl_group': '32.45', 'aut_weyl_index': 15360, 'centralizer': '2.b1', 'complements': ['80.i1'], 'conjugacy_class_count': 24, 'contained_in': ['4.f1', '10.b1', '10.c1'], 'contains': ['40.d1', '40.m1', '100.f1'], 'core': '20.f1', 'coset_action_label': None, 'count': 24, 'diagramx': [1126, 1181, 9111, 8822], 'generators': [3, 320, 4, 800, 8], 'label': '1600.5495.20.f1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.f1', 'normal_contained_in': ['4.f1', '10.b1', '10.c1'], 'normal_contains': ['40.d1', '100.f1'], 'normalizer': '1.a1', 'old_label': '20.f1', 'projective_image': '40.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '20.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017406
{'ambient': '1600.5495', 'aut_centralizer_order': 160, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '64.196', 'aut_weyl_index': 7680, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.g1', '10.a1'], 'contains': ['40.g1', '40.i1', '40.j1', '40.k1', '40.l1', '100.g1'], 'core': '40.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [3057, -1, 6091, -1], 'generators': [1, 80, 320, 4, 8], 'label': '1600.5495.20.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '20.g1', 'projective_image': '40.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017407
{'ambient': '1600.5495', 'aut_centralizer_order': 160, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '64.196', 'aut_weyl_index': 7680, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['4.h1', '10.b1'], 'contains': ['40.g1', '40.m1', '100.h1'], 'core': '40.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [592, -1, 8759, -1], 'generators': [1, 320, 4, 2, 8], 'label': '1600.5495.20.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '10.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '20.h1', 'projective_image': '40.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017408
{'ambient': '1600.5495', 'aut_centralizer_order': 480, 'aut_label': '25.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1024.dia', 'aut_weyl_index': 480, 'centralizer': '4.b1', 'complements': ['64.a1'], 'conjugacy_class_count': 1, 'contained_in': ['5.a1'], 'contains': ['50.a1', '50.b1', '50.c1'], 'core': '25.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [523, 333, 9346, 9211], 'generators': [1, 2, 80], 'label': '1600.5495.25.a1', 'mobius_quo': 0, 'mobius_sub': 5, 'normal_closure': '25.a1', 'normal_contained_in': ['5.a1'], 'normal_contains': ['50.a1', '50.b1', '50.c1'], 'normalizer': '1.a1', 'old_label': '25.a1', 'projective_image': '100.16', 'quotient_action_image': '1.1', 'quotient_action_kernel': '25.2', 'quotient_action_kernel_order': 25, 'quotient_fusion': None, 'short_label': '25.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017409
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '15360.d', 'aut_weyl_index': 32, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.b1', '8.f1', '8.h1', '8.i1', '20.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6814, 6650, 2043, 1904], 'generators': [1, 320, 80, 800, 8, 32], 'label': '1600.5495.4.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.b1', '8.f1', '20.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017428
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.m1', '20.f1', '20.h1'], 'contains': ['80.g1', '200.m1'], 'core': '80.g1', 'coset_action_label': None, 'count': 48, 'diagramx': [1204, -1, 9337, -1], 'generators': [3, 4, 8, 320], 'label': '1600.5495.40.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '40.m1', 'projective_image': '80.46', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017410
{'ambient': '1600.5495', 'aut_centralizer_order': 1024, 'aut_label': '32.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1'], 'contains': ['64.a1', '160.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9310, 9726, 1287, 1629], 'generators': [800, 320, 32], 'label': '1600.5495.32.a1', 'mobius_quo': -5, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['64.a1', '160.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '32.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.36', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017411
{'ambient': '1600.5495', 'aut_centralizer_order': 1024, 'aut_label': '32.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.d1', '16.h1'], 'contains': ['64.a1', '160.b1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8144, 7917, 232, 1068], 'generators': [808, 320, 32], 'label': '1600.5495.32.b1', 'mobius_quo': -5, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.d1'], 'normal_contains': ['64.a1', '160.b1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '32.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.37', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017412
{'ambient': '1600.5495', 'aut_centralizer_order': 256, 'aut_label': '32.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': ['50.c1'], 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '16.d1', '16.e1', '16.i1'], 'contains': ['64.a1', '160.c1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9740, 9086, 584, 507], 'generators': [1, 320, 32], 'label': '1600.5495.32.c1', 'mobius_quo': -5, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.b1', '16.d1', '16.e1'], 'normal_contains': ['64.a1', '160.c1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '32.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.5', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017413
{'ambient': '1600.5495', 'aut_centralizer_order': 1024, 'aut_label': '32.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.e1', '16.f1', '16.g1', '16.j1', '16.k1'], 'contains': ['64.a1', '160.d1'], 'core': '32.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6817, 6976, 3754, 4157], 'generators': [8, 320, 32], 'label': '1600.5495.32.d1', 'mobius_quo': -5, 'mobius_sub': 0, 'normal_closure': '32.d1', 'normal_contained_in': ['16.a1', '16.e1', '16.f1', '16.g1'], 'normal_contains': ['64.a1', '160.d1'], 'normalizer': '1.a1', 'old_label': '32.d1', 'projective_image': '32.22', 'quotient_action_image': '1.1', 'quotient_action_kernel': '32.22', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '32.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017414
{'ambient': '1600.5495', 'aut_centralizer_order': 128, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.c1', '16.h1', '16.i1', '16.j1'], 'contains': ['64.a1', '160.e1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8777, -1, 936, -1], 'generators': [81, 320, 32], 'label': '1600.5495.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '32.e1', 'projective_image': '64.87', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017415
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '40.a1', 'aut_quo_index': 2, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '20.a1', '20.b1', '20.c1'], 'contains': ['80.a1', '80.b1', '80.d1', '80.e1', '200.a1'], 'core': '40.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6698, 6638, 3256, 2799], 'generators': [1, 800, 320, 8], 'label': '1600.5495.40.a1', 'mobius_quo': 8, 'mobius_sub': 0, 'normal_closure': '40.a1', 'normal_contained_in': ['8.a1', '20.a1', '20.b1', '20.c1'], 'normal_contains': ['80.a1', '80.b1', '80.d1', '80.e1', '200.a1'], 'normalizer': '1.a1', 'old_label': '40.a1', 'projective_image': '40.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '40.9', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '40.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017416
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '40.b1', 'aut_quo_index': 2, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['8.b1', '20.a1', '20.d1', '20.e1'], 'contains': ['80.a1', '80.c1', '80.h1', '80.j1', '200.b1'], 'core': '40.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6112, 5767, 3653, 3431], 'generators': [81, 800, 320, 8], 'label': '1600.5495.40.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1', 'normal_contained_in': ['8.b1', '20.a1', '20.d1', '20.e1'], 'normal_contains': ['80.a1', '80.c1', '200.b1'], 'normalizer': '1.a1', 'old_label': '40.b1', 'projective_image': '80.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017417
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '40.c1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.c1', '20.b1', '20.d1'], 'contains': ['80.a1', '80.f1', '200.c1'], 'core': '40.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3368, 3994, 6668, 5994], 'generators': [5, 320, 8, 800], 'label': '1600.5495.40.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1', 'normal_contained_in': ['8.c1', '20.b1', '20.d1'], 'normal_contains': ['80.a1', '80.f1', '200.c1'], 'normalizer': '1.a1', 'old_label': '40.c1', 'projective_image': '40.9', 'quotient_action_image': '1.1', 'quotient_action_kernel': '40.9', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '40.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017418
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '40.d1', 'aut_quo_index': 21, 'aut_stab_index': 6, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['8.d1', '20.b1', '20.e1', '20.f1'], 'contains': ['80.a1', '80.g1', '200.d1'], 'core': '40.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [1771, 2106, 8388, 7656], 'generators': [4, 320, 8, 800], 'label': '1600.5495.40.d1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '40.d1', 'normal_contained_in': ['8.d1', '20.b1', '20.e1', '20.f1'], 'normal_contains': ['80.a1', '80.g1', '200.d1'], 'normalizer': '1.a1', 'old_label': '40.d1', 'projective_image': '40.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '40.14', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '40.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017419
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '40.e1', 'aut_quo_index': 2, 'aut_stab_index': 12, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['8.e1', '20.c1', '20.d1', '20.e1'], 'contains': ['80.a1', '80.k1', '200.e1'], 'core': '40.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [4434, 4935, 5612, 5434], 'generators': [85, 320, 8, 800], 'label': '1600.5495.40.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.e1', 'normal_contained_in': ['8.e1', '20.c1', '20.d1', '20.e1'], 'normal_contains': ['80.a1', '200.e1'], 'normalizer': '1.a1', 'old_label': '40.e1', 'projective_image': '80.45', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.5', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017420
{'ambient': '1600.5495', 'aut_centralizer_order': 64, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '7680.l', 'aut_weyl_index': 64, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.c1', '8.d1', '8.g1', '20.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2326, 2608, 5845, 5715], 'generators': [1, 8, 800, 32, 4, 320], 'label': '1600.5495.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.c1', '8.d1', '8.g1', '20.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '4.2', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017421
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.f1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '32.25', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': ['40.m1'], 'conjugacy_class_count': 24, 'contained_in': ['8.f1', '20.a1'], 'contains': ['80.b1', '80.c1', '80.i1', '200.f1'], 'core': '40.f1', 'coset_action_label': None, 'count': 24, 'diagramx': [8270, 7956, 1754, 1412], 'generators': [1, 800, 320, 80], 'label': '1600.5495.40.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.f1', 'normal_contained_in': ['8.f1', '20.a1'], 'normal_contains': ['80.b1', '80.c1', '200.f1'], 'normalizer': '1.a1', 'old_label': '40.f1', 'projective_image': '80.23', 'quotient_action_image': '2.1', 'quotient_action_kernel': '20.2', 'quotient_action_kernel_order': 20, 'quotient_fusion': None, 'short_label': '40.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017422
{'ambient': '1600.5495', 'aut_centralizer_order': 1280, 'aut_label': '40.g1', 'aut_quo_index': 2, 'aut_stab_index': 24, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 24, 'contained_in': ['8.g1', '20.b1', '20.g1', '20.h1'], 'contains': ['80.e1', '80.f1', '80.g1', '200.g1'], 'core': '40.g1', 'coset_action_label': None, 'count': 24, 'diagramx': [2305, 2899, 7358, 6555], 'generators': [1, 320, 8, 4], 'label': '1600.5495.40.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.g1', 'normal_contained_in': ['8.g1', '20.b1'], 'normal_contains': ['80.e1', '80.f1', '80.g1', '200.g1'], 'normalizer': '1.a1', 'old_label': '40.g1', 'projective_image': '40.10', 'quotient_action_image': '1.1', 'quotient_action_kernel': '40.10', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '40.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017423
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.25', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.h1', '20.a1'], 'contains': ['80.d1', '80.h1', '80.i1', '200.h1'], 'core': '80.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [7584, -1, 1356, -1], 'generators': [1, 880, 320, 808], 'label': '1600.5495.40.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.h1', 'projective_image': '80.24', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017424
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.25', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.i1', '20.a1', '20.g1'], 'contains': ['80.e1', '80.i1', '80.j1', '200.i1'], 'core': '80.e1', 'coset_action_label': None, 'count': 24, 'diagramx': [5627, -1, 2859, -1], 'generators': [1, 80, 320, 8], 'label': '1600.5495.40.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.i1', 'projective_image': '80.21', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017425
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.25', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['8.j1', '20.c1', '20.g1'], 'contains': ['80.e1', '80.k1', '200.j1'], 'core': '80.e1', 'coset_action_label': None, 'count': 24, 'diagramx': [4967, -1, 4909, -1], 'generators': [1, 320, 8, 84], 'label': '1600.5495.40.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.j1', 'projective_image': '80.21', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017426
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.10', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.k1', '20.d1', '20.g1'], 'contains': ['80.f1', '80.j1', '80.k1', '200.k1'], 'core': '80.f1', 'coset_action_label': None, 'count': 48, 'diagramx': [3901, -1, 5261, -1], 'generators': [5, 320, 8, 80], 'label': '1600.5495.40.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '40.k1', 'projective_image': '80.21', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017429
{'ambient': '1600.5495', 'aut_centralizer_order': 3840, 'aut_label': '50.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 3840, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['10.a1', '25.a1'], 'contains': ['100.a1', '100.b1', '100.c1', '100.d1', '100.e1', '100.g1'], 'core': '50.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2056, 2613, 8062, 8271], 'generators': [1, 4, 80, 800], 'label': '1600.5495.50.a1', 'mobius_quo': 0, 'mobius_sub': -5, 'normal_closure': '50.a1', 'normal_contained_in': ['10.a1', '25.a1'], 'normal_contains': ['100.a1', '100.b1', '100.c1', '100.d1', '100.e1'], 'normalizer': '1.a1', 'old_label': '50.a1', 'projective_image': '100.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '25.2', 'quotient_action_kernel_order': 25, 'quotient_fusion': None, 'short_label': '50.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017430
{'ambient': '1600.5495', 'aut_centralizer_order': 3840, 'aut_label': '50.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '64.202', 'aut_weyl_index': 7680, 'centralizer': '2.b1', 'complements': ['32.e1'], 'conjugacy_class_count': 2, 'contained_in': ['10.b1', '25.a1'], 'contains': ['100.b1', '100.f1', '100.h1'], 'core': '50.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [482, 274, 9700, 9761], 'generators': [1, 2, 800], 'label': '1600.5495.50.b1', 'mobius_quo': 0, 'mobius_sub': -5, 'normal_closure': '50.b1', 'normal_contained_in': ['10.b1', '25.a1'], 'normal_contains': ['100.b1', '100.f1'], 'normalizer': '1.a1', 'old_label': '50.b1', 'projective_image': '100.16', 'quotient_action_image': '2.1', 'quotient_action_kernel': '25.2', 'quotient_action_kernel_order': 25, 'quotient_fusion': None, 'short_label': '50.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017431
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '15360.d', 'aut_weyl_index': 32, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '8.e1', '8.j1', '20.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5233, 5727, 3558, 2981], 'generators': [1, 8, 800, 32, 84, 320], 'label': '1600.5495.4.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '8.e1', '20.c1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017432
{'ambient': '1600.5495', 'aut_centralizer_order': 1920, 'aut_label': '50.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '64.202', 'aut_weyl_index': 7680, 'centralizer': '4.b1', 'complements': ['32.e1', '32.c1'], 'conjugacy_class_count': 4, 'contained_in': ['10.c1', '25.a1'], 'contains': ['100.e1', '100.f1'], 'core': '50.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1041, 805, 9409, 9297], 'generators': [81, 2], 'label': '1600.5495.50.c1', 'mobius_quo': 0, 'mobius_sub': -5, 'normal_closure': '50.c1', 'normal_contained_in': ['10.c1', '25.a1'], 'normal_contains': ['100.e1', '100.f1'], 'normalizer': '1.a1', 'old_label': '50.c1', 'projective_image': '200.52', 'quotient_action_image': '2.1', 'quotient_action_kernel': '25.2', 'quotient_action_kernel_order': 25, 'quotient_fusion': None, 'short_label': '50.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
id: 78017433
{'ambient': '1600.5495', 'aut_centralizer_order': 1024, 'aut_label': '64.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '480.218', 'aut_weyl_index': 1024, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1', '32.e1'], 'contains': ['320.a1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9241, 9282, 1113, 1629], 'generators': [32, 320], 'label': '1600.5495.64.a1', 'mobius_quo': 5, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1', '32.d1'], 'normal_contains': ['320.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '64.87', 'quotient_action_image': '1.1', 'quotient_action_kernel': '64.87', 'quotient_action_kernel_order': 64, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017434
{'ambient': '1600.5495', 'aut_centralizer_order': 20480, 'aut_label': '80.a1', 'aut_quo_index': 12, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['16.a1', '40.a1', '40.b1', '40.c1', '40.d1', '40.e1'], 'contains': ['160.a1', '160.b1', '160.d1', '400.a1'], 'core': '80.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6460, 6214, 4809, 5279], 'generators': [8, 320, 800], 'label': '1600.5495.80.a1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '80.a1', 'normal_contained_in': ['16.a1', '40.a1', '40.b1', '40.c1', '40.d1', '40.e1'], 'normal_contains': ['160.a1', '160.b1', '160.d1', '400.a1'], 'normalizer': '1.a1', 'old_label': '80.a1', 'projective_image': '80.45', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.45', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017435
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '80.b1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.b1', '40.a1', '40.f1'], 'contains': ['160.a1', '160.c1', '400.b1'], 'core': '80.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9323, 8097, 2694, 2750], 'generators': [1, 320, 800], 'label': '1600.5495.80.b1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '80.b1', 'normal_contained_in': ['16.b1', '40.a1', '40.f1'], 'normal_contains': ['160.a1', '160.c1', '400.b1'], 'normalizer': '1.a1', 'old_label': '80.b1', 'projective_image': '80.23', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.23', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017436
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '80.c1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': ['20.h1'], 'conjugacy_class_count': 24, 'contained_in': ['16.c1', '40.b1', '40.f1'], 'contains': ['160.a1', '160.e1', '400.c1'], 'core': '80.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [8690, 8737, 3046, 3311], 'generators': [81, 320, 800], 'label': '1600.5495.80.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.c1', 'normal_contained_in': ['16.c1', '40.b1', '40.f1'], 'normal_contains': ['160.a1', '400.c1'], 'normalizer': '1.a1', 'old_label': '80.c1', 'projective_image': '160.190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '40.9', 'quotient_action_kernel_order': 40, 'quotient_fusion': None, 'short_label': '80.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017437
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '80.d1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.d1', '40.a1', '40.h1'], 'contains': ['160.b1', '160.c1', '400.d1'], 'core': '80.d1', 'coset_action_label': None, 'count': 12, 'diagramx': [7626, 7155, 1639, 2190], 'generators': [801, 320, 808], 'label': '1600.5495.80.d1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '80.d1', 'normal_contained_in': ['16.d1', '40.a1'], 'normal_contains': ['160.b1', '160.c1', '400.d1'], 'normalizer': '1.a1', 'old_label': '80.d1', 'projective_image': '80.24', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.24', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017438
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '80.e1', 'aut_quo_index': 2, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.e1', '40.a1', '40.g1', '40.i1', '40.j1'], 'contains': ['160.c1', '160.d1', '400.e1'], 'core': '80.e1', 'coset_action_label': None, 'count': 12, 'diagramx': [6030, 5575, 4106, 4718], 'generators': [1, 320, 8], 'label': '1600.5495.80.e1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '80.e1', 'normal_contained_in': ['16.e1', '40.a1', '40.g1'], 'normal_contains': ['160.c1', '160.d1', '400.e1'], 'normalizer': '1.a1', 'old_label': '80.e1', 'projective_image': '80.21', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.21', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017439
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '80.f1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.f1', '40.c1', '40.g1', '40.k1'], 'contains': ['160.d1', '400.f1'], 'core': '80.f1', 'coset_action_label': None, 'count': 12, 'diagramx': [3478, 4190, 5802, 6276], 'generators': [5, 8, 320], 'label': '1600.5495.80.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.f1', 'normal_contained_in': ['16.f1', '40.c1', '40.g1'], 'normal_contains': ['160.d1', '400.f1'], 'normalizer': '1.a1', 'old_label': '80.f1', 'projective_image': '80.21', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.21', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017440
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '80.g1', 'aut_quo_index': 2, 'aut_stab_index': 12, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 12, 'contained_in': ['16.g1', '40.d1', '40.g1', '40.l1', '40.m1'], 'contains': ['160.d1', '400.g1'], 'core': '80.g1', 'coset_action_label': None, 'count': 12, 'diagramx': [2516, 3123, 6873, 6579], 'generators': [4, 8, 320], 'label': '1600.5495.80.g1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '80.g1', 'normal_contained_in': ['16.g1', '40.d1', '40.g1'], 'normal_contains': ['160.d1', '400.g1'], 'normalizer': '1.a1', 'old_label': '80.g1', 'projective_image': '80.46', 'quotient_action_image': '1.1', 'quotient_action_kernel': '80.46', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '80.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017441
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.h1', '40.b1', '40.h1'], 'contains': ['160.b1', '160.e1', '400.h1'], 'core': '160.b1', 'coset_action_label': None, 'count': 24, 'diagramx': [7094, -1, 1991, -1], 'generators': [881, 320, 808], 'label': '1600.5495.80.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.h1', 'projective_image': '160.191', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017442
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '4.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '7680.l', 'aut_weyl_index': 64, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.c1', '8.e1', '8.k1', '20.d1'], 'core': '4.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3798, 4689, 4702, 3892], 'generators': [5, 8, 800, 32, 80, 320], 'label': '1600.5495.4.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.c1', '8.e1', '20.d1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '8.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017443
{'ambient': '1600.5495', 'aut_centralizer_order': 640, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 48, 'contained_in': ['16.i1', '40.f1', '40.h1', '40.i1'], 'contains': ['160.c1', '160.e1', '400.i1'], 'core': '160.c1', 'coset_action_label': None, 'count': 96, 'diagramx': [8260, -1, 2343, -1], 'generators': [1, 320, 80], 'label': '1600.5495.80.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.i1', 'projective_image': '160.48', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017444
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.j1', '40.b1', '40.i1', '40.k1', '40.l1'], 'contains': ['160.d1', '160.e1', '400.j1'], 'core': '160.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [5600, -1, 4458, -1], 'generators': [81, 320, 8], 'label': '1600.5495.80.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.j1', 'projective_image': '160.176', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017445
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.2', 'aut_weyl_index': 61440, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['16.k1', '40.e1', '40.j1', '40.k1', '40.l1'], 'contains': ['160.d1', '400.k1'], 'core': '160.d1', 'coset_action_label': None, 'count': 24, 'diagramx': [4415, -1, 5612, -1], 'generators': [85, 8, 320], 'label': '1600.5495.80.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '80.k1', 'projective_image': '160.176', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017446
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '100.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['20.a1', '50.a1'], 'contains': ['200.a1', '200.b1', '200.f1', '200.h1', '200.i1'], 'core': '100.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5558, 5426, 3940, 3889], 'generators': [1, 8, 80, 800], 'label': '1600.5495.100.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '100.a1', 'normal_contained_in': ['20.a1', '50.a1'], 'normal_contains': ['200.a1', '200.b1', '200.f1'], 'normalizer': '1.a1', 'old_label': '100.a1', 'projective_image': '200.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '50.5', 'quotient_action_kernel_order': 50, 'quotient_fusion': None, 'short_label': '100.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017447
{'ambient': '1600.5495', 'aut_centralizer_order': 30720, 'aut_label': '100.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 30720, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['20.b1', '50.a1', '50.b1'], 'contains': ['200.a1', '200.c1', '200.d1', '200.g1'], 'core': '100.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1872, 1946, 9072, 9286], 'generators': [1, 4, 800], 'label': '1600.5495.100.b1', 'mobius_quo': 0, 'mobius_sub': 10, 'normal_closure': '100.b1', 'normal_contained_in': ['20.b1', '50.a1', '50.b1'], 'normal_contains': ['200.a1', '200.c1', '200.d1', '200.g1'], 'normalizer': '1.a1', 'old_label': '100.b1', 'projective_image': '100.16', 'quotient_action_image': '1.1', 'quotient_action_kernel': '100.16', 'quotient_action_kernel_order': 100, 'quotient_fusion': None, 'short_label': '100.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017448
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '100.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '32.27', 'aut_weyl_index': 15360, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['20.c1', '50.a1'], 'contains': ['200.a1', '200.e1', '200.j1'], 'core': '100.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4675, 4370, 7013, 7105], 'generators': [1, 84, 800], 'label': '1600.5495.100.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '100.c1', 'normal_contained_in': ['20.c1', '50.a1'], 'normal_contains': ['200.a1', '200.e1'], 'normalizer': '1.a1', 'old_label': '100.c1', 'projective_image': '200.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '50.5', 'quotient_action_kernel_order': 50, 'quotient_fusion': None, 'short_label': '100.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017449
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '100.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['20.d1', '50.a1'], 'contains': ['200.b1', '200.c1', '200.e1', '200.k1'], 'core': '100.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3572, 3755, 8043, 8206], 'generators': [5, 80, 800], 'label': '1600.5495.100.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '100.d1', 'normal_contained_in': ['20.d1', '50.a1'], 'normal_contains': ['200.b1', '200.c1', '200.e1'], 'normalizer': '1.a1', 'old_label': '100.d1', 'projective_image': '200.37', 'quotient_action_image': '2.1', 'quotient_action_kernel': '50.5', 'quotient_action_kernel_order': 50, 'quotient_fusion': None, 'short_label': '100.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017450
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '100.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '16.14', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['20.e1', '50.a1', '50.c1'], 'contains': ['200.b1', '200.d1', '200.e1', '200.l1'], 'core': '100.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [2389, 2715, 8733, 8746], 'generators': [81, 4, 800], 'label': '1600.5495.100.e1', 'mobius_quo': 0, 'mobius_sub': 10, 'normal_closure': '100.e1', 'normal_contained_in': ['20.e1', '50.a1', '50.c1'], 'normal_contains': ['200.b1', '200.d1', '200.e1'], 'normalizer': '1.a1', 'old_label': '100.e1', 'projective_image': '200.52', 'quotient_action_image': '2.1', 'quotient_action_kernel': '50.5', 'quotient_action_kernel_order': 50, 'quotient_fusion': None, 'short_label': '100.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017451
{'ambient': '1600.5495', 'aut_centralizer_order': 15360, 'aut_label': '100.f1', 'aut_quo_index': 3, 'aut_stab_index': 4, 'aut_weyl_group': '8.5', 'aut_weyl_index': 61440, 'centralizer': '2.b1', 'complements': ['16.i1'], 'conjugacy_class_count': 4, 'contained_in': ['20.f1', '50.b1', '50.c1'], 'contains': ['200.d1', '200.m1'], 'core': '100.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [970, 914, 9873, 9792], 'generators': [3, 800], 'label': '1600.5495.100.f1', 'mobius_quo': 0, 'mobius_sub': 10, 'normal_closure': '100.f1', 'normal_contained_in': ['20.f1', '50.b1', '50.c1'], 'normal_contains': ['200.d1'], 'normalizer': '1.a1', 'old_label': '100.f1', 'projective_image': '200.52', 'quotient_action_image': '2.1', 'quotient_action_kernel': '50.5', 'quotient_action_kernel_order': 50, 'quotient_fusion': None, 'short_label': '100.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017452
{'ambient': '1600.5495', 'aut_centralizer_order': 3840, 'aut_label': '100.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 30720, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.g1', '50.a1'], 'contains': ['200.g1', '200.i1', '200.j1', '200.k1', '200.l1'], 'core': '200.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [2954, -1, 7704, -1], 'generators': [1, 4, 80], 'label': '1600.5495.100.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '50.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '100.g1', 'projective_image': '200.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017453
{'ambient': '1600.5495', 'aut_centralizer_order': 32, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '7680.l', 'aut_weyl_index': 64, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.b1', '8.d1', '8.e1', '8.l1', '20.e1'], 'core': '4.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [3099, 3648, 5274, 4804], 'generators': [81, 8, 800, 32, 4, 320], 'label': '1600.5495.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.b1', '8.d1', '8.e1', '20.e1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '8.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017454
{'ambient': '1600.5495', 'aut_centralizer_order': 3840, 'aut_label': '100.h1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '16.11', 'aut_weyl_index': 30720, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.h1', '50.b1'], 'contains': ['200.g1', '200.m1'], 'core': '200.g1', 'coset_action_label': None, 'count': 8, 'diagramx': [476, -1, 9579, -1], 'generators': [1, 2], 'label': '1600.5495.100.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '50.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '100.h1', 'projective_image': '200.38', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017455
{'ambient': '1600.5495', 'aut_centralizer_order': 20480, 'aut_label': '160.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['32.a1', '80.a1', '80.b1', '80.c1'], 'contains': ['320.a1', '800.a1'], 'core': '160.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9123, 8792, 2951, 3311], 'generators': [800, 320], 'label': '1600.5495.160.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.a1', 'normal_contained_in': ['32.a1', '80.a1', '80.b1', '80.c1'], 'normal_contains': ['320.a1', '800.a1'], 'normalizer': '1.a1', 'old_label': '160.a1', 'projective_image': '160.190', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.190', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017456
{'ambient': '1600.5495', 'aut_centralizer_order': 20480, 'aut_label': '160.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['32.b1', '80.a1', '80.d1', '80.h1'], 'contains': ['320.a1', '800.b1'], 'core': '160.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7510, 7304, 2185, 3008], 'generators': [808, 320], 'label': '1600.5495.160.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.b1', 'normal_contained_in': ['32.b1', '80.a1', '80.d1'], 'normal_contains': ['320.a1', '800.b1'], 'normalizer': '1.a1', 'old_label': '160.b1', 'projective_image': '160.191', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.191', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017457
{'ambient': '1600.5495', 'aut_centralizer_order': 5120, 'aut_label': '160.c1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': ['10.c1'], 'conjugacy_class_count': 24, 'contained_in': ['32.c1', '80.b1', '80.d1', '80.e1', '80.i1'], 'contains': ['320.a1', '800.c1'], 'core': '160.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [8888, 8247, 2572, 2706], 'generators': [1, 320], 'label': '1600.5495.160.c1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.c1', 'normal_contained_in': ['32.c1', '80.b1', '80.d1', '80.e1'], 'normal_contains': ['320.a1', '800.c1'], 'normalizer': '1.a1', 'old_label': '160.c1', 'projective_image': '160.48', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.48', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017458
{'ambient': '1600.5495', 'aut_centralizer_order': 20480, 'aut_label': '160.d1', 'aut_quo_index': 4, 'aut_stab_index': 6, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['32.d1', '80.a1', '80.e1', '80.f1', '80.g1', '80.j1', '80.k1'], 'contains': ['320.a1', '800.d1'], 'core': '160.d1', 'coset_action_label': None, 'count': 6, 'diagramx': [6273, 6356, 4809, 5279], 'generators': [8, 320], 'label': '1600.5495.160.d1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '160.d1', 'normal_contained_in': ['32.d1', '80.a1', '80.e1', '80.f1', '80.g1'], 'normal_contains': ['320.a1', '800.d1'], 'normalizer': '1.a1', 'old_label': '160.d1', 'projective_image': '160.176', 'quotient_action_image': '1.1', 'quotient_action_kernel': '160.176', 'quotient_action_kernel_order': 160, 'quotient_fusion': None, 'short_label': '160.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017459
{'ambient': '1600.5495', 'aut_centralizer_order': 2560, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.1', 'aut_weyl_index': 122880, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['32.e1', '80.c1', '80.h1', '80.i1', '80.j1'], 'contains': ['320.a1', '800.e1'], 'core': '320.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8386, -1, 2761, -1], 'generators': [81, 320], 'label': '1600.5495.160.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '160.e1', 'projective_image': '320.907', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017460
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '200.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['40.a1', '100.a1', '100.b1', '100.c1'], 'contains': ['400.a1', '400.b1', '400.d1', '400.e1'], 'core': '200.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5759, 5245, 5252, 5702], 'generators': [1, 8, 800], 'label': '1600.5495.200.a1', 'mobius_quo': -8, 'mobius_sub': 0, 'normal_closure': '200.a1', 'normal_contained_in': ['40.a1', '100.a1', '100.b1', '100.c1'], 'normal_contains': ['400.a1', '400.b1', '400.d1', '400.e1'], 'normalizer': '1.a1', 'old_label': '200.a1', 'projective_image': '200.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.37', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017461
{'ambient': '1600.5495', 'aut_centralizer_order': 61440, 'aut_label': '200.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['40.b1', '100.a1', '100.d1', '100.e1'], 'contains': ['400.a1', '400.c1', '400.h1', '400.j1'], 'core': '200.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5078, 5630, 5429, 5984], 'generators': [81, 8, 800], 'label': '1600.5495.200.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '200.b1', 'normal_contained_in': ['40.b1', '100.a1', '100.d1', '100.e1'], 'normal_contains': ['400.a1', '400.c1'], 'normalizer': '1.a1', 'old_label': '200.b1', 'projective_image': '400.201', 'quotient_action_image': '2.1', 'quotient_action_kernel': '100.16', 'quotient_action_kernel_order': 100, 'quotient_fusion': None, 'short_label': '200.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
id: 78017462
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '200.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['40.c1', '100.b1', '100.d1'], 'contains': ['400.a1', '400.f1'], 'core': '200.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [3442, 3440, 7408, 7432], 'generators': [5, 800], 'label': '1600.5495.200.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '200.c1', 'normal_contained_in': ['40.c1', '100.b1', '100.d1'], 'normal_contains': ['400.a1', '400.f1'], 'normalizer': '1.a1', 'old_label': '200.c1', 'projective_image': '200.37', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.37', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
id: 78017463
{'ambient': '1600.5495', 'aut_centralizer_order': 122880, 'aut_label': '200.d1', 'aut_quo_index': 21, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 122880, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['40.d1', '100.b1', '100.e1', '100.f1'], 'contains': ['400.a1', '400.g1'], 'core': '200.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [2194, 2436, 8560, 8567], 'generators': [4, 800], 'label': '1600.5495.200.d1', 'mobius_quo': 0, 'mobius_sub': -40, 'normal_closure': '200.d1', 'normal_contained_in': ['40.d1', '100.b1', '100.e1', '100.f1'], 'normal_contains': ['400.a1', '400.g1'], 'normalizer': '1.a1', 'old_label': '200.d1', 'projective_image': '200.52', 'quotient_action_image': '1.1', 'quotient_action_kernel': '200.52', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '200.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}

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.